EXPERIMENTAL AND NUMERICAL STUDY OF EVAPORATING FLOW HEAT TRANSFER IN MICRO-CHANNEL HOKI LEE

Transcription

1 EXPERIMENTAL AND NUMERICAL STUDY OF EVAPORATING FLOW HEAT TRANSFER IN MICRO-CHANNEL By HOKI LEE A thesis submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY WASHINGTON STATE UNIVERSITY Shool of Mehanial and Materials Engineering Deember 2008

2 To the Faulty of Washington State University: The members of the Committee appointed to examine the thesis of HOKI LEE find it satisfatory and reommend that it be aepted. Chair ii

3 ACKNOWLEDGEMENTS I am deeply grateful to my advisor Dr. Bob Rihards for his knowledge, patiene guidane and ontinual enouragement through my graduate work. This researh ould not have been done without a ontinuous soure of guidane and helpful omments from Dr. Cill Rihards, Dr. Dave Bahr, and Dr. Jeongmin Ahn in relation to the effiieny of evaporator, experimentation, and fabriation. I am also thankful to Dr. D.J Morris and Tiffany Quy for training me with RTD iruitry design, hrome mask designs and fabriation proedures. I would like to thank Steve Brown, Dawn Findley and Joshah Jennings who have been great at their efforts to keep the leanroom up and running. Finally, I would like to thank the entire MEMS group, both past and present, for helpful omments and being there. I am also grateful for the finanial support provide by the DARPA and the NSF. iii

4 Experimental and Numerial Study of Evaporating Flow Heat Transfer in Miro-Channel Abstrat By HoKi Lee, Ph.D. Washington State University Deember 2008 Chair: Robert Rihards This dissertation presents the design of a MEMS-based miro-hannel evaporator, fabriated and haraterized to maximize the effiieny of evaporation. Effiieny of evaporator is defined to be the amount of energy used to evaporate fluid over the amount of energy input to the miro-hannel evaporator. Experiment and numerial results are presented for steady and transient evaporation heat transfer from open top miro-hannels. The radial hannels were fabriated in two geometries: one was a retangular SU8 wik struture 40µm high and 5µm wide with hannel widths range from 10 to 70µm. The seond was a tapered 40µm high and 80µm wide at the outer radius and narrowing to 5µm wide at inner radius. The radial hannels were fabriated on two membrane materials one was two-miron thik silion and the other was the three hundrednanometer silion nitride. Transient state evaporation tests were done at yle frequenies of 10 Hz, 20Hz and 50Hz. An energy balane was experimentally determined on the radial miro-hannel evaporators, inluding heat into the hannels, ondution heat transfer radially along the hannels and latent heat transfer through evaporation of the working fluid from the hannels. A numerial analysis was used to simulate the experimental measurements. The iv

5 numerial integration alulated ondution heat transfer using axisymmetri FDTD integration and mass transfer from evaporation using heat balane equation in the mirohannel. The experimental and the numerial results were ompared to validate the numerial model. The 40µm high and 5µm wide SU8 features with 70µm hannels and the tapered hannels were found to have the best overall performane of evaporators with silion membrane. These wik dimensions yielded a mass evaporation rate of 6.5mg/min and 6.2mg/min, and wik effiienies of 28% and 26% with an input energy of 34mW for steady state onditions. For transient state onditions of 10Hz 10% duty yle, the tapered hannel evaporator yielded a mass evaporation rate of 8.2mg/min and wik effiieny of 33.6% with an average input power of 34mw. Use of a low ondutivity SiN membrane evaporator inreased the mass evaporation rate to 8.2mg/min and the wik effiieny to 88% for an input energy of 13mW. v

6 TABLE OF CONTENTS Page ACKNOWLEDGEMENTS iii ABSTRACT.... iv LIST OF TABLES.xi LIST OF FIGURES... xiv CHAPTER 1 INTRODUCTION Motivation Conept Literature Review Heat Transfer Single-phase flow Two-phase flow Flow Analysis: Capillary Ation Fabriation Visualization Fixed SU8 Height Researh Objetives FABRICATION vi

7 2.1 Fabriation Overview Preparation of Silion Membranes Preparation of Silion Nitride Membrane Pattering Wafers for Membrane Silion Membrane Fabriation Silion Nitride Membrane Fabriation Fabriation of Miro-hannel evaporator KOH Anisotropi Ething Detailed Fabriation Proedure Fabriation Steps for Silion RTD/Heater Design Fabriation Steps for Silion Nitride RTD/Heater Design Photoresist Fabriation for Gold Eth Photoresist Fabriation for Platinum Lift-off SU Fabriation for 10μm High Miro-hannels SU Fabriation for 40μm High Miro-hannels EXPERIMENT METHOD Experiment Overview Heater/RTDs Design, Evaporator Assembly, RTD Testing Box Heater/RTD Design Evaporator Assembly RTD Testing Box RTD Calibration Steady State Evaporation Tests 60 vii

8 3.5 Transient Evaporation Tests Visualization Unertainties Unertainty of Power Input Unertainty of Heat Transfer aross Membrane Unertainty of Evaporation 76 4 NUMERICAL METHOD Numerial Method Overview Geometry Disretization Equation Derivation for Heat Transfer Energy Balane and Parallel Resistane Network Nodal Temperature Equation Mass Transfer Menisus Appliation Flow Analysis Boundary Conditions Flow Chart EXPERIMENTAL RESULTS Experimental Results Overview Steady State Evaporation Test Results Silion Nitride Evaporation Test Results Summary of Steady State Evaporation Test Results 119 viii

9 5.5 Transient Evaporation Test Results Summary of Transient Evaporation Test Results Visualization Test Results DISCCUSION AND COMPARISON OF EXPERIMENTAL AND NUMERICAL RESULTS Comparison of Results Overview Steady State Evaporation tests Results (Retangular) Steady State Evaporation tests Results (Tapered) Fixed Temperature Boundary Results Steady State Evaporation tests Results (Tapered: SiNx) Transient Test Results (Tapered: Si) Transient Test Results (Tapered: SiNx) Effet of Heat Input Area CONCLUSIONS Conlusions REFERENCES APPENDIX A Cylindrial Condution Equation D Flow Analysis in Miro-Channel Derivation of Menisus APPENDIX B Calibration Test Results APPENDIX C 202 ix

10 1. Steady State Experimental Test Results Transient Operation Experimental Test Results x

11 LIST OF TABLES 1.1 Wik effiienies for 40 and 70µm high hannels Typial Values of the RTD alibration data Summary of Experiment tests Experimental Energy Balane: 10 x 10 x 10 Miro-hannel evaporator Experimental Energy Balane: 40 x 35 x 5 Miro-hannel Evaporator Experimental Energy Balane: 40 x 50 x 5 Miro-hannel Evaporator Experimental Energy Balane: 40 x 70 x 5 Miro-hannel Evaporator Experimental Energy Balane: 40 x 5 ~ 80 Miro-hannel Evaporator Experimental: Silion Nitride (SiNx) Membrane Tapered 40 x 5 ~ 80 Mirohannel Evaporator Experimental Energy Balane: 40 x 5 ~ 80 Miro-hannel evaporator with 10Hz 50% Duty Cyle Experimental Energy Balane: 40 x 5 ~ 80 Miro-hannel evaporator with 10Hz 30% Duty Cyle Experimental Energy Balane: 40 x 5 ~ 80 Miro-hannel evaporator with 20Hz 50% Duty Cyle Experimental Energy Balane: 40 x 5 ~ 80 Miro-hannel evaporator with 20Hz 30% Duty Cyle Experimental Results Summary for Various Transient Conditions Seond Visualization Tests Results Summary of numerial simulations xi

12 6.2 Numerial and Experimental Energy balane for onstant retangular ross setion miro-hannel 40 x35 x Numerial and Experimental Energy balane for onstant retangular ross setion miro-hannel 40 x50 x Numerial and Experimental Energy balane for onstant retangular ross setion miro-hannel 40 x 70 x Numerial and Experimental Energy Balane for Tapered 40 x 5 ~ Numerial Integration of Energy Balane for Critial Heat Flux 40 x 5 ~ 80 Tapered Miro-Channel Evaporator Numerial and Experimental Energy Balane for Tapered hannel 40 x 5 ~ 80 with Edge Temperature Boundary Condition Numerial and Experimental Energy Balane for SiNx membrane Tapered Channel 40 x 5 ~ 80 with Edge temperature Boundary Condition Numerial and Experimental Energy Balanes: Tapered Channel 40 x 5 ~ 80, 10Hz frequeny 50% Duty Cyle with various power inputs Numerial and Experimental Energy Balanes: Tapered Channel 40 x 5 ~ 80, 10Hz frequeny 30% Duty Cyle with various power inputs Numerial Energy Balanes: Tapered Channel 40 x 5 ~ 80, 10Hz frequeny 10% Duty Cyle with various power inputs Numerial and Experimental Energy Balanes: Tapered Channel 40 x 5 ~ 80, 20Hz frequeny 50% Duty Cyle with various power inputs Numerial and Experimental Energy Balanes: Tapered Channel 40 x 5 ~ 80, 20Hz frequeny 30% Duty Cyle with various power inputs..166 xii

13 6.14 Numerial Energy Balanes: Tapered Channel 40 x 5 ~ 80, 20Hz frequeny 10% Duty Cyle with various power inputs Numerial Energy Balanes: Tapered Channel 40 x 5 ~ 80, 10Hz frequeny 50% Duty Cyle with 11mW Power input Numerial Energy Balanes xiii

14 LIST OF FIGURES 1.1 Shemati of Atuator and Miro-Channel Evaporator Calulation of Wik Effiienies Mask for Ething the Oxide to define Membrane Illustration of Photolithography Proess Photolithography Mask for Resistane Heater and Dual RTDs Photolithography Mask for Resistane Heater and Dual RTDs Illustration of Platinum Lift-off SEM examples of 10μm high SU8 Wiks SEM examples of 40μm high SU8 Wiks AutoCad designs of miro-hannels with different hannel widths AutoCad designs of tapered miro-hannels Magnifiation Image typial Masks for Different Wik Geometries SEM photographi image of the tapered hannels Cross Setion of KOH Eth for Different Materials Top View of Completed Evaporator Membrane Layout of a Miro-Channel Evaporator Shemati of the energy balane in the aryli arrier Shemati of Resistane Heater and Dual RTD Shemati of Resistane Heater and Triple RTD Desriptions of Upper and Lower Aryli Die Carrier Components Completed Assembly of Evaporator Die and the Aryli Carrier..56 xiv

15 3.6 Shematis of RTD Testing Box, Multimeters, and RTDs Piture of Calibration Experiment Setup Dual RTD Calibration Curve Triple RTD Calibration Curve Evaporation Experiment Test Setup Shemati and Photograph of Transient Experiment Setup Shemati of Pulse Ciruit Photographi Image of Visualization Experiment Setup Visualization Images from the Experiment Setup Shemati and Photographi Images of Visualization Experiment setup A typial Menisus Image and the Silion Ethed Angle Image A typial Evaporation Test Graph: Mass Change over Time Top View of Arbitrary Temperature Contour Plot for a Retangular Membrane General Shemati of 3-D axisymmetri Geometry Typial Shemati of Disretization for 3-D axisymmetri Model Grid Independent Studies of Different Combinations of Number of Elements Energy Balane for 3-D axisymmetri Element Shemati of Corresponding Points for 2-D and 3-D: Temperature Plot Mass Flux Balane at Liquid-Vapor Interfae Saturation Curve for Fluorinert FC Disretization of Menisus in the Miro-hannel for FDTD model Shemati of Three Dimensional Flows Thermal Boundary Conditions for 3-D Mode..105 xv

16 4.12 Fitting of Model to the Experiment for Determining h eff D Numerial Model Flowhart Evaporation Test Results of Heat Transfer by Condution and Evaporation: 10 x 10 x 10 Miro-Channel Evaporator Evaporation Test Results of Heat Transfer by Condution and Evaporation: 40 x 35 x 5 Miro-Channel Evaporator Evaporation Test Results of Heat Transfer by Condution and Evaporation: 40 x 50 x 5 Miro-Channel Evaporator Evaporation Test Results of Heat Transfer by Condution and Evaporation: 40 x 70 x 5 Miro-Channel Evaporator Evaporation Test Results of Heat Transfer by Condution and Evaporation: 40 x 5 ~ 80 Miro-Channel Evaporator Summary of Miro-Channel Evaporator Maximum Effiienies Typial Temperature Histories for Transient Evaporation Test: 10Hz 50% Duty Cyle with Average Power Input of 34mW Evaporation Test Results of Heat Transfer by Condution and Evaporation: 40 x 5 ~ 80 Miro-Channel Evaporator with 10Hz 50% Duty Cyle Evaporation Test Results of Heat Transfer by Condution and Evaporation: 40 x 5 ~ 80 Miro-Channel Evaporator with 10Hz 30% Duty Cyle Evaporation Test Results of Heat Transfer by Condution and Evaporation: 40 x 5 ~ 80 Miro-Channel Evaporator with 20Hz 50% Duty Cyle Evaporation Test Results of Heat Transfer by Condution and Evaporation: 40 x 5 ~ 80 Miro-Channel Evaporator with 20Hz 30% Duty Cyle 125 xvi

17 5.12 Experimental Results Summary for Various Transient Conditions Visualization of 40 x 35 x 5 Miro-Channel with Various Power inputs Visualization of 40 x 50 x 5 Miro-Channel with Various Power inputs Visualization of 40 x 70 x 5 Miro-Channel with Various Power inputs Mirophotograph of 40 x 50 x5 Miro-Channel with Working Fluid Mirophotograph of Miro-Channel with Working Fluid Dimensions of Constant Retangular Cross Setion Miro-Channels Numerial and Experimental Evaporation Rates and Temperatures for Constant Retangular Cross Setion Miro-Channels 40 x 35 x Numerial and Experimental Evaporation Rates and Temperatures for Constant Retangular Cross Setion Miro-Channels 40 x 50 x Numerial and Experimental Evaporation Rates and Temperatures for Constant Retangular Cross Setion Miro-Channels 40 x 70 x Dimensions of Tapered Miro-Channel Numerial and Experimental Evaporation Rates and Temperatures for Tapered Miro-Channels 40 x 5 ~ Liquid Thikness Profiles along the length of the Channel: Critial Heat Flux Disretization of Menisus in the Miro-Channel for FDTD model Numerial and Experimental Evaporation Rates and Temperatures for Tapered Miro-Channels 40 x 5 ~ 80 with Edge Temperature Boundary Condition Numerial and Experimental Evaporation Rates and Temperatures: SiNx, Tapered Miro-Channels 40 x 5 ~ 80 with Edge Temperature Boundary Condition 151 xvii

18 6.11 Numerial and Experimental Temperatures for Silion Nitride Membrane Tapered Miro-Channels 40 x 5 ~ 80 with Edge Temperature Boundary Condition Numerial and Experimental Evaporation Rate and Temperature: Tapered Channel 40 x 5~80, 10Hz Frequeny 50% Duty Cyle Numerial and Experimental Temperature History: Tapered Channel 40 x 5~80, 10Hz Frequeny 50% Duty Cyle with 34mW Power Input Numerial and Experimental Evaporation Rate and Temperature: Tapered Channel 40 x 5~80, 10Hz Frequeny 30% Duty Cyle Numerial and Experimental Temperature History: Tapered Channel 40 x 5~80, 10Hz Frequeny 30% Duty Cyle with 34mW Power Input Numerial Evaporation Rate and Temperature: Tapered Channel 40 x 5~80, 10Hz Frequeny 10% Duty Cyle Numerial and Experimental Evaporation Rate and Temperature: Tapered Channel 40 x 5~80, 20Hz Frequeny 50% Duty Cyle Numerial and Experimental Temperature History: Tapered Channel 40 x 5~80, 20Hz Frequeny 50% Duty Cyle with 34mW Power Input Numerial and Experimental Evaporation Rate and Temperature: Tapered Channel 40 x 5~80, 20Hz Frequeny 30% Duty Cyle Numerial and Experimental Temperature History: Tapered Channel 40 x 5~80, 20Hz Frequeny 30% Duty Cyle with 34mW Power Input Numerial Evaporation Rate and Temperature: Tapered Channel 40 x 5~80, 20Hz Frequeny 10% Duty Cyle..167 xviii

19 6.21 Numerial Temperature History: Silion Nitride, Tapered Channel 40 x 5~80, 10Hz Frequeny 50% Duty Cyle with 11mW Power Input Numerial Evaporation Rate and Temperature..171 xix

20 CHAPTER 1 INTRODUCTION 1.1 MOTIVATION Thermal atuators are used in MEMS devies suh as pumps, value and gear trains. The variety of appliations has resulted in a diversity of thermal atuation methods. One of the thermal atuation methods uses fores generated by liquid-vapor phase hanges (liquid-evaporation). An appliation example for the thermal atuator is the P3 miro-engine under development at Washington State University (WSU). This devie ontains a avity between two square membranes. The working fluid is heated and evaporates by using heat transfer from the lower (miro-hannel evaporator) membrane. The evaporation auses inrease of pressure inside of avity and deforms the upper membrane. The work is produed by mehanial deformation. This work is foused on design of miro-hannel evaporators for use in phase-hange atuators and engines. The goal of work was to build an effetive design tool for the development of effiient miro-hannel evaporator base on miro-hannel with dimensions from ten to one hundred mirons. 1.2 CONCEPT A typial thermo-pneumati atuator onsists of a sealed avity filled with a thermally expansive medium. A flexible diaphragm bound one side of the pressure avity. 1

21 Figure 1.1 Shemati of atuator and a miro-hannel evaporator As a result of heating the hamber, hamber pressure inreases through gas expansion or vaporization, displaing the diaphragm. The design of the thermal atuator motivating this is shown in Figure 1.1. The atuator onsists of a avity bound by two square membranes. The avity is filled with working fluid, a two-phase mixture of 3M TM Fluorinert FC77. The upper and lower membranes are fabriated from silion or silion nitride. A thin platinum film of resistane heater is fabriated on the lower membrane to provide the heat soure for the atuator. A apillary wiking struture, SU-8, is fabriated on the lower membrane to ontrol the thikness of the working fluid layer over the heat addition region. The miro-hannel evaporator or miro-hannels are used to inrease the evaporation of the working. Use of the miro-hannel on the lower membrane provides a means of ontrolling the thikness, thermal mass, and position of the working fluid relative to the heat soure. The miro-hannel is used to deliver the working fluid over the heater to promote more effiient phase hange in the avity. The goal of the present work was to 2

22 use a ombination of both experimental and numerial work to provide insight into the ontrolling parameters and design onstraints of the miro-hannel evaporator. 1.3 LITERATURE REVIEW Thermal atuators are often used in MEMS devies. One ommon thermal atuation method uses liquid-vapor phase hange (liquid evaporation) to generate fore. A key aspet of the design of a phase hange atuator is the evaporator. To design an effiient evaporator for a thermal atuator it is neessary to understand the fluid flow and heat transfer from miro-hannels. In this literature survey, we will first onsider single-phase flow. We will review experimental heat transfer measurements in miro-hannels. Next, we will review analytial solutions for single flow through miro-hannels. Of great importane is the question of whether lassial ontinuum theory applies in mirohannels. Then we will onsider numerial solution to single phase flow and heat transfer in miro-hannels. Seond, the literature survey is fous on the two-phase flow. We will review experimental heat transfer measurements in miro-hannels. Next, we will review analytial solutions for two-phase through miro-hannels, then we will onsider numerial solution to two-phase flow and heat transfer in miro-hannels. Next, we will onsider apillary ation in the miro-hannel. We will review analytial solutions for the apillary ation. Then this literature survey will review the basi MEMS fabriation methods that inlude photolithography, wet ething, and hemial vapor deposition. Finally, we will review the visualization tehniques for the miro-hannels. 3

23 1.3.1 HEAT TANSFER Thermal atuators are used in MEMS devies, and one of the thermal atuation methods are uses liquid-vapor phase hange (liquid-evaporation) to generates the fores. P. Bergstrom et al. and C. Rih et al have researhed phase-hange atuators in the steady-state ondition that maximize the fore and displaements produed with a minimum of energy used [1,2]. In the phase-hange atuators, miro-hannels an be used as an effetive atuation method due to the potential of miro-hannels for maintain high latent heat transfer rates [3] that auses a greater liquid-vapor volume hange. Miro-hannels have been shown to be very effetive thermal management method in miro-sale deeives. One of the benefits of this heat transfer method is that the miro-hannels an be inluded diretly into the heat generating substrate, and it allows the ontat resistane between the hannel and substrate to be ignored [6]. Miro-hannels are easy to fabriate and are ompat, inexpensive, and maintain relatively high dissipation apaities [4,5]. For these reasons, miro-hannels have been widely onsidered for heating and ooling in miro sale devies [6, 12] and serve to atuate these devies. To design the effetive miro-hannel devies, some of the major hallenges faed in the study of miro-hannel devies are in their heat transfer analysis. The study of heat transfer in miro-hannels is still not ompletely understood, and a better understanding of heat transfer in miro-hannels is needed in order to provide a rational basis for the design of these systems. The heat transfer in a miro-hannel is dependent on physial properties, flow method, hannel geometry, and heat flux. The following literature review exams these dependents to the miro-hannels experimentally and numerially. 4

24 SINGLE-PHASE FLOW The heat transfer from miro-hannels has been a highly interesting area to many researhers sine the early 1980 s. The heat transfer of single-phase flows was explored in the initial researh of miro-hannels, and Y.P. Peles et al. and H.R. Chen et al. showed that the eletronis ould be ooled effetively through fored onvetive flow [3, 7]. T.M. Harms et al. presented experimental data (heat transfer oeffiients and pressure drop) for single-phase fored onvetion in deep retangular miro-hannels. The hannels were fabriated in a 2mm thik silion substrate and overed a total projeted area of 2.5m by 2.5m. All tests were performed with de-ionized water, and a ritial Reynolds number for this laminar-turbulent transition was found to be 1500 [20]. Rahman presented new experimental measurements for pressure drops and heat transfer oeffiients in a miro-hannel heat sink in retangular miro-hannels on a silion wafer. Channels of different depths, 180µm to 320µm, (or aspet ratios, 0.1 to 0.9) were studied [29]. The flow passage dimensions in onvetive heat transfer appliations have been shifting towards smaller dimensions for the heat transfer enhanement, higher heat flux dissipation in miro-eletroni devies, and the emergene of miro-sale devies that all require ooling. Employing smaller hannel dimensions results in higher heat transfer performane, although it is aompanied by a higher pressure drop per unit length [21]. Wang and Peng [26] reported heat transfer experimental data for single-phase fore onvetion of water and methanol in retangular miro-hannels. Channels with 5

25 hydrauli diameters between 311 and 747µm were tested, and results show that heat transfer harateristis annot be desribed well with standard liquid fored onvetion orrelations for retangular duts. However, Peng and Peterson did the heat transfer experimental investigation with single phase fore onvetion in miro-hannels that have hydrauli diameters between 133 and 367µm, and the results show that the hannel aspet ratio has a very strong influene on the heat transfer oeffiient. Muh researh has been done in the analysis of miro-hannels. Most researh is foused on the heat transfer through the miro-hannels. One of the most important steps in the heat transfer analysis is to verify the validity of the lassial ontinuum maro theory on the miro-sale. Heat transfer analysis of miro-hannels is important for validating modeling, numerial analysis, and design of MEMS devies. Many researhers have been attempting to apply maro-sale analysis to the miro-sale. There have been many arguments over whether the lassial ontinuum model e.g. the onventional Navier-Stokes equations are still valid for miro-sale analysis [5, 6, 11, 12]. This argument is involving varying Reynolds numbers, working fluids, Nusselt numbers, flow geometries. This argument is important to determine a valid method for numerial analysis and modeling of both heat transfer and fluid motion through miro-hannels. Kroeker [5] presented the lassial orrelations under predition of the Nusselt values in miro-hannels in his study. Owhaib [12] states in his study that the lassial orrelations still remain valid on the miro-sale (down to 50µm). In Tiselj s publiation [11], the experiments have shown a Reynolds and Prandlt number dependeny of the Nusselt number in laminar flow that strays from the lassial theory. C.B. Sobhan et al. [6] maintained that the onventional theory was valid for miro-hannels as small as 50µm 6

26 assuming that measurements were taken orretly and experimental onditions were identified and simulated orretly. Gad-el-Hat [33] argued that liquids suh as water should be treated as ontinuous media (with lassial theory being appliable) in hannels larger than 1µm. Gao et al. [34] agreed that the lassial laws were valid for gap sizes of 0.5mm or higher. Reviewed experiments seem to agree that the onventional Navier- Stokes and energy equations are valid at the miro-sale (larger than 1µm), and it seems the lassial model an be used for miro-hannel heat transfer and flow analysis. Single-phase flow works for ooling and involves muh less ompliated physis in its modeling and analysis and agreement with the lassial theory is expeted to hold. The majority of the mathematial analysis and the numerial approahes use a very oarse mesh or simple 2-dimensional heat transfer model to determine the possible optimal struture for miro-hannel devies, however three-dimensional heat transfer model also developed. Kou et al. [39] presented a three-dimensional numerial model on the miro-hannel heat sink to study the effets of heat transfer harateristis of various hannel heights and widths. The study investigated the minimum thermal resistane of a heat sink inluding a miro-hannel with a fixed dimension to searh for its optimum hannel width. The results show that a larger flow area, larger flow power, and shorter substrate thikness an result in lower thermal resistane. Kou [39] onluded the optimal hannel width is not signifiantly influened by a derease in the hannel height when the flow power is in the range of at 0.01Watt and 0.1Watt. J.H. Ryu et al [36] presented a three-dimensional analysis for the thermal performane of a miro-hannel heat sink and the optimal fin-hannel shape that minimized the 7

27 thermal resistane. In this analysis a oolant passes through a number of miro-hannels and onvets heat away from a heat dissipating eletroni omponent attahed below. The flow is assumed to be laminar, inompressible, and hydro-dynamially fully developed. All thermo-physial properties were assumed onstant. The hannel depth, the hannel width and the fin thikness were varied for 302µm-320µm, 44µm-50µm, and 50µm-56µm respetively. Among various design variables, the hannel width appeared to be the most ruial quantity in ditating the performane of a miro-hannel heat sink. The optimal dimension of miro hannel was 45.3µm of width and 320µm, and orresponding thermal resistane was [36]. Wen s [40] thermal resistane model is set up to study an optimum thermal design of the heat sink. The lowest total thermal resistane found was o C Cm 2 /W within a hannel aspet ratio of 15, the hannel width of 50µm, and the ratio of the fin width to the hannel width was 0.65µm [40]. Another study by Li, et al [41] developed full three-dimensional numerial simulation (ondution heat transfer model) for heat transfer in silion based miro-hannel heat sink in order to optimize the geometri struture. Under a onstant pumping power of 0.05W for a water-ooled miro-heat sink, the optimized geometri parameters of the struture as determined by the model were a hannel width of 60µm and a hannel depth of 700µm. The overall ooling apaity ould be enhaned by more than 20% using the optimized spaing and hannel dimensions, the overall thermal resistane was o C/W for a pumping power of 2W [41]. K.K Ambatipudi and M.M. Rahman [30] developed a three-dimensional numerial model for ondution heat transfer in miro-hannels. The numerial model was used to 8

28 investigate variation of the hannel depth, hannel width, the number of hannels, and different flow rates through the hannel. Heat transfer results ompared reasonably well with experimental measurement [20, 29]. It was found that the Nusselt number is more for a system with a larger number of hannels and larger Reynolds number. For Re=673, the optimum hannel depth was 300µm. Also, results showed that the outlet temperature as well as the maximum temperature inside the solid dereases with Reynolds number beause a larger mass of fluid is available to arry away the heat. J. Li et al. [22] developed a three-dimensional numerial simulation for heat transfer in silion based miro-hannel heat sinks in order to optimize the geometri struture. J. Li et al. [22] performed a detailed numerial simulation for single-phase flow and found that the thermo-physial properties of the working fluid an also greatly affet the heat transfer harateristis of the devie. Shevade and Rahman [53] analyzed the onvetive heat transfer in miro-hannels with retangular and square ross setions for volumetri heat generation in the substrate. The onservation of mass and momentum equations were used. A thorough investigation for veloity and temperature distributions performed by varying hydrauli diameter (0.06~0.2m), Reynolds number (Re=1600~3000), and heat generation rate in the substrate (g o =6.4E8 W/m 3 ). The results showed that by inreasing the Reynolds number, the outlet temperature dereases and an average Nusselt number inreasings. In 1995, Bailey et al [23] did the extensive review of the available ooling data for single-phase miro-hannel flows, and showed that single-phase miro-hannels an effetively ool miniature devies. However, L. Zhang et al. [24] showed that one disadvantage of single-phase flow is a large temperature gradient in the devie from the 9

29 rise in oolant temperature ompared to the two-phase flow that takes less pumping power to maintain a given thermal resistane TWO-PHASE FLOW Two-phase flow is a more effiient heat dissipation method than single-phase flow [7,8]. Two-phase heat dissipation an ahieve very high heat fluxes for a onstant flow rate while maintaining a relatively onstant surfae temperature. The latent heat of vaporization of the fluid an be used in the two-phase flow to maximize the heat transfer rate. Browers and Mudawar [25] performed an experimental study of boiling flow with a miro-hannel (d=510µm) heat sink. This study showed that a high value of heat flux ould be ahieved with two-phase flow. L. Zhang et al. [24] developed silion test devies with nearly onstant heat flux boundary onditions to study two-phase fored boiling onvetion in miro-hannels with dimensions below 100µm. Heat transfer was optimized with hydrauli diameters between 25 and 65µm. The hannel wall widths are below 350µm, whih minimizes solid ondution and redues variations in the heat flux boundary ondition. Two-phase flows involve more diffiult physis in their modeling and analysis ompared to the single-phase flows. However, due to the potential of miro-hannels for maintaining a high heat dissipation rate, a better understanding of evaporative heat transfer in miro-hannel is needed in order to provide a rational basis for the design of phase-hange atuator. Like single-phase flows, muh researh has been done in the analysis of two-phase flow in miro-hannels. Again, most researh is foused on the 10

30 heat transfer through the miro-hannels, and heat transfer analysis of miro-hannels is important for validating modeling, numerial analysis, and design of MEMS devies. Most of reent researh has been foused on the retangular miro-hannels. The fluid flow and the heat transfer harateristis of the hannels ould be hanged by hanging the hannel geometry beause of the aspet ratio of a retangular hannel influenes apillary pumping power in the miro-hannel [24]. Landerman [31] developed an analytial model for two-phase boiling heat transfer in a high aspet ratio retangular hannel, and the heat transfer and wall temperature was evaluated. In these high aspet ratio hannels, the role of sub-ooled boiling was found to be insignifiant relative to saturated boiling. R.H. Nilson et al. [32] presented analytial solutions of an axially tapered mirohannel with a high aspet ratio for evaporative ooling devies and ompared it with a retangular miro-hannel. The results demonstrate that tapered hannels provide substantially better heat transfer apaity than straight hannels of retangular ross setion, partiularly under opposing gravitational fores. S.W. Thikanda et al. [43] derived analytial expressions for the mean veloity of a liquid flowing in an open retangular miro-hannel based on the Navier-Stokes equations. Solutions were deomposed into additive omponents driven by pressure gradients and by shear stresses on the liquid-vapor interfae. Speed were omputed for menisus ontat angles ranging from 0 o to 90 o, arbitrary hannel aspet rations, and for wetting regimes from liquid-full to nearly-dry orner flows. These numerial results were used to guide the development of analytial expressions for the mean veloity. 11

31 Reently, some efforts have been made to analyze the possible optimal struture for miro-hannel devies. Ryu [36] used a very oarse mesh (three dimensional) to determine the optimal dimension of the miro-hannel heat sink. Hwang [35] used a simple 2-dimensional heat transfer model to determine the optimal dimensions of miro hannel. Knight [37] even used a simple one-dimensional model as an approximation for the thermal ondution along the hannel height. Koh et al. [38] used Dary s law to desribe the fluid flow. Peles et al. [52] presented a quasi-one-dimensional model to investigated two-phase laminar flow in a heated apillary slot, driven by liquid evaporation from the interfae. The theoretial desription of the phenomenon was based on the assumption of uniform distribution of hydrodynami and thermal parameters over the ross-setion of the liquid and vapor flows. With this approximation, the mass, thermal and momentum equations for the average parameters were obtained. The developed model allowed the estimation of the effets of apillary, inertia, fritional and gravity fores on the shape of the interfae surfae as well as the veloity and temperature distributions. Sott [9, 10] used a 2-dimensional axisymmetri finite differene ondution model to study a liquid-vapor phase hange membrane atuator, and it was found that the devie effiieny was maximized when the energy input into the atuator was equal to the energy required to dry out the evaporator. Browers and Mudawar [28] developed the mathematial model for the pressure drop in the miro-hannels using Collier and Wallis homogenous equilibrium model. This homogenous equilibrium model assumes the liquid and vapor phases are a homogenous 12

32 mixture with uniform veloity, and properties were assumed to be uniform with eah phase. L. Zhang et al. [24] developed a homogeneous two-phase onvetion model with finite volume method. The results showed that optimum heat transfer ourred in retangular hannels with hydrauli diameters between 25 to 60µm. The two-phase miro-hannel flow model yielded preditions in reasonable agreement with the measured pressure drop and wall temperature distribution. Nilson et al. [32, 42] derived numerial and analytial solutions for steady evaporating flow in open miro-hannels. Nilson et al. onsidered miro-hannels of a retangular ross setion with uniform depth (500µm) and a width that dereases along the hannel axis (tapered hannel). The heat transfer results of tapered hannel were ompared to uniform retangular hannel analytial solution [42], and the results showed the tapered hannels having better performane. Wang et al. [45] presented investigation of an evaporating menisus in a miro-hannel using the Young-Laplae model (Capillary pressure alulation) and the kineti theorybased expression for mass transport aross a liquid-vapor interfae. The results showed that thin layer of liquid had relatively larger mass evaporation than the thik layer of liquid. Kim et al. [46] developed a mathematial model (based on fore balane, mass onservation, and momentum equation) for heat and mass transfer in a miniature heat pipe with a grooved wik struture and solved analytially to yield the maximum heat transfer rate and the overall thermal resistane under steady-state onditions. The model is used for the thermal optimization of the grooved wik struture with respet to the 13

33 width and the groove height. The effets of the liquid-vapor interfaial shear stress, the ontat angle, and the amount of initial liquid harge have been onsidered in the model. The alulation showed a narrow and deep groove had higher heat transport apability and higher overall thermal resistane. Kyu Hyung et al. [47] developed a mathematial model for prediting the thermal performane of a flat miro heat pipe with a retangular grooved wik struture. The axial variations of the wall temperature and the evaporation and ondensation rates were onsidered by solving the one-dimensional ondution equation for the wall and the evaporation. Kyu Hyung et al. [47] showed that the maximum heat transport rate is 128W under the optimum onditions of groove width=0.1437mm and height=0.525mm for vapor temperature=90 o C, whih reflets an enhanement of approximately 20% ompared to the experimental result obtained by Hopkins et al [48]. Hopkins et al. [48] experimentally showed that a 120mm long flat heat pipe with an inner hydrauli diameter of 900µm had a temperature drop from the evaporator to the ondenser end ap of 25 o C at a heat load of 100W. This showed that the axial variations of the wall temperature and the evaporation and ondensation rates should be taken into aount to aurately predit the thermal performane of a miro heat pipe. Park and Lee [49,50] developed a mathematial model (onservation and fore balane equation) that desribes the two-phase flow and thermal harateristis of the extended menisus region in an open miro-apillary hannel. A working fluid in an open miroapillary hannel evaporates due to the applied heat, resulting in the thinner liquid film thikness and an inreased in the radius of urvature at the liquid-vapor interfae. The 14

34 results showed that the loal heat transfer has an extremely large value in the thin film region. A.J. Jiao et al. [51] developed a mathematial model prediting the effet of ontat angle on the menisus radius of thin film profile and heat flux distribution ourring in the miro heat pipe. This was done to have a better understanding of thin film evaporation and its behavior on the effetive thermal ondutivity in a grooved heat pipe and ontribute to the optimize the design of onventional grooved heat pipes. The numerial results showed that while the apillary governs the heat transport apability in a heat pipe, the thin film evaporation determines the effetive thermal ondutivity in a pipe. The ratio of the heat transfer through the thin film region to the total heat transfer through the wall to the vapor phase dereased when the ontat angle inreased FLOW ANALYSIS: CAPILLARY ACTION Capillary ation or apillary motion is the tendeny of a liquid to flow in narrow tubes or hannels. Capillarity is a result of intermoleular attration within the liquid and solid materials. Capillary ation ours by the axial gradient of apillary pressure, and apillary ation an eliminate the need for ative pumping. The apillary ation is ontrolled by the surfae tension, radius of the interfae (menisus), and wetting angle of the liquid on the surfae of the apillary. A great deal of work has been done on apillary pumping by researhers motivated by the optimization of heat pipes. One measure of the performane of a heat pipe is the maximum heat flux, the apillary limit or dry out point, supported by apillary pumping. An investigation of evaporation from single grooves is useful beause the overall 15

35 performane of a heat pipe is a funtion of the apability of the individual grooves [54]. Catton and Stores [55] presented a one-dimensional, semi-analytial model for predition of the wetted length supported by inlined triangular apillary grooves subjet to heating from below. The model utilizes a marosopi approah employing the onept of an apparent ontat angle. The onept of aommodation theory is introdued to aount for the hange in the radius of urvature of the liquid-vapor interfae between the liquid reservoir and the groove proper. The results showed a series of design urves that an be used to estimate the apillary limit in inlined heated triangular apillary grooves for a variety of operating onditions. R.H. Nilson et al. [32] presented results of an analytial study showed that straightretangular miro-hannels have a disadvantage in omparison to triangular grooves in apillary ation. The apillary pressure in a retangular hannel varies with the liquid height in the hannel only if the menisus remains attahed to the top orners of the hannel. S.W. Thikanda et al. [43] presented analytial and numerial solutions of the mean veloity of a liquid flowing in a retangular miro-hannel for ontat angles ranging from 0 o to 90 o. The overall solutions are deomposed into two omponents. The first one is the flow driven by apillary fores, and the seond omponent is the flow driven by pressure. The range of hannel aspet ratios (width/height) was 0.65 to 2. The pressure-driven solutions apply equally well to flows driven by apillary or gravity fores as well as applied pressures. R.H. Nilson et al. [42] presented relations between flow geometry and apillary pressure. They showed that a flatter entry menisus, and hene a larger ontat angle, inreases the liquid pressure at the inlet, thereby providing a larger pressure differene to 16

36 drive the axial apillary flow. Therefore the ontat angle between liquid and solid wall an range anywhere from 0 to 90 degree angle assoiated with the fluid to solid interfae energy. They define a dead zone, a region in whih the ontat angle remains onstant and the menisus moves down the hannel wall. In the dead zone there is no apillary pressure differential. Geometri onstrains ensure that the fluid may be no deeper than half the hannel width. T.S. Sheu et al [56] presented a study that explores the effet of surfae harateristis on apillary flow in miro-grooves. In this experimental study, they verified the theoretial model presented by Peterson and Ha [57] and their model an estimate the dryout loation in the triangular grooves by the losed-form solution of a simplified governing equation. T.S. Sheu et al. [56] used a series of triangular miro-grooves with upper width (W) of 0.4mm and the vertex angle (α) of 60 o was mahined on oxygen-free opper plate. The mirogrooves plates inlude one with non-ethed surfae texture with lined inisions left by mahining tool, and another with hemially ethed surfae texture with miro avities. Methanol and ethanol were used as working fluid. The study showed that the ethed miro-grooves surfae texture with miro avities has inreased the apillary performane by 10-35% for the ethed miro-grooves surfaes ompared to the non-ethed surfae. The surfae harateristi proved to have larger influenes on the apillary performane of working fluid (Ethanol) with lower surfae energy. W.R. Jong, et al. [58] formulated a mathematial model of flow in miro-hannel driven by apillary fore and gravity from the Navaier-Stokes equations to predit flow time. The flow time is period time required for flow moves inlet to outlet. The results showed that when the miro-hannel height is 150µm or smaller, the effets of gravity 17

37 fore beome less obvious; the apillary fore beomes the dominant soure to drive flow in the miro-hannel. Naoki et al. [59] did an extended analytial theory of the apillary rise problem for a retangular miro-hannel, and it was presented to study the interfae motion driven by apillary ation in a miro-hannel. They examined experiments with glass retangular tubes with sizes of about 50 to 100µm square and PDMS miro-hannels with dimensions of 85 x 68µm and 75 x 45µm. They ompared the experimental results with the theory and introdued dimensionless driving fore variables (for glass-water, glass ethanol, and PDMS-ethanol) to predit for the interfae motion for any size of retangular hannels. D. Yan et al. [60] presented a theoretial model to analyze the finite-reservoir effet in a retangular miro-hannel to estimate the flow veloity profile. The proposed model has been verified by experiment using miro-piv (Partile Image Veloimetry) tehnique. They found that the size of the hannels ross setion signifiantly affets the effetive pumping period FABRICATION Basi MEMS fabriation methods, photolithography, wet ething, and hemial vapor deposition (CVD) are used to fabriate most miro-hannels [13]. The tehnique used depends on the miro-hannel material and design, and ommon materials used to fabriate miro-hannels are silion, opper and SU8. The ommon problems and hallenges assoiated with these fabriation methods inlude wet ething ontamination, 18

38 thik film stress, overing hannels without wafer bonding and obtaining an adequate hannel depth [14]. The miro-hannel materials are often desired to have a high thermal ondutivity to be used as heat sinks, and both opper and silion are appropriate material hoie for this type of appliation. Copper hannels an be fabriated through photolithography and ething, and silion hannels an be fabriated through a wet and dry ething proess. Other fabriation tehniques are being developed to aid in the heat transfer analysis of miro-fluidi hannels. One of other material hoies to forming the miro-hannel is SU8. SU8 is a photosensitive epoxy resist developed and patented by IBM in SU8 has beome very important in miro-fabriation due to its thermal properties, thermal and hemial stability, and its ability to form high aspet ratio with high resolutions. SU8 an be stable up to 200 o C and deomposes near 340 o C, and forms single layers from 2-200µm thik. SU8 forms high aspet ratio up to 25:1 with standard UV lithography. SU8 is a unique miro fabriation material that is deposited in a relatively simple photolithography proess. SU8 is a negative resist meaning that whatever material is exposed will stay on the substrate while the unexposed portion is removed during development. The basi fabriation proess begins with the leaning and dehydration of the substrate, the SU8 is then spun on, soft baked, exposed to UV light, post baked, ooled, developed, rinsed, and finally hard baked if the devie will be used in a high temperature thermal devie. This is the ommon proess for SU8 fabriation, however SU8 fabriation has a few hallenges. J.H. Daniel et al. [15] disuss some of the fabriation hallenges of SU8 resists. SU8 fabriation proess is sensitive to both heat and UV light due to the hemistry of the resist. 19

39 If the resist is either over or under baked, the ross-linking an be improperly developed whih an make the material brittle. This an form raks in the surfae or the shearing of fine features and lak of adhesion [16]. The raking lithographi features are aused by internal stresses in SU8 mirostruture, and a lot of researh is urrently being done to study different methods to proess and develop SU8 to maintain its desirable thermal, eletrial and mehanial properties while dereasing the inherent internal stresses developed during proessing. Johnson et al [17] is fousing on developing omposites of SU8 to redue stress raking of mirostrutures. In this study, SU8 is mixed with low moleular weight aromati epoxies and developed to test some of its major properties suh as adhesion, resolution, aspet ratio, and feature raking of the omposite mixture. Feng and Farris [18] foused on developing different fabriation proedures and studying different property results. They studied to see how the thermal and mehanial properties of SU8 hange by different proessing onditions suh as soft bake time, exposure time, post exposure bake time, development time, and different substrate materials. SU8 thikness of 50mm, 100mm, and 220mm were studied to optimize properties suh as sidewall profile and film adherene. In the past, removal of SU8 has also been major hallenge. This proess has been perfeted with the use of the Omnioat layer with a reently developed Remover PG SU8 Stripper. The Remover PG SU8 Stripper is an important development in the use of SU8 beause this remover makes SU8 more appliable for a variety of uses [19]. Although a lot of researh is being done, the SU8 fabriation proess is sensitive to all steps inluding baking times and temperatures, ooling or resting times, exposure, and development times. 20

40 C.W. Liu et al. [13] developed a fabriation proedure for miro-hannel systems that an be used to study the flow and the loal heat transfer oeffiient within the hannel. The proess forms a one-hannel wall that is uniformly heated with the opposing wall well insulated. This design is meant to minimize the heat loss through the substrate. In this work, SU8 is used to form the miro-hannels to aid in the heat transfer analysis of miro-hannels. SU8 is used to form the hannels and its thikness an easily be varied using varying visosities and spin speeds during photolithography. Temperature sensors an be fabriated on the hannel walls to reord their temperatures and find the loal heat transfer oeffiient of the flow [7] VISUALIZATION Visualization of the flow in miro-hannels is an important tehnique to yield a better understanding of what is happening inside the hannels. Visualization tehniques of the flow in miro-hannels have been used to see the motion of the liquid-vapor interfae in two-phase flow, and the flow due to apillary ation [24]. However visualization of flow in miro-hannels has its own hallenges. Due to the length to width ration of most miro-hannel, it is diffiult to visualize throughout the length of a miro-hannel. Fluid motion is also diffiult to apture. Different dyes and lighting tehniques have been used to illuminate the fluid to observe its motion through the hannel. Among the many requirements (and some problems to be solved) to obtain worthwhile images of miro-hannel fluid flow are visualization tools with resolutions down to the miro level, flexible lighting, and methods to deal with internal refletion from the hannels [8]. 21

41 K.H. Chang and Chin Pan [61] used a harge-oupled devie (CCD) amera with a miro lens to observe the two-phase flow pattern in the miro-hannel with hydrauli diameter of 86.3µm. The width and depth of eah hannel were 99.4µm and 76.3µm, respetively. The maximum frame rate available of the amera was 10,000 frame/s and the maximum shutter speed is 1/20,000s. R.H. Liu et al. [62] also used a CCD Camera to apture a image of passive mixing in the miro-hannel. The width and depth of eah hannel were 300µm and 150µm, respetively. Images of the hanging olor of phenolphthalein dye during the mixing proess are aptured through an Olympus BX60 mirosope at 40 times magnifiation with a Sony 8-bit CCD amera. The mirosope lens has a depth of fous of 7µm at this magnifiation. This setup gives lear images of the purple phenolphthalein dye, but only allows images to be obtained at positions where the silion wafer is ethed ompletely through. S.S. Hsieh et al. [63] used a MPIV, miro partile image veloimetry, system for visualize the liquid flow in a miro-hannel. The size of hannel was 115µm deep, 200µm wide and 24,000µm long with a hydrauli diameter of about 146µm. The MPIV system onsists of a new wave solo PIV Nd:, Yag double resonant tube laser providing frequeny-doubled (λ=532nm) pulsed emission of 50mJ/pulse (maximum) via a Q- swithing modules with a pulse duration of approximately 10ns. The light from the laser was delivered into the mirosope illumination path with a fiber light guide fitted to the mirosope. Partile images are reorded using a Dente HiSense CCD amera with a 1280x1024 pixel array and 12-bit resolution. With the aid of omputer, the mirosope and CCD amera built into the MPIV system an reord the images of the flow pattern 22

42 evolution in the miro-hannel at 20 frames/s. A Sony DCR-TRV34 olor video amera with an area of 320x240 pixels for eah frame was used. S. Hardt [64] used a high-speed amera mounted on mirosope to visualize the flow patterns emerging during evaporation in parallel miro-hannels. The width and depth of eah hannel were 50µm and 50µm, and a length was 64.5mm. A limiting fator for the flow-pattern visualization with the high-speed amera was the amount of light available for one frame. The amount of light olleted is redued by using a mirosope and limiting the visible area of the hip surfae. The brightness of images is further redued by inreasing the shutter speed of amera. With these onstraints a maximum frame rate of 5000 frames/s ould be reahed when using four independent light soures. 1.4 FIXED SU8 HEIGHT The goal of the present work was to use a ombination of both experimental and numerial work to provide insight into the ontrolling parameters and design onstraints of the miro-hannel evaporator. One of the ontrolling parameter was the dimension of miro-hannels. The dimensions of these miro-hannels were varied to determine how this fator affets the test results. The dimension fators inlude miro-hannel geometry, miro-hannel width, and SU8 height. The SU8 height used in this work is fixed at 40µm and this value was determined by previous work by Tiffany [74]. Tiffany onsidered effet of miro-hannel height and a summary of these results are shown in the Figure 1.2 and table 1.1. In general, the higher miro-hannel dereases aspet ratio fluid mirohannel and inrease the fluid mass over the membrane. 23

43 Figure 1.2 Calulation of wik effiienies for 40 and 70µm hannel heights for 50mW of power input assuming onstant evaporation rates, Courtesy T.A. Quy Table 1.1 Wik effiienies for 40 and 70µm high hannels, Courtesy T.A. Quy 24

44 Table 1.1 shows the effiienies of the 40µm high miro-hannels are mostly higher than the effiienies of the 70µm high miro-hannels. However, the omparisons of the miro-hannel evaporator performanes were not aurate due to varied power inputs. The onstant power input needs to be used to make an aurate omparison of the mirohannel evaporator performanes sine the miro-hannel evaporator effiienies were defined as the ratio of evaporation power over power input. The hoie of 50mW was used for all experiments performed on 40µm and 70µm high wik strutures. Figure 1.2 shows this omparison results. The 40µm high wiks reahed a maximum effiieny at a hannel width of 70µm. A general effiieny trend of the 40µm high wiks was higher than the effiieny of the 70µm high wiks. The effiieny of the 10µm high wik hannels was also tested and ompared, however the Figure 1.2 did not indiate the results of 10µm high wik hannels beause the effiieny values were signifiantly low ompared to the effiienies of 40µm and 70µm high wik hannels. Sine the results of previous work [74] onlude the 40µm high wik hannels reahed maximum effiieny ompared to other hannel heights, it was reasonable deision to use this 40µm high wik hannels in this present work. 1.5 RESEARCH OBJECTIVES Phase hange atuators funtion by dissipating eletrial power to heat a working fluid and hange its phase. However the effiieny of onversion from eletrial to mehanial power is very low. To maximize or optimize the mehanial power produed it is required to study the miro-hannel evaporator, to inrease the effetiveness of heat addition and evaporation. 25

45 The present work builds upon previous experimental and numerial work [65, 66, 67] to develop and validate a numerial model of evaporative heat transfer for square opentop miro-hannels. The objetive of the numerial work is to develop a threedimensional finite-differene time domain integration for the analysis of the sensible and latent heat transfer. The objetive of the evaporation experiment is to validate the numerial model by douments the performane of the miro-hannel evaporator with varying miro-hannel dimensions and membrane materials. The ultimate goal of the work is to build an effetive design tool for the development of effiient miro-hannel evaporator with dimensions from ten to one hundred mirons and to find the overall most effetive mirohannel evaporator geometry and dimensions. 26

46 CHAPTER 2 FABRICATION 2.1 FABRICATION OVERVIEW A miro-system is an engineering system that ontains MEMS omponents, and many MEMS omponents an be produed in the size of mirometers. These miro-size omponents are not able to be fabriated with the traditional mehanial tehniques suh as mahining, drilling, milling, forging, asting, and welding. The tehnologies used to produe these miro-size omponents are alled miro-fabriation [68]. Almost all mirofabriation tehniques or proesses involve physial and hemial treatment. Most of the miro-fabriation tehniques used in this dissertation are photolithography, wet ething, and physial vapor deposition (Sputtering). The fabriation of the mirohannel evaporator presented in this dissertation used the most fundamental and proven miro-fabriation tehniques and materials. The signifiant miro-fabriated omponents mentioned in this hapter onsist of a heater membrane, resistane thermometer devie (RTD), and apillary wiking struture. 2.2 PREPARATION OF SILICON (Si) MEMBRANES A boron doped silion membrane is used for the basi building blok for fabriation of the miro-hannel evaporator omponents. The substrate wafer used in this dissertation is a standard three-inh diameter, double side polished, and [100] orientation silion wafer. The thikness of the wafer is approximately 400µm with a tolerane of ±25µm. High Temperature Oxidation (HTO) is used for the first proessing step of the 27

47 fabriation in order to grow a layer of SiO 2 on both front side and bakside of the wafer. Wafers are baked in a furnae at 1000 o C for 120 minutes to ahieve 500nm oxide thikness. The wafer is soaked in a 10:1Buffered Oxide Eth (BOE) solution for 15 minutes to remove oxide on the front side of the wafer and to prepare boron doping. The boron doping is used as an eth stop for the wet ethants used in the fabriation proess. The final thikness of the fabriated membrane is determined by the thikness of the boron layer. The thikness of the final membrane used in this dissertation is 2.2µm. The boron diffusion ours by plaing boron nitride disks parallel to the exposed surfae of the wafer at elevated temperatures. Plaing the wafers in the furnae at 1125 o C for 110 minutes produed a boron layer of 2.2µm. Several proessing steps are still needed to omplete the substrate wafer after boron diffusion. The appearane of the boron-doped surfae is non-uniform olor beause of the borosiliate glass that is built up on the wafer. A three step proess is needed to remove the borosiliate glass, and the three step proess onsists of a BOE eth, sarifiial oxide growth and a seond BOE eth. The wafer is soaked in the BOE for 15 minutes to remove the borosiliate glass. A low temperature oxide (LTO) proess is grown onto the wafer at 850 o C for 60 minutes. The sarifiial oxide and residual oxide from HTO are removed by soaking the wafer in BOE for 10 minutes. The final low temperature oxide (LTO) is grown onto the surfae of the wafer to at as an eletrial insulation layer. Finally, the substrate silion wafer is ready for the next proessing step. 28

48 2.3 PREPARATION OF SILICON NITRIDE (SiNx) MEMBRANES Silion nitride membranes are also used as the membrane material in this work. A 300nm layer of silion nitride (SiNx) is deposited on both front and bakside of [100] orientation silion wafer using a Low-Pressure hemial vapor deposition (LPCVD) proess instead of adding a boron-doped layer to the wafer. The bulk of silion nitride wafers are ordered from outside of Washington State University (WSU) beause of the LPCVD proess is not available at WSU. The deposited silion nitride on the front side of wafer forms the final membrane, and the deposited silion nitride on the bakside of wafer ats as an eth stop for KOH ethant. 2.4 PATTERNING WAFERS FOR MEMBRANE The same photolithography tehnique is used to define membrane size, resistane heater, RTD, and miro-hannel evaporator for both silion and silion nitride membranes. Figure 2.1 shows a typial mask for defining 5mm square membrane for both silion and silion nitride membranes. The thin horizontal and vertial lines in the figure form an 18mm by 10mm retangle and are used for diing guides. The four small rosses are used for alignment purposes. The masks are designed for positive proessing. Figure 2.1 shows the positive field of design but the negative of mask image is atually used for fabriation. The patterning on the silion and silion nitride wafers seem to have a lot in ommon, however two different proesses are used to pattern membranes on eah type. The proess for the silion membrane is explained in setion and for the silion nitride membrane is explained in setion

49 Figure 2.1 Mask for ething the oxide to define membranes SILICON (Si) MEMBRANE FABRICATION Fabriation of silion membranes begins with a prepared silion wafer as desribed in setion 2.2. The first step is to sputter 500nm of gold on the bakside of the wafer along with a TiW adhesion layer. The hexamethyldisilazane (HMDS) is spin-oated to serve as an adhesion promoter. The HMDS is spun for 30 seonds at 3000 rpm. The wafer is immediately spin-oated with AZ5214 photoresist at 3000 rpm for 30 seonds, and baked for one minute at 110 o C. The bakside of wafer is now patterned with the mask shown in figure 2.1 using a UV light soure with exposure time of 12 seonds. AZ5214 is a positive photoresist, whih means that the exposed portion of the wafer is removed away by developer. 30

50 Figure 2.2 Illustration of photolithography proess 400K-photoresist developer is used in this work with a 1:4 ratio with water (e.g. 12mL 400K with 48mL DI water). The photoresist works as an eth stop for ething through the gold, TiW, and SiO 2 layer during the bakside of wafer proessing. The wafer is plaed in the gold ethant with onstant agitation until gold is ethed away and then the wafer is soaked in hydrogen peroxide for 40 seonds with onstant agitation to remove TiW adhesion layer from the membrane pattern. The wafer is then plaed in the Buffered Oxide Eth (BOE) for 15 minutes to remove the SiO 2 layer for membrane ething. The wafer is now plaed in the spin-rinse dryer to be washed thoroughly. The gold on the bakside of wafer is an eth stop for KOH membrane ething. The photolithography proess used in this work is illustrated in Figure

51 Figure 2.3 Photolithography mask for resistane heater and dual RTDs With the bakside patterning ompleted, the front side is now patterned using a lift-off proess. The platinum lift-off proess is used to fabriate the internal platinum resistane heater and the onentri Resistane Temperature Detetor (RTD) strutures. The photolithography mask for the resistane heater and the dual RTDs is shown in Figure 2.3. The outside radius of the internal heater is 0.8mm, and the average radius of the inner RTD and outer RTD is 1.7mm and 2.4mm respetively. Again, the thin horizontal and vertial lines in the figure forms an 18mm by 10mm retangle are used for diing guides. The four small rosses are used for alignment purposes. More design details for onentri resistane heater and RTDs are explained in hapter 3. 32

52 Figure 2.4 Photolithography mask for resistane heater and triple RTDs A new photolithography mask has features of a resistane heater and triple RTDs. The new mask shown in Figure 2.4 has exatly the same features as the old mask shown in Figure 2.3, however the new mask has one more RTD around the 5mm square membrane defined in the bakside patterning. This third RTD feature in the new mask is used to find the fixed boundary ondition temperature for numerial alulations. To fabriate the internal platinum resistane heater and onentri RTD strutures, first the wafer is spun with an adhesion promoter HMDS at 1500rpm for 30 seonds. The positive photoresist AZ5214 is used to pattern the heater and RTD strutures. The spin rate and time for the photoresist is 1500rpm for 30 seonds, and soft baked for 1 minute at 110 o C. The wafer is exposed for 15seonds using the orret negative field mask shown in Figure 2.3 and

53 Figure 2.5 Illustration of platinum lift-off proess The wafer is overed in photoresist, and the heater and RTD designs are the only fration of the wafer not overed with photoresist. The desired features are developed using the 400K-photoresist developer with a mixed ratio of a 1:4 with DI water. Platinum is now sputtered over the photoresist at a thikness of 175nm. After sputtering, the wafer is soaked in aetone for 30 or more minutes to remove the sarifiial photoresist layer and unwanted Platinum. The wafer needs to be blasted with aetone to remove any small hunks of Platinum remaining on the surfae of wafer. The wafer is then leaned and heked under the mirosope. The features should be solid and lear. If there is still unwanted Platinum left on the wafer, soaking or blasting longer is required until it is mostly removed. The illustration of the platinum lift-off proess is shown in Figure 2.5. The wafer is now annealed at a temperature of 650 o C for duration of ten minutes in the vertial furnae that lowers the internal resistane of the platinum strutures and 34

54 homogenizes the gold to help with potassium-hydroxide (KOH) membrane ething SILICON Nitride (SiNx) MEMBRANE FABRICATION The fabriation of silion membranes begins with a prepared silion wafer as desribed in setion 2.3. Photolithography begins by spinning an adhesion promoter, HMDS, at 3000rpm for 30seonds and soft baked at 110 o C for one minute. The wafer is then spinoated with AZ5214 photoresist on the silion nitride wafer to define a membrane pattern. The wafer is exposed to UV light for about 12 seonds, and developed to ahieve the desired pattern. The photoresist ats as an eth stop during the reative-ion ething proess. The desired pattern used in this work is the same as that shown in Figure 2.1. The wafer is exposed to a CF 4 reative-ion ether (RIE) plasma to eth the bakside of silion nitride layer from the membrane squares. The bakside silion nitride layer ats as an eth stop for KOH membrane ething. The patterning proess of front side of silion nitride membrane is the same proess with silion membrane patterning. The remaining fabriation steps are patterning, platinum lift-off, and annealing of the wafer. The detail patterning proess of the front side membrane is explained in setion The same masks are also used to pattern the resistane heater and RTDs on the silion nitride membrane. The masks used in this work are shown in the Figure 2.3 and Figure FABRICATION OF MICROCHANNEL EVAPORATOR After the wafer is patterned with membranes on both the front side and bakside and annealed, the wafer is now ready to be fabriated with miro-hannel evaporator on the 35

55 substrate surfae. The miro-hannel evaporator is fabriated onentrially over the platinum strutures on the substrate membrane. The miro-hannel evaporator is used to draw a thin layer of working fluid, and maintain the working fluid. Sine the mirohannel evaporator is fabriated on the resistane heater, the miro-hannel need to be able to tolerate high temperatures for the heat addition proess of this work. SU8 is the material hosen for the miro-hannel evaporator beause of its fabriation ability, high aspet ratios forming ability, and good thermal properties. More details about SU8 materials are explained in setion SU8 is a negative photoresist, so the exposed hemial remains on the wafer while the unexposed fration is removed during development. Two types of SU8 polymer are used. SU is used for forming the 10µm high miro-hannel evaporator, and SU is used for 40µm high mirohannel evaporator. Several different miro-hannel evaporator dimensions are presented in this dissertation. The one type of miro-hannel evaporator onsists of hannels 10µm in width and 10µm high, and 10µm thik walls of SU8 delineate these hannels. The other type of miro-hannel evaporator was fabriated by spinning on 40µm height of SU8 with width of 35, 50 and 70 hannels bounded by 5µm wide SU8 walls. Finally, the 80µm narrow to 5µm wide tapered hannels and SU8 walls with 40µm height mirohannel evaporator are fabriated. The material is very sensitive to eah proess, so MiroChem publishes fabriation guidelines for all of their SU8 resists. Although SU8 is fabriated using a standard lithography tehnique, eah fabriation proess step needs to be reanalyzed for eah hannel thikness and geometry beause the appliation parameters suh as exposure equipment, bake times and methods, and development times are all affet the fabriation results. 36

56 Figure 2.6 SEM examples of 10µm high SU8 wiks, Courtesy J. Martinez To fabriate 10µm high miro-hannel evaporator on the surfae of the heater membranes, the photosensitive SU epoxy is used. The first step for 10µm high miro-hannel is the spin oating of Omnioat at 3000rpm for 30 seonds as an adhesion layer. After Omnioat deposition, the Omnioat layer is baked 1 minute at 200 o C and left to ool to room temperature. The wafer is now spin-oated with SU at 2000rpm for 30 seonds, and soft baked at 65 o C for 1minute and at 95 o C for 2minutes. The SU8 is now exposed via UV light for 15seonds and then post baked. The post bake times are at 65 o C for 2minutes and at 95 o C for 3minutes, then again at 65 o C for one minute. With baking ompleted, the SU8 is developed via 3minutes with strong agitation in the MiroChem SU8 developer. The desired 10µm high miro-hannel evaporators are now fabriated on top of the platinum heater and RTDs. Figure 2.6 shows the SEM photograph for an example of 10µm high SU8 miro-hannel evaporator. 37

57 Figure 2.7 SEM examples of 40µm high SU8 miro-hannels, Courtesy T. Quy 40µm high miro-hannel evaporators are fabriated on the surfae of the heater membranes using the photosensitive SU epoxy. Figure 2.7 shows the SEM photograph for an example of 40µm high SU8 miro-hannel evaporators. To fabriate these miro-hannel evaporators, an adhesion layer Omnioat is spin oated at 3000rpm for 30seonds and soft bake at 200 o C for 1minute. SU is pre-spun at 500rpm for 7se with aeleration of 100rpm/s, and is heked for any bubbles that might have ourred. If bubbles our during the pre spin oat proess, it is neessary to pop or remove the bubbles for suessful fabriation. With bubbles removed, SU is now post spun at 2000rpm for 30seonds with an aeleration of 300rpm/s for 40µm height. Next, SU is soft bake at 65 o C for 2minutes 30 seonds and then post bake at 95 o C for one hour in a onvetion oven. The SU is now exposed via UV light soure with predetermined time. Exposed time for 35µm wide hannels are 55seonds, and the rest of hannels sizes for 65 seonds. 38

58 Figure 2.8 AutoCad designs of miro-hannels with different hannel widths Figure 2.9 AutoCad designs of tapered miro-hannels 39

59 (a) 70µm wide hannels with 5µm wide SU8 walls (b) 80µm narrow to 5µm wide tapered hannels and SU8 walls Figure 2.10 Magnifiation Image typial Masks for Different Wik Geometries 40

60 Figure 2.11 SEM photographi image of the tapered hannels High-resolution hrome masks are used to define the shape of the miro-hannel evaporator during UV light exposure. The hrome masks are made at the University of Minnesota Nano Fabriation Center (NFC) from an AutoCad template. The AutoCad design for SU8 mask is shown in Figure 2.8 and 2.9. Figure 2.8 shows the design of miro-hannels with different width, and Figure 2.9 shows the design of the tapered hannels. With ompletion of UV light expose proess, the SU8 is post baked at 65 o C for one minute on first hot plate, then plae on the seond hot plate for 4minutes at 95 o C. To prevent raking of the fabriated wafer, it is now ool to room temperature. Finally, SU is developed using a full immersion in SU8 Developer for 5minutes and 15seonds with onstant strong agitation. This leaves the desired SU mirohannel evaporator on top of the platinum heaters and RTDs. 41

61 Figure 2.10 shows magnifiation image typial masks for different miro-hannel geometries as shown in Figures 2.8 and 2.9. The radius of eah pattern shown in Figure 2.10 is 5mm. Beause the features are so small relative to the membrane size, only a small portion of entire feature is shown. Figure 2.11 is a Sanning Eletron Mirosope (SEM) photographi image of a portion of the tapered hannels that has orresponding dimensions to Figure 2.10 (b). 2.6 KOH ANISOTROPIC ETCHING The final fabriation proess in membrane reation is ething the wafer to define the membrane strutures. A potassium hydroxide (KOH) solution is a highly seletive wet eth for this proess. The KOH solution is the mixture of 250g of KOH dry pellets with 400mL of deionized water, and this solution is heated to a temperature approximately 80 o C. If the KOH solution temperature is between 70 o C and 80 o C, the solution is now ready for use. The wafer is plaed and sealed in a arrier devie, and immersed in the ething solution. The bakside of wafer is exposed to the solution for about 5 to 6 hours depending on the eth rate. Sine KOH solution is highly dependent on temperature to ontrol eth rate, the ething progress should be heked frequently. Ething is ompleted when the membranes beome transluent and the forming of bubbles on the ething surfae slow. The bubble forming is slowed down beause the KOH solution has now reahed to the boron doped layer or the silion nitride layer. Cross setions of the ethed strutures for silion (Si) membrane and silion nitride (SiNx) membrane are shown in figure

62 (a) Cross setion of KOH eth for silion (Si) membrane (b) Cross setion of KOH eth for silion nitride (SiNx) membrane Figure 2.12 Cross setion of KOH eth for different materials Figure 2.13 shows a top view of a ompeted evaporator membrane. The figure shows that lear images of the annular lines in the middle that forms the resistane hater and two onentri annular sets of lines that make up the two RTDs. The blak radial lines on the top of the resistane heater and RTDs form the miro-hannel evaporator. Figure 2.14 shows the layout of a miro-hannel evaporator. 43

63 Figure 2.13 Top view of ompleted evaporator membrane Figure 2.14 Layout of a miro-hannel evaporator 44

64 2.7 DETAILED FABRICATION PROCEDURE The ompleted evaporator onsist an internal platinum resistane heater, onentri platinum RTDs, and miro-hannels. To fabriate this miro-hannel evaporator, several fabriation proesses are needed as mentioned in setions from setion 2.2 to setion 2.6. Sine these setions explained eah proess, the omplete proessing list for the fabriation is provided in this setion FABRICATION STEPS FOR SILICON RTD/HEATER DESIGN 1) Sputter 500nm of gold on bakside of stok LTO, boron doped wafer. 2) Spin both side of wafer with photoresist. 3) Pattern the bakside of wafer with oxide pattern. 4) Develop photoresist and eth gold to leave oxide pattern gold free (see setion 2.7.3). 5) Soak wafer in BOE to eth silion dioxide from wafer. 6) Clean in the spin rinse dryer. 7) Pattern the front side of wafer with Dual or Triple RTD and onentri heater pattern. 8) Supper front of wafer with Platinum. 9) Lift-off sarifiial Pt with aetone (see setion 2.7.4). 10) Anneal the wafer in the vertial furnae. 11) Spin wafer with SU8 to fabriate wiks over the RTDs and heater (see setion and setion 2.7.6). 12) Eth membranes with KOH (see setion 2.6) 45

65 2.7.2 FABRICATION STEPS FOR SILICON NITRIDE RTD/HEATER DESIGN 1) Spin both sides of wafer with photoresist. 2) Pattern the bakside of wafer with oxide pattern. 3) Remove SiNx in RIE. 4) Pattern the front side of wafer with Dual or Triple RTD and heater pattern. 5) Sputter front of wafer with platinum. 6) Lift-off sarifiial Pt with aetone (see setion 2.7.4). 7) Anneal the wafer in the vertial furnae. 8) Spin wafer with SU8 to fabriate wiks over the RTDs and heater (see setion and setion 2.7.6). 9) Eth membrane with KOH (see setion 2.6) PHOTORESIST FABRICATION FOR GOLD ETCH 1) Sputter wafer with desired gold thikness. 2) Turn on mask aligner and set hot plate to 110 o C. 3) Clean wafer using 5-step proess (Aetone, IPA, DI, Aetone, IPA, dry). 4) Dehydrate wafer for 1minute at 110 o C. 5) Spin wafer with HMDS for 30seonds at 3000rpm for both side. 6) Spin wafer with AZ5214 photoresist for 30seonds at 3000rpm for both side. 7) Bake for 1minute at 110 o C. 8) Expose for 12 seonds using orret negative field mask. 9) Develop using 400K-photoresist developer (mixed at a 1:4 ratio with water) with onstant agitation about 1 minute and rinse with DI. 46

66 10) Soak in gold eth with onstant agitation until gold is gone (should be 45seonds to 2minutes depending on gold thikness) and rinse with DI. 11) Soak in hydrogen peroxide for 40seonds with onstant agitation for eth TiW adhesion layer. 12) Going though BOE to remove SiO 2 layer for membrane ething. Turn on the rinse tank and spin rinse dryer. Plae wafer in white wafer arrier and submerge arrier into BOE for 15 minutes Rinse for 1minute in eah rinse tank. Remove from hood and plae in spin rinse dryer to wash thoroughly PHOTORESIST FABRICATION FOR PLATINUM LIFT-OFF 1) Turn on mask aligner and set hot plate to 110 o C. 2) Clean wafer using 5-step proess (Aetone, IPA, DI, Aetone, IPA, dry) 3) Dehydrate wafer for 1minute at 110 o C. 4) Spin wafer with HMDS for 30seonds at 1500rpm. 5) Spin wafer with AZ5214 photoresist for 30 seonds at 1500 rpm. 6) Bake for 1minute at 110 o C. 7) Expose for 15seonds using orret negative field mask. 8) Develop using 400K-photoresist developer (mixed at a 1:4 ratio with water) with onstant agitation about 1minute and rinse with DI. 9) Sputter wafer with 175nm platinum. 10) Soak wafer in aetone for 30 or more minutes to remove sarifiial photoresist and 47

67 unwanted platinum with NO agitation. 11) Blast wafer with aetone until small hunks of platinum an no longer be seen. 12) Clean and dry wafer and inspet under mirosope. 13) If still a lot of unwanted platinum left on the wafer, soak or blast longer until it is gone. 14) Clean wafer when lift-off omplete. 15) Anneal wafer in the vertial furnae at 650 o C SU FABRICTION FOR 10µm HIGH MICRO-CHANNELS 1) Clean wafer with 5-step proess. (Aetone, IPA, DI, Aetone, IPA, dry) 2) Plae on hotplate at 200 o C for 5minutes to dehydrate wafer. 3) Spin on Omnioat at 3000rpm for 30seonds. 4) Bake Omnioat layer 1minute at 200 o C and let ool to room temperature. 5) Spin oats the wafer with SU at 2000rpm for 30seonds for a 10µm thikness. 6) Soft bake the wafer at 65 o C for 1minute and immediately following 95 o C for 2minutes (on other hot plate). 7) Expose wafer using predetermined time for substrate and desired pattern (15 seonds for platinum patterns) 8) Post exposure bake for 2minutes at 65 o C and 2minutes at 95 o C, then again at 65 o C for 1minute. 9) Let wafer ool on workbenh for 5minutes after baking to help prevent raking. 10) Develop wafer using a full immersion in SU8 Developer for 3minutes with onstant strong agitation. 48

68 11) Rinse with IPA, DI, and dry. * SU8 Removal: Plae wafer in Remover PG solvent at 80 o C about 30minutes or more to remove SU8 if needed SU FABRICTION FOR 40µm HIGH MICRO-CHANNELS 1) Clean wafer with 5-step proess. (Aetone, IPA, DI, Aetone, IPA, dry) 2) Plae on hotplate at 200 o C for 5minutes to dehydrate wafer. 3) Spin on Omnioat at 3000rpm for 30seonds. 4) Bake Omnioat layer 1minute at 200 o C and let ool to room temperature. 5) Spin oats the wafer with SU at 500rpm for 7seonds with aeleration of 100rpm/s. Chek to see if any bubbles have ourred. If so, pop with razor blade. 6) Spin wafer for another 30seonds at 2000rpm with an aeleration of 300rpm/s for a 40µm thikness. 7) Soft bake the wafer at 65 o C for 2minute and 30seonds on hot plate. 8) Bake for one hour at 95 o C in onvetion oven. 9) Expose wafer using predetermined time for substrate and desired pattern (55seonds for 35µm hannels and 65seonds for the rest of the wafer) 10) Post exposure bake for 1minutes at 65 o C and 4minutes at 95 o C on the seond hot plate. 11) Let wafer ool on workbenh for 10minutes after baking to help prevent raking. 12) Develop wafer using a full immersion in SU8 Developer for 5minutes and 15seonds with onstant strong agitation. 13) Rinse with IPA, DI, and dry. 49

69 CHAPTER 3 EXPERIMENTAL METHOD 3.1 EXPERIMENT OVERVIEW Figure 3.1 Shemati of the energy balane in the aryli arrier The goal of the experiments desribed in this dissertation is to determine the effiieny of eah miro-hannel evaporator through an energy balane. The shemati of the energy balane in the aryli arrier is shown in Figure 3.1. The energy balane inludes heat ondution from the miro-hannel and eletrial energy dissipated as heat in the enter of the membrane aross a miro-hannel evaporator membrane, evaporation. Three different sets of experiments are performed in this work. The first set of experiments disussed is steady state evaporation experiments in whih eletrial power is ontinuously dissipated as heat in the miro-hannel evaporator. The seond set of experiments is the transient evaporation experiments in whih eletrial power dissipated as heat in the membrane is yles on and off to result in transient operation. Calibration 50

70 of the temperature measurement devies, RTDs was required for both of these sets of experiment. Finally, the last set of experiments is the visualization of the liquid vapor interfae in the apillary hannels. The visualization test provides a view of the plaement of liquid vapor interfae, as well as the ontat angle of liquid wall interfae. The details of the experiment setup inluding equipment and experimental proedures are explained in next several setions. 3.2 HEATER/RTDs DESIGN, EVAPORATOR ASSEMBLY, RTD TESTING BOX This experimental study was onduted using radial miro-hannel evaporators fabriated on test die miro-mahined from three-inh wafers (Si and SiNx). Eah test die onsisted of a irular platinum resistane heater, onentri annular platinum resistane thermometers (RTDs), and radial miro-hannels. The test die is mounted in two 3 x3 aryli arrier with an outer reservoir of working fluid ontained between two O-rings. The working fluid is hoose for its latent heat of vaporization value of J/g and value is determined at 25 o C with ambient pressure. The probes are bonded into the arrier for eletrial ontat to the heater and RTD s. The two O-rings ontrol the working fluid flowing from the outer reservoir. Capillary fores pumped fluid from the outer reservoir under the inner O-ring and into the miro-hannels overing the membrane. A shemati of the miro-hannel evaporator die mounted in the aryli arrier is shown in Figure 3.1. The die and aryli arrier are plaed on a sale with a preision of ±0.5mg. The major terms of interest in the experiments are the: (1) eletrial power dissipated as heat in the entral resistane heater, (2) sensible heat onduted radially outward through the membrane, and (3) latent heat arried away from 51

71 the membrane by the evaporation of the working fluid. To aomplish the experiments performed in this work, the design of the onentri heater and RTDs need to be explained, and the evaporator needs to be assembled with the miro-hannel evaporator arrier. The RTD box is used to onvert the RTD resistane to the orresponding voltage. The design details of the heater and the RTDs as well as the assembly details are explained in the setion and setion respetively. The details of the RTD testing box are explained in the setion HEATER/RTD DESIGN Heat is added the enter of the miro-hannel evaporator through the use of the resistane heater. The onentri heater used in the experiment to adding heat to the miro-hannel evaporator onsisted of a platinum resistane heater. The platinum resistane heater is onneted to the two inner eletrodes for the onnetion of a power soure as shown in Figure 3.1. The resistane of the platinum onentri heater is approximately 500Ω. The high resistane ensures that the heat is dissipated on the membrane and not in the resistane heater leads. The resistane is determined by its material resistivity, length, and ross-setional area. The heater is made of 50µm wide lines with 50µm wide gaps in between and using an outside radius of 0.8mm. Heat transfer by ondution is determined the average temperature at two radial temperatures on the evaporator. These radial temperatures on the membrane are measured via two RTDs as shown in Figure 3.2. The overall heat ondution is alulated by assuming the radially symmetri heat ondution. The RTDs measure temperature with a hange in resistane. The RTDs typial resistanes are between 500Ω and 1000 Ω. 52

72 3.2 Shemati of resistane heater and dual RTD Figure 3.3 Shemati of resistane heater and triple RTD The RTDs are onneted to large eletrodes to ensure that the leads do not affet the RTDs temperature measurements, thus the error an be minimized. The two onentri radial dual RTDs are designed with an inner radius of 1.7mm and outer radius of 2.4mm. The ring features of the RTDs are designed as 50µm wide lines with 50µm wide gaps. The third RTD is plaed at the edge of the defined membrane square (off of the membrane) and is 5mm by 5mm. The third RTD is intended to measure the temperature boundary ondition at the edge of the evaporator membrane boundary as shown in Figure 3.3. The temperature measurement from this third RTD is then used to fix the temperature boundary ondition in the numerial alulations. 53

73 3.2.2 EVAPORATOR ASSEMBLY The Si die on whih the miro-hannel evaporator membrane and wiking strutures are fabriated is mounted in a die arrier for the experiments. First, the die is heked to ensure that it is operational for the experiments. To do this, the resistane of eah of the platinum resistane thermometers and the platinum resistane heater on the membrane are first measured to determine the resistane values of the RTDs and heater do not exeed aeptable limits. Seond, the die is heked to verify that a full array of wiks overs the membrane. After onfirming that the membrane is operational, the miro-hannel evaporator is mounted in the miro-hannel evaporator arrier. The arrier is designed to hold the miro-hannel evaporator in the working fluid, and seal the working fluid while providing eletrial aess to the heater and RTDs. PMMA aryli is the material used for the miro-hannel evaporator arrier in this work. The important features of the aryli arrier are shown in Figure 3.4. The arrier assembly onsists of upper and lower aryli miro-hannel evaporator arrier plates whih are squares of the size of 10m by 10m by 1/4 thik. The arriers ontain drilled though-holes to provide eletrial aess to the heater and the RTDs for data olletion. A entral hole loated above the membranes provides optial aess for miro-hannel visualization. Eah arrier plate also ontains through holes for alignment purposes. Mahine srews at the orners provide the lamping fore to seal the evaporator die in the working fluid. The miro-hannel evaporator is first plaed on semiondutor tape on the lower aryli die arrier. A small O-ring is plaed on top of membrane. 54

74 Figure 3.4 Desriptions of upper and lower aryli die arrier omponents A larger O-ring is plaed on the lower arrier omponents to ontain the liquid reservoir as shown in Figure 3.4. The upper arrier omponent is now positioned in plae, ensuring that the probes line up with the orresponding eletrodes. One the arriers are aligned, the four srews are tightened to omplete the assembly. The srews are tightened to prevent a working fluid leakage and also provide good eletrial onnetions between probes and eletrodes. However, if the srews are too tight, the lamping fore between arrier omponents an break the miro-hannel evaporator membrane. The eletrode wires are heked to verify eletrial onnetion after assembling all the omponents. If the resistane reading is stable and shows the initial resistane of the heater and RTDs, the miro-hannel evaporator membrane and arrier assembly is omplete. If the resistane reading is not stable or poor, the assembly is realigned. Figure 3.5 shows a ompleted assembly of the miro-hannel evaporator membrane and the aryli arrier. 55

75 Figure 3.5 Completed assembly of miro-hannel evaporator and the aryli arrier Figure 3.6 Shematis of RTD testing box, multimeters, and RTDs 56

76 3.2.3 RTD TESTING BOX The RTD testing box onsists of Wheatstone bridge iruit. The Wheatstone bridge iruit onsists of four resistors, an input for a voltage signal from the RTDs, an output to the voltage gage, two potentiometers used to zero the iruit, an outside DC power input, an amplifiation hip and four nine volt batteries to power the amplifiation hip. The four resistors onsist of two known resistors, one variable resistor, and one unknown resistor from RTD. The Wheatstone bridge iruit is balaned using the variable resistor and a multimeter to measure the voltage aross the iruit. The multimeter reads zero when the iruit is balaned. If the resistane hanges from any of the four resistors, a voltage hange is displayed on the multimeter. The multimeter thus beomes an indiator of the balane of the iruit. The amplifiation hip amplifies the RTD signals. This is neessary beause the signals from the RTDs are often smaller than the level of the noise in the system. Four nine volt batteries are used to power the amplifiation hip, and an AC power adapter with 1.5V output and 700mA is used to power the RTD box. Figure 3.6 shows a shemati of the Wheatstone bridge iruit onneted to the RTDs and two multimeters. 3.3 RTD CALIBRATION Before any experiments are run the RTD s on the miro-hannel evaporators are alibrated. A series of alibration results are present in Appendix B. The RTD alibration experiment setup onsists of the miro-hannel evaporator arrier assembly, two RTD testing boxes, a deionized water bath, a hot plate, a stir bar, an aryli ring, a thermometer, and three multimeters. Figure 3.7 shows a photograph of the setup. 57

77 Figure 3.7 Piture of alibration experiment set up First, the aryli ring and stir bar are plaed into the water bath. To maintain onstant stirring without disruption of the miro-hannel evaporator arrier, the magneti stir bar is kept in the enter of the aryli ring. Seond, with all onnetions heked, the mirohannel evaporator arrier is immersed into the water bath and entered on the aryli ring. Sine the membrane is 2.2µm thik and very fragile, dropping the miro-hannel evaporator arrier an be ause the membrane to break. Next, the water bath is plaed onto the hotplate, and the four RTD wires are onneted to the RTD box. The RTD box outputs are onneted to multimeters. The heater eletrode wires are diretly onneted to a third multimeter. The third multimeter measures the voltage hange aross the heater during the alibration. A thermometer is plaed into the water bath to measure the water temperature during the alibration. 58

78 Figure 3.8 Dual RTD alibration urve Figure 3.9 Triple RTD alibration urve 59

79 With the setup omplete, the initial water temperature and voltage values are reorded. The hotplate and stir bar are then turned on. Slow stirring and slow heating is desired to derease the eletrial noise in the measurements and to avoid physial disturbane of the die arrier. Doing so dereases the variane in the alibration and the unertainties in the RTD measurements. The temperature of the water bath and multimeter display values are heked regularly. Measurements are reorded at every degree of temperature inrease, over a range from 20 o C to 45 o C. The results are plotted as an RTD alibration urve of water bath temperature versus the voltage from the Wheatstone bridge iruit. The measurements are voltage measurements. The least squares linear measurements versus voltage measurements fit is used to orrelate the temperature. The desired R 2 value is at least Figure 3.8 and Figure 3.9 show typial dual RTD alibration urves and typial triple RTD alibration urves respetively. 3.4 STEADY STATE EVAPORATION TESTS An experiment starts by introduing the Fluorinert FC77 working fluid at the outer irumferene of the radial hannels. Capillary fores wik the working fluid from the outer irumferene into the enter of the membrane. Eletrial power is dissipated as heat in the entral thin-film resistane heater. Sensible heat then onduts radially outward through the membrane, driving liquid working fluid to evaporate from the radial hannels. An energy balane is then experimentally determined for the miro-hannel evaporator test die. The major terms of interest in the energy balane are the: (1) eletrial power dissipated as heat in the entral resistane heater, (2) sensible heat onduted radially outward through the membrane, and (3) latent heat arried away from 60

80 the membrane by the evaporation of the working fluid. In the present set of experiments introdued in this dissertation, 30mW to 60mW of eletrial power input is dissipated in the thin-film heater at the enter of the testing membrane of the miro-hannel evaporator. The power dissipated as heat in the thin-film heater is determined by measuring the voltage drop aross the platinum resistane hater and the voltage drop aross a power resistor in series with the heater. The sensible heat onduted radially outward through the membrane is determined by using the temperatures from the two-onentri annular RTDs on eah miro-hannel evaporator. Condution heat transfer out of the membrane is assumed to be radially symmetri so the RTD measurements are used with the ylindrial ondution heat transfer equation to alulate the heat flux onduted aross the membrane. Evaporation tests are performed to aount for the balane of energy, in the miro-hannel evaporator: the eletrial energy dissipated as heat in the enter of the miro-hannel evaporator, the energy onduted as sensible heat aross the membrane, and the energy as latent heat arried away from the membrane by evaporation of working fluid. The effiieny of a miro-hannel evaporator is then determined from this energy balane. The evaporation test setup onsists of the miro-hannel evaporator, the arrier assembly, the RTD boxes, multimeters, power resistors, a power supply, Fluorinert refrigerant (FC77) working fluid, a sale, and a timer. An evaporation test begins by plaing the arrier assembly on the sale. The RTDs are attahed to the RTD box inputs. The RTD box outputs are onneted to multimeters. The multimeters are zeroed at room temperature. The resistane heater is onneted to the power supply in series with the power resistor (50W 10.3Ω). The FC77 working fluid is added to the miro-hannel arrier, to fill the liquid reservoir. 61

81 Figure 3.10 Evaporation experiment test set up The initial mass of the system is reorded. Capillary fores pump fluid from the outer reservoir, under the inner O-ring and into the miro-hannels overing the membrane. The power supply is turned on to the desired voltage setting. The measurements of the mass of system, RTD outputs, and voltage aross the heater and power resistor are reorded in five minute intervals for minutes (at least 30 minutes). Figure 3.10 shows a photograph of the evaporation experiment test setup. The temperatures taken by the two annular RTDs are used to measure temperatures at two radial positions on the membrane. Assuming radial symmetry, the ondution heat transfer radially out of the membrane, Q s is then: 62

82 Q s 2 hk ( Ti To ) = π (3.1) ln( r / r ) o i Here r o and r i are the radii of the outer and inner RTDs (2.4mm and 1.7mm), k is the thermal ondutivity of silion (k=153w/mk) or silion nitride (k=15w/mk), h is the thikness of the silion membrane (h=2µm) or silion nitride (h=300nm), and (T i -T o ) is the differene of inner and outer RTD temperatures. The voltage aross the heater and power resistor is used to alulate the power input to the system from Ohm s Law. V = IR (3.2) P= VI (3.3) In equations 3.2 and 3.3, V is voltage, I is urrent, R is resistane, P is power. The latent heat arried away by the evaporation of the working fluid is determined gravimetrially. The mass of the working fluid that has evaporated from the miro-hannel evaporator die is found from the derease in mass of the entire set-up as measured by the sale, over the ourse of an evaporation experiment. The latent heat transfer rate from the miro-hannel evaporator is taken to be: Q l = jh fg (3.4) 63

83 where j is the rate of mass transfer by evaporation of working fluid from the mirohannels, and h fg is the latent heat of evaporation of the working fluid, J/g. The average power into evaporation is added to the ondution power and balaned with the total heat input to omplete the energy balane. The shemati of the energy balane in the aryli arrier is shown in Figure 3.1. The energy balane error is taken as the differene between the input power and the outgoing power whih inludes the heat transfer rate by ondution and the heat transfer rate by evaporation, divided by the total power input. Pin Pond Pevap % Error = 100 (3.5) Pin In equation 3.5, P in is the total power input, P ond is the sensible heat transfer rate by ondution, P evap is the latent heat transfer by rate by evaporation. The miro-hannel evaporator effiieny, η wik, is defined to be the ratio of latent heat transfer rate by evaporation to the total power input: = P evap η wik (3.6) Pin 64

84 3.5 TRANSIENT EVAPORATION TESTS The transient evaporation experiments are very similar to the steady state experiments. An experiment starts by introduing the Fluorinert FC77 working fluid at the outer irumferene of the radial hannels. Capillary fores wik the working fluid from the outer irumferene into the enter of the membrane. Pulsed eletrial power is dissipated as heat in the entral thin-film resistane heater. Power or heat is pulsed to the testing membrane by applying a periodi voltage aross the resistane heater. Sensible heat then onduts radially outward through the membrane, driving liquid working fluid to evaporate from the radial hannels. An energy balane is then experimentally determined for the miro-hannel evaporator test die. The major terms of interest in the energy balane are the: (1) eletrial power dissipated as heat in the entral resistane heater, (2) sensible heat onduted radially outward through the membrane, and (3) latent heat arried away from the membrane by the evaporation of the working fluid. In the present set of experiments introdued in this dissertation, 30mW to 60mW of pulsed eletrial power input is dissipated in the thin-film heater at the enter of the testing membrane of the test die. The power dissipated as heat in the thin-film heater is determined by measuring the voltage drop aross the platinum resistane hater and the voltage drop aross a power resistor in series with the heater. The sensible heat onduted radially outward through the membrane is determined by using the temperatures from the two-onentri annular RTDs on eah miro-hannel evaporator. Condution heat transfer out of the membrane is assumed to be radially symmetri so the RTD measurements are used with the ylindrial ondution heat transfer equation to alulate the heat flux onduted aross the membrane. 65

85 (a) Shemati of transient experiment set up (b) Photograph image of transient experiment set up Figure 3.11 Shemati and photograph of transient experiment set up Shemati and photograph views of the experiment setup are as shown in Figure (a) and (b). Again, a power resistor (50W 10.3Ω) is onneted in series with the resistane heater to determine the urrent flow through the heater. A funtion generator is used to determine the shape of the wave and ontrol the frequeny and duty yle of the pulses. In the present experiments, a square wave is used. A DC power supply is used to 66

86 ontrol the amplitude. In the steady-state experiment a DC power supply is onneted diretly aross the resistane heater and power resistor (50W 10.3Ω). In the transient experiment a pulse iruit is used to regulate the urrent flow based on the signal supplied from the funtion generator. An osillosope is then used to measure the signals from the RTDs and the periodi eletrial input to the resistane heater. A shemati of the pulse iruit is shown in the Figure The pulsed signal is made possible by onneting a pulse iruit in series with the heater and power supply. The funtion generator is onnet to the TTL(+) and GND. A funtion generator is used to ontrol the pulse parameters: frequeny and duty yle. A range of frequenies and duty yles (10Hz to 40Hz of frequeny and 50% to 10% duty yle) are used to test the heat ondution response of the membrane while the evaporation rate is reorded from the sale. In the transient experiment, the time domain must be onsidered when alulating the heat ondution, Ohm s Law and latent heat transfer rate. Those results are then used to derive the energy balane. In the transient experiment the energy measurement unit is in Joules (J) beause the experiment is time dependent whereas the steady state experiment uses power measurement Watts (W). In this work, several different resonant frequenies are tested: 10Hz, 20Hz, and 50Hz. Duty yles of 50%, 30%, and 10% are used. Power input was hold onstant as frequeny and duty yle was hanged. For example, 34mW at frequeny of 10Hz with 100% duty yle an be ompared with 68mW at 10Hz frequeny with 50% duty yle. In this example the 100% duty yle with 34mW of power result in a total energy input of 3.4mJ per pulse. Likewise the total energy input for the 50% duty yle at 64mw is also 3.4mJ per pulse. 67

87 Figure 3.12 Shemati of pulse Ciruit, Courtesy S. Whalen 3.6 VISUALIZATION The position of liquid working fluid within the miro-hannel evaporations is visualized two ways. First experiment the movement of the liquid interfae for working fluid is traked in the miro-hannel evaporator at different power inputs. Seond the menisus ontat angles for the liquid working fluid in the miro-hannels is visualized. In the first visualization experiments, TSI Partile Image Veloimetry (PIV) amera is onneted to a Questar QM MKIII long distane mirosope, as shown in Figure The amera is plaed and mounted on a sled along with the optial mirosope. The miro-hannel evaporator arrier holder is assembled on another sled. A 45degree-angled mirror is mounted on the sled to visualize the membrane from beneath. A fiber opti light soure is used to illuminate the miro-hannel evaporator and liquid working fluid. The foal length of the mirosope is determined before any visualization experiments are done. A 4-point font number printout is taped to a square piee of aryli and set in the arrier holder. The printout is lit from above with the fiber opti light. 68

88 Figure 3.13 Photographi image of visualization experiment set up Figure 3.14 Visualization images from the experiment set up shown in Figure

89 The amera ollets images. The Exposure Mode Free and Capture Mode Continuous of the Insight data olletion software are used. The sled is moved until the number printout is in fous. One the amera is foused, the miro-hannel evaporator arrier is plaed on the arrier holder. The fiber opti light soure is plaed diretly above the membrane. Yellow tissue paper is used to diffuse the intensity of the light soure. The resistane heater is onneted to the power supply. The miro-hannels and reservoir are filled with the working fluid. Several images of the working fluid movement as the power to the mirohannel evaporator are varied (30mW ~ 60mW). Typial images of 40µm high and 70µm wide miro hannels are shown in Figure The menisus formed by the working fluid in the miro-hannels is visualized using a digital amera oupled to a mirosope. In partiular, the liquid menisus and liquid ontat angles are aptured. In this seond setup a digital amera is oupled to a mirosope. No power supply is onneted to the heater eletrodes. The shemati and photographi images of the seond visualization experiment setup are shown in Figure A typial image is shown in Figure The testing die is mounted on a sled that allows the testing die to stand at a 90degree angle. A Fiber Lite High Intensity Illuminator is used to light the membrane from above. This mirophotography tehnique is espeially useful to visualize the menisus ontat angles in the miro-hannels. Pitures are taken of the ontat angles and are measured those ontat angles using a protrator. The auray of measurements made in this way is verified by measuring a silion-ethed pit with a known angle. This silion-ethed angle (54.75degree) is shown in Figure The angle is measured to be o. 70

90 Figure 3.15 Shemati and photographi images of visualization experiment setup Figure 3.16 A typial menisus image and the silion ethed angle image 71

91 3.7 UNCERTAINTIES Unertainties for the priniple measurements taken during experiments are now presented. The priniple measurements inlude the power input, the heat transfer rate aross the membrane, and the evaporation rate UNCERTAINTY OF POWER INPUT The unertainty of the eletrial power dissipated as heat in the resistane heater at the enter of the miro-hannel evaporator is onsidered first. The power dissipated in the resistane heater is measured with two Multimeters, a load resistor, and an osillosope. The Fluke 189 multimeter used to measure resistane of the resistor (shown in Figure 3.11 (a)). The voltage drop aross the load resistor is measured with a multimeter during the steady state experiments. A Tektronix TDS-224 digital osillosope is used to measure the voltage drop aross the load resistor during transient state experiments. The urrent flow through the load resistor is found from Ohm s Law, V = I R (3.7) load e load where V is voltage drop of the load resistor, I is urrent of load resistor, and R is the resistane of the load resistor. The unertainty of the urrent flow through the load resistor is first determined to alulate the unertainty of the power input. 72

92 The power input is alulated with Ohm s Law, P= IV (3.8) where P is power, I is urrent, and V is voltage of heater. The method of Kline and M Clintok [69] is used to determine the unertainty of the urrent and the power input. W R = n i= 1 F xi w xi 2 (3.9) where W R is the unertainty, F is the funtion of interest, x i is the parameter that has an unertainty of W xi, and n is number of ontributing variables [70]. If the mutimeter measures the resistane of the load resistor to be 10Ω, the unertainty for this measurement is ±0.005Ω. If the voltage drop aross the load resistor is measured to be 6V with the multimeter or the osillosope, the unertainty of this voltage drop is ±0.003V. An unertainty of the urrent is alulated using the typial value of V load =6V and R load =10Ω by substituting equation 3.7 into equation V I = (0.003V ) + (0.005Ω) = A 2 (3.10) 10Ω 10Ω W d

93 A typial value for urrent, I e = 0.6A, is found by using equation 3.8 and again with V load =6V and R load =10Ω. The unertainty of instantaneous power is alulated using typial values of V heater =4V and I e = 0.6A by substituting equation 3.8 into equation 3.9. W d 2 2 ((0.6 A)(0.003V )) + ((4V )(0.0004A)) = 0. W I = 002 (3.11) The ±2mW unertainty on P (P= I e V heater =2.4W) orresponds to 0.10% of the measurement. The error does not hange appreiably during over the range of power inputs applied during the experiments UNCERTAINTY OF HEAT TRANSFER RATE ACROSS MEMBRANE Heat transfer by ondution radially out of the membrane is determine by applied Fourier s Law in ylindrial oordination and using the two radial temperature measurements supplied by the two onentri RTDs. The unertainty in this heat transfer measurement is alulated as follows. First, the unertainty of the two RTD measurements is alulated from the alibration data from the RTDs. The residual (R) temperatures between the thermometer and RTD alibrations are used. The residual temperature differene between the alibration results and the measured temperature is alulated first. R= x i x m (3.12) 74

94 The average residual (R avg ) and the sum of the squares (SS) are also found in equation 3.13 and R ( = ( x x )) n (3.13) avg i m / 2 SS = ( x i xm ) (3.14) The standard deviation (σ) is determined by using the number of alibration measurements taken (n). SS σ = (3.15) ( n 1) Table 3.1. Typial values of the RTD alibration data For example, R avg and σ are 0.6 o C and 0.8 o C respetively are the values found from Table 3.1 for RTD 2 when alibration relationship is temperature T=4.1442x To find the measurement error (error at ), a t-value (1.96) for small sample sizes and a 95% onfidene interval are used. The upper and lower onfidene intervals are found by the equation

95 error at σ = Ravg ± t (3.16) n where x i is temperature alulation, x m is measured temperature, and n is the number of measurements. The upper and lower bound for eah RTD is used to alulate for the maximum error possible in the power alulation aross the membrane. The unertainties of the indiviual temperature measurements are added together when alulating the temperature differential aross the membrane. The maximum aeptable unertainty for these measurements is taken as ±0.5 o C. The RTD masks are printed on the transpareny mask at Washington State University, and the printing dimensions are limited to 20µm. Less than 1% error ours in this proess, so this is not onsidered as a ontributor to overall unertainty UNCERTAINTY OF EVAPORATION RATE The evaporation rate from the miro-hannel evaporator is determined gravimetrially. The unertainty in this measure of evaporation rate is determined. An Aulab sale is used to measure the mass of the miro-hannel evaporator arrier assembly and working fluid. As eletrial power is dissipated as heat in the resistane heater at the enter of the miro-hannel evaporator, working fluid evaporates and the mass of arrier assembly dereases. A typial mass evaporation versus time is shown in Figure

96 Figure 3.17 A typial evaporation test graph: mass hange over time The unertainty in the measured evaporation rate is alulated using a linear regression tehnique. First the mass data and time date are used to find the line fit y = mx + b. The sums (S xy, S yy, S xx ) are alulated to find the slope (m). S = x x ) ( y y ) (3.17) xy = y ( avg avg 2 S yy ( yavg ) (3.18) = x 2 S xx ( xavg ) (3.19) where x is time data, y is mass evaporation data, and avg is the average value of data. xy = (3.20) Slope m= S S xx The interept (b) is found. 77

97 Interept= b= y m x ) (3.21) avg ( avg The results for slope and interept for typial the ase shown in Figure 3.18 are and The unertainty of the slope is alulated using equation S yy ( m S xx ) S = (3.22) r ( N 2) where S r is the unertainty of the slope, and N is number of data taken. The unertainty of the evaporation rate is S r = ±0.07mg/min for a typial ase shown in Figure The drift of the sale over time is determined. By plaing a alibration weight, of 57.8 mg, on the sale. The mass is measured every 15 minutes for two hours. The drift is then the slope of the least squares line fit through the mass versus time plot. The drift of the sale found in this way is ±0.16mg/min. This drift rate is seen to be the dominant error in measurements of evaporation rate. 78

98 CHAPTER 4 NUMERICAL METHOD 4.1 NUMERICAL MODEL OVERVIEW A FORTRAN based numerial model is developed and used to simulate heat and mass transfer from a miro-hannel evaporator. The model is developed as a design tool for the development of effiient miro-hannel evaporators. The model in this work predits the energy balane with in an evaporator. The energy balane is inludes the ondution heat transfer aross the membrane and latent heat transfer due to the evaporation of working fluid. In addition the model predits working fluid flow rate and working fluid thikness inside the miro-hannels. The numerial model alulates ondution heat transfer using axisymmetri finite differene time domain (FDTD) integration. Mass transfer due to evaporation from the miro-hannels is alulated using onservation of energy at the liquid-vapor interfae. Fluid flow through the miro-hannel is alulated using fore balane in the hannel and Yong-Laplae equation. The geometry, disretization, derivation of governing equations and alulations, and boundary onditions are disussed below: 4.2 GEOMETRY A 2.2μm silion thikness, 80nm silion oxide thikness, and 40μm wiking struture thikness are used for the retangular miro-hannel simulation ases. 79

99 Figure 4.1 Top view of arbitrary temperature ontour plot for a retangular membrane, Courtesy Sott Whalen Figure 4.2 General shemati of 3-D axisymmetri geometry 80

100 Channel width varied for 35μm, 50μm, and 70μm. The varied liquid thiknesses (14μm, 20μm, 28μm, and 35μm) are tested to find liquid thikness of the experiments. For the tapered miro-hannel ases, a 2.2μm silion thikness, 80nm silion oxide thikness, and 40μm wiking struture thikness are used. The 40μm liquid thikness is initially used while outer edge starts at 80μm and narrows to 5μm wide. Then liquid thikness is alulated in the tapered miro-hannel ases. The platinum thin film onentri heater and RTDs are not inluded in the numerial model in order to derease omputational time. A 3-D axisymmetri geometry is assumed instead of modeling the whole evaporator geometry to derease the omputation time. The 3-D axisymmetri geometry assumption is built based on the previous 2-D numerial work [9]. This 2-D numerial work is developed and verified. Figure 4.1 illustrates a temperature ontour plot for a 3mm retangular membrane where onentri irles indiate lines of arbitrary onstant temperature [9]. The heat transfer behaves radially for square membranes exept near the far orners as shown in Figure 4.1. The ontrol volume of interest is shaped as a wedge beause the heat transfer behaves radially. Figure 4.2 shows the 3-D axisymmetri geometry with the membrane, working fluid, and wiking struture is indiated. An effetive radius for 3-D axisymmetri model is alulated sine the model approximates a square membrane, with a irular membrane. The effetive radius r o is taken to be the radius of a irle that has an equivalent area to the surfae area for a square membrane. The effetive radius r o is determined as follow Equations 4.1 and

101 A 2 2 =π ro = As = L (4.1) 2 L r o = (4.2) π where A is the irular area, A s is the surfae area for a square membrane, L is the edge length for square membrane, and r o is the effetive radius. A typial square membrane used in this work is L=5mm. The effetive radius r o =2.84mm. 4.3 DISCRETIZATION The 3-D axisymmetri geometry is disretized into a grid of elements. Eah element is wedge shaped. A non-uniform grid is used. A oarse mesh in the vertial (z) diretion and a fine mesh in the horizontal (r) diretion are used. This is due to the high aspet ratio of the evaporator, an aspet ratio approximately 1:100. The meshed model is shown in Figure 4.3. The non-uniform grid is required to save the integration time while keeping the aurate alulation results. A grid independent study is prepared to determine the optimal number of elements needed for an aurate alulation for this numerial integration. A grid independene study is ompleted by inreasing the number of elements in all three diretions until the solutions onverge. Typial solutions for temperature at RTD loations are shown for several ombinations of the number of elements in Figure 4.4 (a) and (b). 82

102 Figure 4.3 Typial shemati of disretization for 3-D axisymmetri model (a) Grid independent study of inside RTD temperature plot 83

103 (b) Grid independent study of outside RTD temperature plot () Grid independent study of ondution heat transfer aross the membrane 84

104 (d) Grid independent study of evaporation rate Figure 4.4 Grid independent studies of different ombinations of number of elements A typial solutions for ondution heat transfer rates and evaporation rate obtained for the several ombinations of number of elements are shown in Figure 4.4 () and (d). The omputational results for the grid independent study shows that the numerial alulation beomes grid independent at 21 x 21 x 7 elements in r, z, and θ diretions respetively. Numerial alulation with 21 x 21x 7 elements produed results that are almost idential to the results produed by 18 x 21 x9 elements. The differene between the results produed with 21 x 21 x 7 elements and 18 x21 x9 elements is only 0.06%. 85

105 4.4 EQUATION DERIVATION FOR HEAT TRANSFER The impliit finite differene time domain (FDTD) method is used to alulate heat transfer by ondution and the temperature at eah node. The impliit finite differene time domain method is formulated by starting from the governing partial differential equation of the heat diffusion equation. The heat diffusion equation is applied at eah node with finite differenes employed to approximate differentials. A matrix is established from the resulting set of nodal equation. The following setions show details of how the derivation of the impliit finite time differene time domain equations is arried in the 3-D axisymmetri ontrol volumes. Finite differene equations to solve for ondution heat transfer and the temperature field in the miro-hannel evaporator are find by applying energy onservation to the finite element. First, an energy balane equation is imposed on eah element and then parallel resistane network is defined. Finally, a nodal temperature is solved from energy balane and parallel resistane ENERGY BALANCE AND PARALLEL RESISTANCE NETWORK The heat diffusion equation is applied to the element 2 1 dt T = (4.3) α dt where T is temperature, α is thermal diffusivity, and t is time. 86

106 Figure 4.5 An energy balane for a 3-D axisymmetri element An energy balane for one element is shown in Figure 4.5. A network of parallel resistanes is used to approximate ondution heat transfer aross the north, south, east, west, front and bak faes of element. The energy balane for eah element is E E = E (4.4) in out stored where E + in = qw, r + qs, z q f,θ (4.4a) E out qe, r + qn, z + qb, θ = (4.4b) E = q = q + q + q ) ( q + q + q ) (4.4) stored st ( w, r s, z f, θ e, r n, z b, θ 87

107 88 Here the q terms are the heat transfer out of eah fae of the element as illustrated in Figure 4.5, and q st is the stored energy. Heat ondution is found using Fourier s Law: dx dt q ka = (4.5) where k is thermal ondutivity, A is aross setional area, T is temperature Defining the thermal resistanes z r r k r R k j i r w = θ ) 2 (,,, (4.6a) r r k z R k j i z s = θ ) (,,, (4.6b) z r k r R k j i f = θ θ ) (,,, (4.6) z r r k r R k j i r e + = θ ) 2 (,,, (4.6d) r r k z R k j i z n = θ ) (,,, (4.6e) z r k r R k j i b = θ θ ) (,,, (4.6f) Then Equation 4.5 is beome Equation 4.5 (a-f) for eah fae of element ) ( 1, 1,,,,, p k j i p k j i r w r w T T R q = (4.5a) ) ( 1 1,,,,,, p k j i p k j i z s z s T T R q = (4.5b) ) ( 1 1,,,,,, p k j i p k j i f f T T R q = θ θ (4.5) ) ( 1,,, 1,,, p k j i p k j i r e r e T T R q = + (4.5d) ) ( 1,, 1,,,, p k j i p k j i z n z n T T R q = + (4.5e) ) ( 1,, 1,,,, p k j i p k j i r w b T T R q = + θ (4.5f)

108 Equations 4.5 (a~f) are substitute into Equation 4.4. Energy stored is alulated from Equation 4.4. Again approximating differentials with finite differenes gives: q st = p p Ti j k T + 1 (,, i, j, k ) ρ C p ( ri, j, k ) θ r z (4.7) t Here subsripts i, j, k are grid point for r, θ, z diretion, R refers an equivalent thermal resistane, ρ is density, C p is heat apaity, Δr, Δθ, Δz are the spatial step size in the eah diretion as shown in Figure 4.5, Δt is the temporal step, and p+1 is the time step being solved for. The previews derivation omposed of a single element. Setion only represents the energy balane and parallel resistane network for an element. However, the different onditions of elements are presented in the numerial model (Appendix D) and these onditions are the nodes at orners (elements loated at orner of ontrol volume), faes with no material interfae (elements loated at fae of ontrol volume with no interfae), faes with material interfae (elements loated at fae of ontrol volume with interfae), interiors with no material interfae (elements loated at inside of ontrol volume with no interfae), and interiors with material interfae (elements loated at inside of ontrol volume with interfae). Governing equations are different for eah type of elements but the solving proedure is idential to setion and following setion

109 4.4.2 NODAL TEMPERATURE EQUATION The temperature at eah node solved for eah time step using the energy balane and parallel resistane network just derived. Again, ase for elements omposed of a single element is presented in this setion. First, equations 4.6 are substituted into the orresponding equation of equations 4.5 to omplete the ondution heat transfer equation at eah fae. The omplete equations of equations 4.5 and equation 4.7 are substituted into the Equation 4.4 to omplete the energy balane equation and to solve temperatures at the next time step, T p+ 1 i, j, k. To simplify the energy balane equation, following terms are defined: A = ρ C r ) θ r z p ( i, j, k t (4.8a) B = k ( ri, j, k r ) θ z 2 r (4.8.b) C = k ( ri, j, k r + ) θ z 2 r (4.8.) D = k ( ri, j, k ) θ r z (4.8.d) E = k ( ri, j, k ) θ r z (4.8.e) k r z F = (4.8.f) ) θ ( r i, j, k k r z G = (4.8.g) ) θ ( r i, j, k the nodal temperature equation simplifies to: 1 A p ( A+ B+ C + D + E + F + G) T p T i, j, k = [ i, j, k p p p p p p BT i 1, j, k CTi+ 1, j, k DTi, j, k 1 ETi, j, k+ 1 FTi, j 1, k GTi, j+ 1, k ] (4.9) 90

110 (a) Shemati of 2-D & 3-D (b) Temperature omparison Figure 4.6 Shemati of orresponding points for 2-D and 3-D: temperature plot 91

111 The nodal temperature equations for elements omposed of more than one material are different for eah type of elements. These equations are given in appendix B. The 3-D numerial alulation results are ompared with the 2-D numerial model previously work developed at Washington State University [9]. Results for a single uniform silion material and oarse mesh are alulated using in both of the models and are shown in Figure 4.6 (a) and (b). The 2-D model uses a mesh size of 5 x 3 and the 3-D model uses a mesh size of 5 x 3 x 3 to ompare. Thus there are 13 nodes for the 2-D model and 28 nodes for the 3-D model as shown in Figure 4.6 (a) and (b). The omparison shows idential results for both models for the silion material. 4.5 MASS TRANSFER A mass transfer model is used aount for heat transfer from the liquid-vapor interfaes due to evaporation. The mass transfer model is based on assumption that mass transfer ours at the liquid-vapor interfae, and that phase hange at the periphery of the silion membrane is negligible. Sine this area is relatively small ompared to the total surfae area of the liquid on the membrane it is assumed to have effet on mass transfer rates. A detailed flow analysis using the fore balane in the hannel and Yong-Laplae equation [72] are presented in setion 4.6. The net vapor flux or mass transfer rate assoiated with evaporation from the liquid-vapor interfae is determined from kineti theory [71]: To alulate the evaporation rate j, onservation of energy is used at the liquid-vapor interfae. The amount of heat transferred through the liquid layer is equal to the heat arried away from the liquid layer by phase hange. The energy balane at the interfae beomes: 92

112 Figure 4.7 Mass flux balane at liquid-vapor interfae, Courtesy Sott Whalen q q = 0 (4.10) v l The latent heat of vaporization arried away by evaporation is: q v = jah fg (4.11) The sensible heat ondution through the liquid layer is: q l k l A = ( Tsl Tl ) (4.12) L Figure 4.7 shows the net mass flux j at the liquid-vapor interfae. The net mass flux is the differene between the inlet vapor flux, j +, from ondensation and the outlet vapor flux, j-, from the evaporation. j = M 2πR p v T v p l T l (4.13) where j is the mass flux, M was the moleular weight of the working fluid (0.416 kg/mol for FC77), R is universal gas onstant (8.314 J/kmol K), h fg is the latent heat of vaporization, P and T are the vapor pressure and temperature subsripts v and l referring to the vapor and liquid surfae of a homogenous material. 93

113 Figure 4.8 Saturation urve for Fluorinert FC77 Equations 4.10 to 4.13 are ombined to form heat balane equation: M 2πR p v T v p l T l h fg + k l L ( T sl T l ) = 0 (4.14) The only unknown in the equation 4.14 is the vapor temperature T v. The value of T v whih satisfies Equation 4.14 is determined by iteration. Hene the seant method is used with a onvergene riterion of o C. Details of the seant method are presented in the appendix D with the omplete FORTRAN CODE. 94

114 4.6 MENISCUS APPLICATION Figure 4.9 Disretization of menisus in the miro-hannel for FDTD model The menisus is formed in the miro-hannel as shown in Figure 4.9. The menisus is a urve in the surfae of a liquid and is produed in response to the surfae of the hannel. The menisus is formed as a irular shape in general and an be desribed mathematially as shown in Appendix A. To have more aurate numerial alulation results, the numerial model should onsider the menisus shape. Figure 4.9 shows that the how the menisus shape is aounted in the numerial model. The oarse mesh is used in the alulation to save omputational time. The liquid thikness at enter of hannel, H, is found: H w = D tanθ (4.15) 2 where H is working fluid thikness from enter of hannel, D is height of wik strutures, w is width of hannel, and θ is ontat angle found from visualization test. 95

115 The liquid apillary pressure in the hannel is found: P 2γ osθ = (4.16) w where P is apillary pressure, γ is surfae tension (8x10-3 N/m), θ is ontat angle (41 o ), and w is miro-hannel width. 4.7 FLOW ANALYSYS To determine the liquid thikness, the fore balane equation is derived for the veloity of a liquid flowing in an open miro-hannel. Consider the flow through the miro-hannel shown in Figure In Figure 4.10, the fore balane for steady state from in the x-diretion is F x = Pdydz Pdydz dpdydz 2τ dxdz τdxdy = 0 (4.17) where P is pressure, x is the distane along with the hannel, y is distane of width of hannel, z is the distane of height of the wall. Simplifying: dpdydz 2 τ dxdz τdxdy = 0 (4.18) 96

116 Figure 4.10 Shemati of Three dimensional flows Divide both sides by dxdydz dp dτ dτ = 2 + (4.19) dx dy dz Apply the definition of shear fore: du τ = µ dy, then equation 4.19 beome: 1 dp µ dx = 2 d u 2 2 dy + 2 d u 2 dz (4.20) The boundary onditions are the no slip ondition applied at the walls and the assumptions of zero shear stress at the liquid-vapor interfae: 3D B.C: (a) u=0 where y=-w () u=0 where z=0 (b) u=0 where y=+w (d) du/dz=0 where z=h 97

117 We make the reasonable assumption that the liquid veloity found in the 3D model is lower than the liquid veloity in the 2D model. This assumption an be made more reasonable by remembering that the 2D model is represented as two parallel plates with shear fores on both of the sidewalls, and no shear fore on the bottom or top. The veloity of 2D flow is found in Appendix A (u= 1 dp 2 ( y w 2 ) ), the veloity of 4 µ dx 3D flow an then be found by subtrating an arbitrary veloity from the veloity of the 2D flow. This arbitrary veloity is a funtion of y and z. Therefore, the veloity of a 3D flow an be written as: u ( y, z) = u(2d veloity ) + u ( y, z) (4.21) Equation 4.21 an be rewritten using the veloity of the 2-D flow (u= 1 dp 2 ( y w 2 ) ) 4 µ dx 1 dp 2 2 u ( y, z) = ( y w ) + u ( y, z) 4µ dx (4.22) The first and seond derivatives of u with respet to y are: du ( y, z ) 1 dp du ( y, z ) = y + dy 2 dx dy 2 2 d u y z ) 1 dp d = + 2µ dx 2 2 µ (4.23) ( dy, u ( y, z) dy The first and seond derivatives with respet to z are: 98

118 du du ( y, z) dz dz 2 2 = d u d u ( y 2 2 dz, z) = (4.24) dz Substituting the seond derivatives in Equation 4.23 and Equation 4.24 in to equation 4.20 gives: 1 µ dx 2 2 dp 1 dp d u ( y, z) d u = 2 + 2µ dx dy 2 + ( y, z) 2 dz (4.25) Thus 4.25 beome: d u ( y, z) d + 2 dy u ( y, z) dz = 0 (4.26) 3-D boundary onditions (no slip ondition applied at the walls, the assumptions of zero shear stress at the liquid-vapor interfae) are applied to Equation 4.22 to find new boundary onditions for the arbitrary veloity, ( y, z) are: u. The new boundary onditions New 3D B.C: (a) u ( y, z) = 0, where y=-w (b) u ( y, z) = 0, where y=+w du ( y, z) 1 dp 2 2 () = 0, where z=h (d) u ( y, z) = ( y w ), where z=0 dz 4µ dx The variable u ( y, z) an be founded using separation of variables. u ( y, z) = F ( y) G( z) (4.27) 99

119 Substituting Equation 4.26 to the Equation 4.27 gives d dy 2 d F ( y) G( z) + F ( y) G( z) = 0 dz (4.28) Separating variables gives: F 2 ( y) 2 d F ( y) 2 dy = G 1 ( z) 2 d G( z) 2 dz 2 = λ (4.29) From Equation 4.29, first solution for y is 2 2 d F ( y) λ + F ( y) = 0 2 dy 2 (4.30) and the new 3D boundary onditions (a) u ( y, z) = 0, where y=-w and (b) u ( y, z) = 0, where y=+w imply F ( ±w) = 0 (4.31) 2 nπ 2 Equation 4.29 gives eigenvalue λ = ( ) and orresponding nonzero solutions 2w nπ F ( y) = sin( y) n = 1,2, (4.32) 2w 2 nπ 2 The ODE for G(z) with eigenvalue λ = ( ) then beomes 2w 100

120 2 d G dz ( 2 2 y) λ G( z) = 0 (4.33) The general solution of equation 4.33 is nπ nπ G( z) = A osh λ z+ B sinh λz = A osh( z) + B sinh( z) 2w 2w n = 1,2, (4.34) 1 dp 2 2 The new 3D boundary ondition (d) u ( y, z) = ( y w ), where z=0 4µ dx 1 dp dp 2 2 implies that G(0) = ( y w ) ; that is, G(0) = A= ( y w ). This gives 4 µ dx 4µ dx G( z) = 1 4µ dp dx ( y 2 w 2 nπz nπz ) osh( ) + B sinh( ) 2w 2w n = 1,2, (4.35) Substituting Equations 4.32 and 4.35 into 4.27 ( u ( y, z) = F ( y) G( z) ), gives u ( y, z) = F ( y) G( z) = 1 4µ dp dx ( y 2 w 2 nπz nπy nπz nπy ) osh( ) sin( ) + B sinh( ) sin( ) 2w 2w 2w 2w n = 1,2, (4.36) du ( y, z) du ( y, H ) The new 3D boundary ondition () = 0, where z=h implies that = 0, dz dz and this gives 101

121 du y, H ) = 0= dz 1 dp ( y 4µ dx ( 2 2 w nπ )( sinh 2w nπh nπ ) + B( osh 2w 2w nπh ) 2w From Equation 4.37, B is found to be n = 1,2, (4.37) 1 dp 2 nπh B= ( y w 2 ) tanh( ) n = 1,2, (4.38) 4µ dx 2w Substituting Equation 4.38 into Equation 4.36, the final form of u ( y, z) is u ( y, z) = F ( y) G( z) = 1 4µ dp dx ( y 2 w 2 nπz nπh nπz nπy )(osh( ) tanh( ) sinh( )) sin( ) 2w 2w 2w 2w n = 1,2, (4.39) Substituting Equation 4.39 into Equation 4.22 ( 1 dp 2 2 u ( y, z) = ( y w ) + u ( y, z) ), now we have the veloity of 3D flow equation as follows. 4µ dx u( y, z) = 1 4µ dp dx ( y 2 w 2 )(1 n= 1 nπz nπh nπz nπy (osh( ) tanh( ) sinh( )) sin( )) 2w 2w 2w 2w n = 1,2, (4.40) 102

122 By simplifying Equation 4.40 with trigonometri definitions ( e x = osh x+ sinh x, e x = osh x sinh x ) and identities, the final form of the axial speed of flow in the miro-hannel is u( y, z) = 1 4µ dp dx ( y 2 w 2 ) (4.41) From the axial speed of flow (Equation 4.41), mass flow rate in the miro-hannel an be alulated by multiply the area of flow moving in and density of fluid to axial speed. Then we an alulate how muh mass is added to eah element for eah time step. Again, liquid thikness an be alulated by dividing this mass with density and bottom area of element. The pressure of eah element is already determined with Yong-Laplae equation and the onstant ontat angle (41 o ), 2γ osθ p =, where γ is surfae tension w of fluid (FC77=8x10-3 N/m), θ is ontat angle (41 o ), and w is width of hannel. With this pressure dp is being alulated. 4.8 BOUNDARY CONDITIONS The pressure, temperature, and vapor volume of eah element ell are determined individually based on the net mass of vapor generated in eah ell obtained by solving the ideal gas law as explained in setion 4.5 and the boundary onditions. The boundary onditions applied to the numerial solution determined in this work are desribed below and shown in Figure Five boundary onditions are applied. Eah boundary ondition imposed is desribed in turn. (1) The west fae, whih represents the enter of the die, is insulated due to the axisymmetri geometri approximation. (2) The 103

123 south fae of onentri heater (D=1.6mm), whih represents the inner portion at the bottom of the silion membrane, is subjeted to a onstant heat flux. (3) The east fae of the silion membrane, whih represents the periphery of the silion die, onduts heat to the bulk. (4) The north fae, whih represents top of the membrane, has a onvetive boundary ondition. (5) The front and bak faes are insulated due to the axisymmetri geometry. These boundary onditions are applied to individual nodes or over an entire surfae when exeuting the numerial ode. Two simulations are run to examine the effet of onvetive boundary onditions and show a differene of only 0.5%. The free (h=100w/mk) and fored gas onvetive (h=300w/mk) oeffiients are found [73]. This h value represents the onvetive heat transfer on the north fae. A onvetive oeffiient less than 300w/mK is atually expeted sine the north fae is overed by an environment air. The average onvetive (h=250w/mk) boundary onditions an be used sine it shows only small differene and the evaporator is overed by air. The east fae boundary ondition is determined the in previous 2-D numerial work [9]. The east fae is bounded by the gasket, and this surfae is assumed to be insulated exept where the membranes join the bulk silion die. Newton s law of ooling is used to approximate heat transfer from the membrane to the bulk silion to save omputation time. The effetive onvetive oeffiient h eff = 135,000 W/m 2 K was determined by Whalen [9]. Whalen fit his 2-D numerial model to experimental data obtained for a devie assembled with air as the working fluid. Heat was applied at the indiated loation using a single ring resistane heater pulsed for 5ms and delivering 9.2mJ. The result Taken from [9] is shown in Figure

124 Figure 4.11 Thermal boundary onditions for 3-D model Figure 4.12 Fitting of model to the experiment for determining h eff, Courtesy Sott Whalen 105

125 The 3-D numerial model was run employing this effetive onvetive oeffiient, h eff. The result was good agreement with 2-D model results. However, this h eff boundary ondition was found to be valid only for evaporators with silion membranes. Numerial simulations run for evaporators with SiNx membranes gave poor results. In order the numerially simulate SiNx membranes, a new boundary ondition for the east fae was required. Sine the membrane thikness and the bulk thikness are signifiantly different, the temperature at the edge of square membrane was assumed to be uniform. For this reason a onstant surfae temperature boundary ondition was employed [54]. To verify the assumption of onstant temperature at the edge of the membrane triple RTDs, as shown in Figure 2.4, were fabriated to measure the membrane edge temperature. The 3-D numerial results with the fixed temperature boundary onditions were the ompared to measured results from the experiment. Good agreement between numerially simulated and experimentally measure results were found. A detailed omparison of the numerial results and experiment results are presented in the Chapter FLOWCHART The flow hart shown in Figure 4.13 illustrates the solution proedure for the numerial work presented in this dissertation. First, the initial onditions of material temperatures and thermodynami properties are set before omputation. The numerial model is disretized to define mesh size and grid spaing. Next the material properties and boundary onditions are defined for eah individual element. 106

126 Figure D numerial model flowhart The first time step of temperatures are alulated with the impliit finite time domain method and the nodal temperature equation as explained in setion 4.4. The evaporation mass fluxes for eah element are then alulated as explained in setion 4.5. The mass flow rate of liquid working fluid is then found for the tapered mirohannels ase. The program iterates returning to the temperature alulations using the FDTD method, with nodal temperature equation. Evaporation mass fluxes and liquid 107

127 mass flow rates are found. Iteration repeats until the speified solution time (Input time to the program) is satisfied. 108

128 CHAPTER 5 EXPERIMENTAL RESULTS 5.1 EXPERIMENTAL RESULTS OVERVIEW The results of heat and mass transfer measurements performed on miro-hannel evaporators are presented in this hapter. Steady-state evaporation and transient evaporation tests used to haraterize the performane of different miro-hannel evaporators are presented. Two geometries of miro-hannel evaporators are onsidered. Constant ross setion hannels are onsidered first. Dimensions of onstant retangular ross setion mirohannels are desribed as hannel depth x hannel width x hannel wall thikness. For example 10 x 10 x 10 refers to a miro-hannel that is 10µm deep, 10µm wide with eah hannel formed between 10µm thik walls. Tapered miro-hannels are onsidered next. Dimensions of tapered miro-hannels are 40µm deep and their width is 80µm at the outer radius of the miro-hannel. Eah miro-hannel width tapers down to 5µm at the inner radius of the miro-hannel. The walls dividing miro-hannels also are 80µm wide at their outer radius and taper down to a width of 5µm at their inner radius. Sine the wall thikness and hannel width are tapered same dimensions, dimensions of tapered mirohannels an be desribed as 40 x 5~80. Finally, evaporators with membranes fabriated of two different materials, silion and silion-nitride are tested. A series of steady state evaporation tests and transient operation tests are presented in this hapter and appendix C. The list of the test onditions is shown in Table

129 (a) Steady state onditions (b) Transient operation onditions Table 5.1 Summary of experiment tests 5.2 STEADY STATE EVAPORATION TEST RESULTS Figure 5.1 Evaporation test results of heat transfer by ondution and evaporation: 10 x 10 x 10 miro-hannel evaporator 110

130 Power into Heater Inside RTD Temp Outside RTD Temp Power aross Membrane Energy into Evap Effiieny (mw) ( o C) ( o C) (mw) (mw) (%) 10µm high µm wide µm thik miro hannels Table 5.2 Experimental energy balane: 10 x 10 x 10 miro-hannel evaporator A series of steady state evaporation tests are presented. Results from experimental measurements for onstant retangular ross setion miro-hannels with 10µm depth, 10µm width and 5µm thik hannel walls are shown in Figure 5.1 and tabulated in Table 5.2. The membrane material for the evaporator is silion. Results are given for power inputs of 27mW to 41mW. In Figure 5.1, experimental values of sensible heat transfer by radial ondution (blak solid irles) and latent heat transfer by evaporation of working fluid (white irles) are plotted against the eletrial power dissipated in the thin-film heater at the enter of the evaporator membrane. Results given in Table 5.2 show that over the power range studied, the temperature of inner and outer RTD ranged from 37 o C to 41 o C and 32 o C to 34 o C respetively with temperature unertainty of ±0.5 o C. The mass evaporation rate ranged from 28.7µg/se to 31.7µg/se with an unertainty of ±2.5µg/se. Thus the energy balane indiates that approximately 90% to 95% of the power dissipated in the resistane heater is onduted out through the silion membrane, while only 5% to 10% of the power is arried away by the latent heat of evaporation. 111

131 Figure 5.2 Evaporation test results of heat transfer by ondution and evaporation: 40 x 35 x 5 miro-hannel evaporator Table 5.3 Experimental energy balane: 40 x 35 x 5 miro-hannel evaporator 112

132 Figure 5.2 shows experimental results for a onstant retangular ross setion mirohannels with 40µm depth, 35µm width and 5µm thik hannel walls with thermal power inputs of 34, 44 and 55mW. Again, the sensible heat transfer by radial ondution is indiated by blak solid irles and the latent heat transfer by evaporation of working fluid is indiated by white irles. On Figure 5.2, the heat transfer rates and evaporation rates are plotted against total power inputs. Results of the evaporation experiments given in Table 5.3 show that over the power range studied, the inner RTD temperature ranged from 33 o C to 39 o C, while the outer RTD temperature ranged from 29 o C to 32 o C with temperature unertainty of ±0.5 o C. The evaporation rate ranged from 85µg/se to 108µg/se with unertainty of ±2.5µg/se. The experimental energy balane indiates that approximately 79% to 84% of the power dissipated in the resistane heater is onduted out through the silion membrane, while only 16% to 21% of the power is arried away by the latent heat of evaporation. Condution heat transfer rates (blak solid irles) and evaporation rates (white irles) for 40 x 50 x 5 miro-hannel evaporators are plotted in Figure 5.3. The miro-hannel evaporator membrane is silion. Both Figure 5.3 and Table 5.4 show experimental results for thermal power inputs of 35.5, 49.9, and 70.3mW. For this power range the inner RTD temperature ranged from 31 o C to 42 o C while the outer RTD temperature ranged from 27 o C to 31 o C with ±0.5 o C. The mass evaporation rates ranged from 95µg/se to 134µg/se with ±2.5 µg/se. The experimental energy balane indiates that approximately 77% to 84% of the power dissipated in the resistane heater is onduted out through the silion membrane, while only 16% to 23% of the power is arried away by the latent heat of evaporation. 113

133 Figure 5.3 Evaporation test results of heat transfer by ondution and evaporation: 40 x 50 x 5 miro-hannel evaporator Table 5.4 Experimental energy balane: 40 x 50 x 5 miro-hannel evaporator 114

134 Figure 5.4 Evaporation test results of heat transfer by ondution and evaporation: 40 x 70 x 5 miro-hannel evaporator Table 5.5 Experimental results of energy balane: 40 x 70 x 5 miro-hannel evaporator 115

135 Results from the evaporation experiments for 40 x 70 x 5 miro-hannel evaporator are given in Figure 5.4. Experimental results are given for power inputs of 32mW to 54mW. In Figure 5.4, experimental values of sensible heat transfer by ondution radially out of the membrane are marked with blak irles and latent heat transfer by evaporation of working fluid is marked with white irles. Both experimental values of heat transfer by ondution and evaporation are plotted against the eletrial power dissipated in the resistane heater at the enter of the evaporator membrane. Table 5.5 also shows the evaporation experiment results over the power range. The inner RTD temperatures ranged from 32 o C to 41 o C while the outer RTD temperatures ranged from 28 o C to 34 o C with an unertainty of ±0.5 o C. The evaporation rate ranged from 108µg/se to 137µg/se with an unertainty of ±2.5µg/se. The experimental energy balane indiates that approximately 71% to 89% of the power dissipated in the resistane heater is onduted out through the silion membrane. Only 21% to 29% of the power is arried away by the latent heat of evaporation. One major onlusion from the results in Figures 5.1 to 5.4 and Tables 5.2 to 5.5 is that evaporator effiieny dereased as power input inreased. Results from evaporation experiments for tapered miro-hannel evaporators (40µm deep with 5µm to 80µm wide miro-hannel) are given next. Figure 5.5 and Table 5.6 shows the results of heat transfer rate and evaporation rate measurements for the tapered miro-hannel evaporator. Results are given for thermal power inputs of 33.6, 43.7, 57.7mW. For this tapered miro-hannel evaporator, the inner and outer RTD temperature ranged from 33 o C to 42 o C and 29 o C to 34 o C. The evaporation rate ranged from 103µg/se to 127µg/se. 116

136 Figure 5.5 Evaporation test results of heat transfer by ondution and evaporation: Tapered 40 x 5~80 miro-hannel evaporator Table 5.6 Experimental energy balane: Tapered 40 x 5~80 miro-hannel evaporator 117

137 The experimental energy balane indiates that approximately 74% to 81% of the power is onduted out through the silion evaporator membrane while 21% to 26% of power is arried away by the latent heat of evaporation. Miro-hannel evaporator effiienies dereased as power inputs inreased for the tapered miro-hannel evaporators just as they did for the retangular miro-hannel evaporators. 5.3 SILICON NITRIDE (SiNx) EVAPORATION TEST RESULTS Tapered miro-hannels was fabriated on 300nm thik Silion Nitride membranes. Silion nitride membranes were used for two reasons. First, the thermal ondutivity of Silion Nitride is muh lower than Silion: 15W/mK vs. 148W/mK. Seond, Silion Nitride membranes an be fabriated to be muh thinner than silion membranes: 300nm vs. 2µm. The tapered miro-hannels were idential to the tapered miro-hannel fabriated on Silion membranes as before. A single steady state heat transfer experiment was onduted with this SiNx membrane miro-hannel evaporator. The results of this experiment are tabulated in Table 5.7. The Table 5.7 shows that for a power input of 13.7mW, the inner RTD temperature is 43 o C, and the outer RTD temperature is 28 o C. The evaporation rate is 140μg/se. The experimental energy balane indiates that approximately 14% of the power dissipated in the resistane heater is onduted out through the silion nitride (SiNx) membrane, while 86% of the power is arried away by the latent heat of evaporation. The effiieny of the miro-hannel based on silion nitride membrane shows a signifiant improvement over miro-hannel evaporators based on Silion membranes. However, diret omparison was diffiult sine the power input was different for the two ases. 118

138 Table 5.7 Experimental energy balane: Silion Nitride (SiNx) membrane Tapered 40 x 5~80 miro-hannel evaporator 5.4 SUMMARY OF STEADY STATE EVAPORATION TEST RESULTS. Figure 5.6 Summary of miro-hannel evaporator maximum effiienies The bar graph shown in Figure 5.6 summarizes the steady state evaporation test results. The effiienies shown on Figure 5.6 are the maximum effiienies for eah different geometry of miro-hannel evaporator. The effiieny results from Figure 5.6 shows no signifiant differene in maximum evaporator effiieny between the different mirohannel geometries. However, Figure 5.6 shows signifiant differene in maximum 119

139 evaporator effiieny between the different membrane materials (Si and SiNx). The effiienies are seen to range from 20% to 28% for power input of 34mW for mirohannel evaporator on Silion membrane. The effiieny is 85% for power input of 13.7mW for miro-hannel evaporator on Silion Nitride membrane. 5.5 TRANSIENT EVAPORATION TEST RESULTS Next we onsider the performane of the miro-hannel evaporator hanges during the transient operation. The same power inputs (34mW, 44mW, and 57mW) are used to aid in the omparison of transient results with the steady state results. Only one miro-hannel geometry, the 40μm deep, the 80μm wide to 5μm wide tapered hannels are used in the transient evaporation tests. Reall that previous results indiate that the miro-hannel geometry has little effet on the effiieny of the miro-hannel evaporators (see Figure 5.6). Figure 5.7 shows typial temperature histories for a transient evaporation test. Sine the transient ondition is applied to the testing membrane, the temperature measurements from the RTDs are in a waveform. Results from the transient evaporation experiment of 10Hz frequeny and 50% duty yles with average thermal power inputs of 34mW, 44mW, and 57mW are shown in Figure 5.8 and Table 5.8. Experimental values of sensible heat transfer by radial ondution and latent heat transfer are plotted against the average eletrial power dissipated in the resistane heater at enter of the membrane. The blak irles and white irles show the experimental values of heat transfer by ondution and evaporation respetively. 120

140 Figure 5.7 Typial temperature histories for transient evaporation test: 10Hz with 50% duty yle with average power input of 34mW Figure 5.8 Evaporation test results of heat transfer by ondution and evaporation: Tapered 40 x 5~80 miro-hannel evaporator with 10Hz 50% duty yle 121

141 Table 5.8 Experimental energy balane: Tapered 40 x 5~80 miro-hannel evaporator with 10Hz 50% duty yle Inner average RTD temperatures range from 34 o C to 36 o C and outer average RTD temperatures range from 30 o C to 36 o C with the average power input ranging from 34mW to 57mW. The results of experimental energy balane indiate that approximately 70% to 78% of the power dissipated in the resistane heater is onduted out through the silion membrane while 22% to 30% of the power is arried away by the latent heat of evaporation. The evaporation rate measured in this experiment is 120μg/se to 147μg/se with an unertainty of ±2.5µg/se. Results from the transient evaporation experiment of 10Hz frequeny and 30% duty yles with average thermal power inputs of 34mW, 44mW, and 57mW are shown in Figure 5.9 and Table 5.9. Results from the ondution heat transfer and evaporation heat transfer is denoted with blak irles and white irles respetively in Figure 5.9. Results given in Table 5.9 show that over the power range studied (34mW~57mW), the inner average RTD temperature ranged from 37 o C to 49 o C, the outer average RTD temperature ranged from 33 o C to 42 o C with temperature unertainty of ±0.5 o C. The evaporation rate ranged from 130μg/se to 167μg/se with evaporation rate unertainty of ± 2.5μg/se. 122

142 Figure 5.9 Evaporation test results of heat transfer by ondution and evaporation: Tapered 40 x 5~80 miro-hannel evaporator with 10Hz 30% duty yle Table 5.9 Experimental energy balane: Tapered 40 x 5~80 miro-hannel evaporator with 10Hz 30% duty yle 123

143 Figure 5.10 Evaporation test results of heat transfer by ondution and evaporation: Tapered 40 x 5~80 miro-hannel evaporator with 20Hz 50% duty yle Table 5.10 Experimental energy balane: Tapered 40 x 5~80 miro-hannel evaporator with 20Hz 50% duty yle 124

144 Figure 5.11 Evaporation test results of heat transfer by ondution and evaporation: Tapered 40 x 5~80 miro-hannel evaporator with 20Hz 30% duty yle Table 5.11 Experimental energy balane: Tapered 40 x 5~80 miro-hannel evaporator with 20Hz 30% duty yle 125

145 Several attempts were made to ondut transient evaporation test at 10Hz with a 10% duty yle. However at 10Hz with a 10% duty yle the transient experiments failed [membrane broke] due to sharp and high thermal effets. Heat transfer rate results for ondution (blak irles) and evaporation (white irles) for 20Hz with a 50% duty yle are plotted in Figure Both Figure 5.10 and Table 5.10 show experimental results for average thermal power inputs 34mW, 44.0mW, and 58mW. With this power range the temperatures resulted in the inner average RTD temperature ranged from 34 o C to 44 o C and the outer average RTD temperature ranged from 31 o C to 36 o C with unertainty of ±0.5 o C. Also, the mass evaporation rates are found from 120µg/se to 147µg/se with unertainty of ±2.5µg/se. Heat transfer rate results of ondution (blak irles) and evaporation (white irles) for 20Hz with a 30% duty yle are plotted in Figure Both Figure 5.11 and Table 5.11 show experimental results for average thermal power inputs of 34mW, 44mW, and 567mW. With this power range the results in the inner average RTD temperatures ranged from approximately 35 o C to 47 o C and the outer average RTD temperatures ranged from approximately 31 o C to 40 o C with ±0.5 o C. The mass evaporation rates were found to range from 123µg/se to 158µg/se with ±2.5µg/se. 5.6 SUMMARY OF TRANSIENT EVAPORATION TEST RESULTS The bar graph in Figure 5.12 shows a omparison of effiienies for transient evaporation test results at eah different transient ondition. The effiieny results from Figure 5.12 shows no signifiant differene between the transient onditions. However effiienies are higher ases with at 10Hz duty yles than at ases with 20Hz duty yles. 126

146 Figure 5.12 Experimental results summary for various transient onditions Also, Figure 5.12 show that miro-hannel evaporator effiienies dereased as power inputs are inreased as in the transient operation test results. The effiienies ranged from 29% to 32% at the same power inputs. Transient ases have approximately 10% better effiieny than the steady state ases with same average power inputs. However, the transient state evaporation test miro-hannel evaporator effiienies do not show signifiant improvement. 5.7 VISUALIZATION TEST RESULTS The movement of the liquid vapor interfae was visualized for onstant ross setion retangular miro-hannel evaporators at power inputs of 34mW, 44mW and 57mW. Figures 5.13, 5.14, and 5.15 show the top view of the miro-hannel evaporator for 40 x 35 x 5, 40 x 50 x 5, and 40 x 70 x 5 respetively. 127

147 Figure 5.13 Visualization of 40 x 35 x 5 miro-hannels with various power inputs Figure 5.14 Visualization of 40 x 50 x 5 miro-hannels with various power inputs 128

148 Figure 5.15 Visualization of 40 x 70 x 5 miro-hannels with various power inputs The top-left piture in Figures 5.13, 5.14, and 5.15 show the miro-hannels before working fluid is added and before power is input to the resistane heater in the mirohannel evaporator. Eah suessive piture shows the miro-hannels for inreasing power. The magnitude of eah power input is shown on the pitures. Figures 5.13, 5.14, and 5.15 show the shadows loated lose to the wik strutures darken as power inputs are inreased. In other words, the higher power input makes the working fluid layer thinner and deformation of the menisus stronger. Results from a different miro-hannel visualization test are shown in Figure In Figure 5.16, four mirographs are shown as the working fluid evaporates from 40 x 50 x 5 miro-hannels. No power input is applied in these photos. The first mirograph illustrates the empty miro-hannels. In next two mirographs, the liquid menisus is seen to desend in the miro-hannels. In the last mirograph, the working fluid is seen to 129

149 have retreated to two disonneted orners. In these images, the ontat angle θ of the menisus remains onstant at 41±1 as the level of the working fluid dereases. The radius of urvature of the menisus remains onstant at 33±1μm. Based on this radius of urvature, the apillary pressure in the 50μm wide hannels is found to be approximately 700Pa. Using similar mirographs the ontat angle and radius of urvature of the menisus for the 35μm wide hannels are measured to be 41 and 24µm (see Figure 5.17). The apillary pressure in the 35μm wide miro-hannels is found to be approximately 1000Pa. Likewise the ontat angle and radius of urvature of menisus for the 70μm wide hannels are measured to be 42 and 47μm (see Figure 5.17).. The apillary pressure in the 70μm wide hannels is found to be approximately 500Pa. Mirographs of 35μm and 70μm wide miro-hannels are also taken using the same tehnique as shown in Figure The seond visualization test results are tabulated in Table The apillary pressure equation is shown in equation 5.1. P 2γ osθ r = (5.1) where P is apillary pressure, γ is surfae tension (8x10-3 N/m), θ is ontat angle (41 o ) 130

150 Figure 5.16 Mirophotograph of 40 x 50 x5 miro-hannels with working fluid, FC77 Figure 5.17 Mirophotograph of miro-hannels with working fluid, FC77 SU8 Height Channel Width Contat angle Radius of Curvature Capillary Pressure (µm) (µm) (º) (µm) (Pa) Table 5.12 Seond visualization tests results 131

151 CHAPTER 6 DISSCUSION AND COMPARISON OF EXPERIMENAL AND NUMERICAL RESULTS 6.1 COMPARISON OF RESULTS OVERVIEW Numerial results are presented for steady evaporation and transient evaporation from open top square miro-hannels evaporator, and ompared to experimental measurements. The miro-hannels used in the numerial models math those found in the experimental study. Two geometries are onsidered: First a geometry that onsists of miro-hannels of onstant retangular ross setion. Eah miro-hannel is 40µm deep and has onstant widths of 35µm, 50µm or 70µm. Miro-hannel walls are 5µm thik. The seond geometry onsists of miro-hannels with tapered retangular ross setion. Eah mirohannel is 40µm deep. The width of the miro-hannels tapers from 80µm at the mirohannels outer radius, down to 5µm at the miro-hannels inner radius. The walls of the miro-hannels also taper in width from 80µm at their outer radius down to 5µm at their inner radius. The miro-hannels walls are assumed to be fabriated of SU8 and fabriated on either a 2µm thik Silion membrane or a 300nm thik Silion Nitride membrane. A table summarizing the numerial simulations is given in Table 6.1 (a) and (b). Table 6.1 (a) shows the numerial simulation onditions of the steady state in this hapter. Table 6.2 (a) shows the numerial simulation onditions of the transient operation. 132

152 (a) Steady State Conditions (b) Transient Operation Conditions Table 6.1 Summary of numerial simulations 6.2 STEADY STATE EVAPORATION TESTS RESULTS (Retangular Channel) Steady state evaporation from open top onstant ross setion miro-hannels are onsidered first. Dimensions of onstant retangular ross setion miro-hannels are desribed as hannel depth x hannel width x hannel wall thikness. For example 40 x 35 x 5 refers to a miro-hannel that is 40µm deep, 35µm wide with eah hannel formed between 5µm thik walls as shown in Figure 7.1. Unless otherwise stated all mirohannel evaporators are fabriated of SU8 hannel walls fabriated atop 2µm thik silion membrane. In these numerial simulations the liquid working fluid thikness in the miro-hannels has been speified a priori. 133

153 Figure 6.1 Dimensions of Constant Retangular Cross Setion Miro-Channels Table 6.2 Numerial and Experimental Energy balanes for onstant retangular ross setion miro-hannel 40 x 35 x 5 134

154 (a) Numerial and Experimental Evaporation Rates (b) Numerial and Experimental Temperatures Figure 6.2 Numerial and Experimental Evaporation Rates and Temperatures for onstant retangular ross setion miro-hannels 40 x 35 x 5 135

155 Results from experimental measurements and numerial alulations for onstant retangular ross setion miro-hannels with 40µm depth, 35µm width and 5µm thik hannel walls are shown in Figure 6.2 and tabulated in Table 6.2. In eah figure, numerial alulations are indiated with lines, and experimental measurements are indiated with filled irles. Figure 6.2 (a) shows predited evaporation rates from the miro-hannels plotted versus the thermal power input. Predited evaporation rates are plotted for assumed liquid working fluid thiknesses of 14, 20, 28, and 35µm. Figure 6.2 (b) shows predited temperatures for the loations of the two annular RTD is plotted versus thermal power input. One again, predited temperatures are plotted for assumed liquid working fluid thiknesses of 14, 20, 28, and 35µm.On Figure 6.2 (a) experimental measurements of evaporator rates for three thermal power inputs: 34mW, 48mW, and 57mW are also plotted. On Figure 6.2 (b) experimental measurements of temperatures for the two annular RTDs are plotted for the same three thermal power inputs 34mW, 48mW, and 57mW (see Appendix C). A omparison of the experimental temperatures and evaporation rates with the numerial alulations reveals that the experimental measurements mostly fall between the numerial simulations assuming liquid working fluid thiknesses of 28µm and 35µm. Thus the assumption of a liquid working fluid thikness of 32µm ±4µm leads to a good math between model and measurements. Results from experimental measurements and numerial alulations for onstant retangular ross setion miro-hannels with 40µm depth, 50µm width and 5µm thik hannel walls are shown in Figure 6.3 and tabulated in Table 6.3. In eah figure, numerial alulations are indiated with lines, and experimental measurements are indiated with filled irles. 136

156 Table 6.3 Numerial and Experimental Energy balanes for onstant retangular ross setion miro-hannel 40 x 50 x 5 (a) Numerial and Experimental Evaporation Rates 137

157 (b) Numerial and Experimental Temperatures Figure 6.3 Numerial and Experimental Evaporation Rates and Temperatures for onstant retangular ross setion miro-hannels 40 x 50 x 5 Figure 6.3 (a) shows predited evaporation rates from the miro-hannels plotted versus the thermal power input. Predited evaporation rates are plotted for assumed liquid working fluid thiknesses of 14, 20, 28, and 35µm. Figure 6.3 (b) shows predited temperatures for the loations of the two annular RTD is plotted versus thermal power input. One again, predited temperatures are plotted for assumed liquid working fluid thiknesses of 14, 20, 28, and 35µm. On Figure 6.3 (a) experimental measurements of evaporator rates for three thermal power inputs: 34mW, 47mW, and 62mW are also plotted. On Figure 6.3 (b) experimental measurements of temperatures for the two annular RTDs are plotted for the same three thermal power inputs 34mW, 47mW, and 62mW (see Appendix C). A omparison of the experimental temperatures and 138

158 evaporation rates with the numerial alulations reveals that the experimental measurements mostly fall between the numerial simulations assuming liquid working fluid thiknesses of 28µm and 35µm. Thus the assumption of a liquid working fluid thikness of 32µm ±4µm leads to a good math between model and measurements. Finally, results from experimental measurements and numerial alulations for onstant retangular ross setion miro-hannels with 40µm depth, 70µm width and 5µm thik hannel walls are shown in Figure 6.4 and tabulated in Table 6.4. In eah figure, numerial alulations are indiated with solid lines, and experimental measurements are indiated with filled irles. Figure 6.4 (a) shows predited evaporation rates from the miro-hannels plotted versus the thermal power input. Predited evaporation rates are plotted for assumed liquid working fluid thiknesses of 20, 30, and 36µm. Figure 6.4 (b) shows predited temperatures for the loations of the two annular RTD is plotted versus thermal power input. One again, predited temperatures are plotted for assumed liquid working fluid thiknesses of 20, 30, and 36µm. On Figure 6.4 (a) experimental measurements of evaporator rates for three thermal power inputs: 32mW, 43mW, and 54mW are also plotted. On Figure 6.4 (b) experimental measurements of temperatures for the two annular RTDs are plotted for the same three thermal power inputs 32mW, 43mW, and 54mW (see Appendix C). A omparison of the experimental temperatures and evaporation rates with the numerial alulations reveals that the experimental measurements mostly fall between the numerial simulations assuming liquid working fluid thiknesses of 30µm and 36µm. Thus the assumption of a liquid working fluid thikness of 33µm ±3µm leads to a good math between model and measurements. 139

159 (a) Numerial and Experimental Evaporation Rates (b) Numerial and Experimental Temperatures Figure 6.4 Numerial and Experimental Evaporation Rates and Temperatures for onstant retangular ross setion miro-hannels 40 x 70 x 5 140

160 Table 6.4 Numerial and Experimental Energy balanes for onstant retangular ross setion miro-hannel 40 x 70 x 5 Comparison of the results of the numerial simulations with the results of the evaporation experiments for onstant retangular ross setion miro-hannels indiates that given an appropriate assumed liquid working fluid thikness in the miro-hannel, evaporation rates, sensible heat transfer rates and miro-hannel temperatures an be predited with fair auray. 6.3 STEADY STATE EVAPORATION TESTS RESULTS (Tapered Channel) Steady state evaporation from open top tapered miro-hannels are onsidered next. Dimensions of tapered miro-hannels are 40µm deep and their width is 80µm at the outer radius of the miro-hannel. Eah miro-hannel width tapers down to 5µm at the inner radius of the miro-hannel. The walls dividing miro-hannels also are 80µm wide at their outer radius and taper down to a width of 5µm at their inner radius. 141

161 Figure 6.5 Dimensions of Tapered Miro-Channel Table 6.5 Numerial and Experimental Energy balanes for Tapered miro-hannel 40 x 5~80 142

162 (a) Numerial and Experimental Evaporation rate (b) Numerial and Experimental Temperatures Figure 6.6 Numerial and Experimental Evaporation Rates and Temperatures for Tapered miro-hannels 40 x 5~80 143

163 As before the miro-hannel evaporators are fabriated of SU8 hannel walls fabriated on 2µm thik silion membrane. Sine the wall thikness and hannel width are tapered same dimensions, dimensions of tapered miro-hannels an be desribed as 40 x 5~80. The dimensions of tapered miro-hannels are shown in Figure 6.5. In these numerial simulations, the liquid working fluid thikness in the miro-hannels is not speified a priori. The miro-hannels are initially assumed to be filled with liquid. At all subsequent times, the liquid working fluid thikness is alulated. Thus Figures 6.6 through 6.20 shows results from the numerial model that inludes alulation of the liquid fluid flow through the open miro-hannels based on the fore balane equations. Figure 6.6 shows numerial and experimental results for tapered miro-hannels 40µm deep with widths tapering from 80µm to 5µm for thermal power inputs of 34, 44, and 58mW (see Appendix C). The numerial results are indiated with lines, and the experimental results are indiated with symbols. Figure 6.6 (a) shows evaporation rates. Figure 6.6 (b) shows temperatures at the inner (solid line) and outer (dotted line) annular RTDs versus thermal power inputs. Measured evaporation rates (blak irles) and measured temperatures for the inner (blak irles) and outer (white irles) annular RTDs show good agreement with the numerial results. Table 6.5 shows that for the tapered miro-hannel (40µm deep with 5µm to 80µm tapered width) the inner and outer RTD temperature ranged from 33 o C to 44 o C and 29 o C to 35 o C. The evaporation rate ranged from 103.3µg/se to 135.6µg/se. Both experimental and numerial energy balanes indiates that approximately 70% to 80% of the power dissipated in the resistane heater is onduted out through the silion membrane, while 20% to 30% of power is arried away by the latent heat of evaporation. 144

164 Figure 6.7 Liquid thikness profiles along the length of the hannel: Critial heat flux Figure 6.8 Disretization of menisus in the miro-hannel for FDTD model Table 6.6 Numerial integration of energy balane for ritial heat flux Tapered 40 x 5~80 miro-hannel evaporator 145

165 Results also show that miro-hannel evaporator effiienies dereased as power inputs inreased in the tapered miro-hannels. Figure 6.7 shows preditions of the liquid thikness profile along the length of the hannel alulated by the near the wall of the miro-hannel numerial model. The initial liquid thikness is set at 40µm (D in Figure 6.8). The initial liquid thikness near the enter of the miro-hannel (H in Figure 6.8) is alulated using Equation 6.1. w H = D tanθ (6.1) 2 where H is working fluid thikness from enter of hannel (see Figure 6.7), D is height of wik strutures, w is width of hannel, and θ is ontat angle (41 o ). The plot shows the liquid thikness dereases where the resistane heaters are loated. Liquid thikness also dereases as the power input inreases. The ritial heat flux is found by inreasing the power input until the liquid thikness at enter of hannel reahes zero. The liquid thikness reahes zero when power input reahes 124mW. Table 6.6 shows the alulated radial temperatures, the evaporation rates, the sensible heat transfer rates and the latent heat transfer rates as the liquid thikness at enter of the hannel goes to zero with inreasing the power input. Results also showed miro-hannel evaporation effiienies derease as power input inreases until power input reahes the ritial heat flux. If the power input is inreased past the ritial heat flux value, the alulated temperature will not onverge beause of the liquid dry out. 146

166 6.4 FIXED TEMPERATURE BOUNDARY RESULTS Two approahes were used to model the boundary onditions at the edge of the membrane for the numerial alulations as explained in Chapter 4. First, a Newton s law of ooling boundary ondition was used. The effetive onvetive oeffiient was determined by fitting the numerial model to experimental data as explained in Chapter 4. Using a Newton s law of ooling boundary ondition with an effetive onvetive oeffiient in the numerial model worked well predit the experimental results for miro-hannel evaporators on silion membrane. However, use of a new effetive onvetive oeffiient boundary would need to be found for any other kinds of mirohannel evaporators. To effetively predit heat transfer rates for miro-hannel evaporators on other membrane material suh as silion nitride, a new boundary ondition was preferred. To meet this need a onstant temperature boundary ondition, employing the temperature at the edge of the square membrane was used. To establish this onstant temperature boundary ondition, a third RTD was fabriated to measure the membrane edge temperature. This edge temperature was then used as fixed temperature boundary onditions in the numerial alulations. The numerial results with the fixed temperature boundary onditions taken the experimental measurements are plotted alongside to the experimental results in Figure 6.9. Figure 6.9 shows numerial and experimental results for a tapered miro-hannel with a depth of 40µm high and width that tapered from 80µm down to 5µm. The membrane supporting the miro-hannel was a 2µm thik silion membrane. Results are shown for thermal power inputs of 34, 44, and 57mW (see Appendix C). The edge temperatures used as the fixed temperature boundary onditions are shown in Table

167 (a) Numerial and Experimental Evaporation rate (b) Numerial and Experimental Temperature Figure 6.9 Numerial and Experimental Evaporation Rates and Temperatures for Tapered miro-hannels 40 x 5~80with edge temperature boundary ondition 148

168 Table 6.7 Numerial and Experimental Energy balanes for Tapered hannel 40 x 5~80 with edge temperature boundary ondition Figure 6.9 (a) shows alulated evaporation rates versus thermal power input. Figure 6.9 (b) shows alulated temperatures at the inner and outer RTDs versus thermal power input. Numerially predited evaporation rates and temperatures are shown to agree well with measured evaporation rates and inner and outer annular RTD measurements. Like the numerial model that uses the effetive onvetive oeffiient, Table 6.7 shows that over the power inputs studied, the numerial model employing a fixed temperature boundary ondition is seen to predit temperatures and sensible and latent heat transfer rates as well as the numerial model employing a Newton s law of ooling boundary ondition with an effetive heat transfer oeffiient. As will be seen in the next setion the numerial model with the fixed temperature boundary ondition an be used to predit results for a miro-hannel evaporator built on a silion nitride membrane just as well. 149

169 6.5 STEADY STATE EVAPORATION TESTS RESULTS (Tapered Channel: SiNx) A seond set of tapered miro-hannels was fabriated on 300nm thik Silion Nitride membranes. Silion Nitride membranes were used for two reasons. First, the thermal ondutivity of Silion Nitride is muh lower than Silion: 15W/mK vs.148 W/mK. Seond Silion Nitride membranes an be fabriated to be muh thinner than silion membranes: 300nm vs. 2µm. The tapered miro-hannels were idential to the tapered miro-hannels fabriated on Silion membranes as shown in Figure 6.4. As before the tapered miro-hannels were 40µm deep with hannel widths that tapered from 80µm at their outer radius to 5µm at their inner radius. Likewise hannel wall thikness tapered from 80µm down to 5µm. Numerial and experimental results are shown in Figure 6.10, Figure 6.11 and Table 6.8. Results from the evaporation experiments are indiated with symbols and results from the numerial simulations are indiated with lines in Figure 6.10 and Figure Figure 6.10 (a) shows omparison of evaporation rates. Figure 6.10 (b) shows omparison of temperatures at the inner and outer RTD versus thermal power inputs, and Figure 6.11 shows the omparison of temperatures along with the length of membrane. In Figure 6.10, experimental results are given for power inputs of 12.6mW and 13.7mW (see Appendix C). The reasons why the low 13mW of power inputs are used in the silion nitride membrane were previously explained in Chapter 5. Diffiulty in satisfying the energy balane in the silion nitride membrane simulations resulted in 6% and 10% energy balane errors for 13.7mW and 12.6mW power inputs respetively. However, Figure 6.10 shows the numerial alulations and the experimental measurements ompare well. The fixed temperature boundary ondition used in the Figure 6.10 is the edge temperature measured for the experiment at 13.7mW power input. 150

170 (a) Numerial and Experimental Evaporation rate for SiNx membrane (b) Numerial and Experimental Temperature for SiNx membrane Figure 6.10 Numerial and Experimental Evaporation rate and temperature: SiNx Tapered hannel 40 x 5~80 with edge temperature boundary ondition 151

171 Figure 6.11 Numerial and Experimental Temperature for silion nitride membrane Tapered hannel 40 x 5~80 with edge temperature boundary ondition Table 6.8 Numerial and Experimental Energy balanes for SiNx membrane Tapered hannel 40 x 5~80 with edge temperature boundary ondition 152

172 The fixed temperature was measured to be 22.8 o C with an unertainty of ±0.5 o C. Figure 6.11 shows temperature measurements for the inner and outer RTD temperatures at a thermal power input of 13.7mW. Figure 6.11 shows that the numerial result for the inner RTD temperature losely math the temperature from the experimental measurements. However the predited outer RTD temperature is lower than the measured temperature beause of model assumptions. The numerial model assures a radially symmetri geometry were the experimental miro-hannel evaporator is a square geometry. This mismath auses greater error near the outside of the square mirohannel evaporator. Table 6.8 shows that miro-hannel evaporator built in a silion nitride membrane (with miro-hannel 40µm high and tapered 5µm to 80µm wide) has the best wik effiieny at the highest thermal power input of 13.7mW. The results of the numerial simulations given in Table 6.8 show that over the power range studied, the inner and outer RTD temperature ranged from 38 o C to 42 o C and approximately 25 o C respetively. The evaporation rate ranged from 72µg/se to 137µg/se. Both experimental and numerial energy balanes indiate that only 12% to 15% of the power dissipated in the resistane heater is onduted out through the silion membrane, while 85% to 88% of the power is arried away by the latent heat of evaporation. 6.6 TRANSIENT TEST RESULTS (Tapered Miro-hannel: Si) The experimental and numerial results for transient operation of the miro-hannel evaporator are presented next. The same average power inputs as the steady-state runs of approximately 34mW, 44mW, and 57mW are used (see Appendix C). 153

173 (a) Numerial and Experimental Evaporation rate (b) Numerial and Experimental Temperature Figure 6.12 Numerial and Experimental Evaporation rate and temperature: Tapered hannel 40 x 5~80, 10Hz frequeny 50% duty yle with various power inputs 154

174 Figure 6.13 Numerial and Experimental Temperature History: Tapered hannel 40 x 5~80, 10Hz frequeny 50% duty yle with 34mW power input Table 6.9 Experimental and Numerial Energy balanes: Tapered hannel 40 x 5~80, 10Hz frequeny 50% duty yle with various power inputs 155

175 Operation frequenies explored are 10Hz, 20Hz and 50Hz. Duty yles onsidered are 50%, 30% and 10%. All experiments and numerial simulations foused on the tapered miro-hannel geometry. That is all experiments and numerial simulations were run with miro-hannels 40µm deep, with widths that tapered from 80µm at their outer radius to 5µm at their inner radius. Figure 6.12 shows numerial and experimental results for the tapered miro-hannel evaporator operated at a frequeny of 10Hz and duty yle of 50% for thermal power inputs of 34, 44, and 57mW (see Appendix C). Figure 6.12 (a) shows alulated evaporation rates (solid line) versus thermal power input. Figure 6.12 (b) shows alulated temperatures at the inner (solid line) and outer (dotted line) RTD versus thermal power inputs. Both measured evaporation rates (blak irles) and measured temperature for the inner (blak irles) and outer (white irles) annular RTD show good agreement with the numerial model. Figure 6.13 shows transient temperature histories for transient evaporation with the onditions of 10Hz 50% duty yle and 34mW power input. In Figure 6.13, numerial alulations of inside RTD temperature profile is indiated with a solid line, and experimental measurements of inside RTD temperature is indiated with a dotted line. Table 6.9 shows the inner and outer RTD temperature ranged from 34 o C to 46 o C and 31 o C to 38 o C. The evaporation rate ranged from 120µg/se to 152µg/se. Both experimental and numerial energy balanes indiate that approximately 70% to 78% of the power dissipated in the resistane heater is onduted out through the silion membrane. Only 22% to 30% of the power is arried away by the latent heat of evaporation. 156

176 (a) Numerial and Experimental Evaporation (b) Numerial and Experimental Temperature Figure 6.14 Numerial and Experimental Evaporation rate and temperature: Tapered hannel 40 x 5~80, 10Hz frequeny 30% duty yle with various power inputs 157

177 Figure 6.15 Numerial and Experimental Temperature History: Tapered hannel 40 x 5~80, 10Hz frequeny 30% duty yle with 34mW power input Table 6.10 Numerial and Experimental Energy balanes: Tapered hannel 40 x 5~80, 10Hz frequeny 30% duty yle with various power inputs 158

178 Figure 6.14 shows numerial and experimental results for transient operation at a frequeny of 10Hz and duty yle of 30% for thermal power inputs of 34, 44, and 57mW (see Appendix C). Figure 6.14 (a) shows alulated evaporation rates versus thermal power input. Figure 6.14 (b) shows alulated temperatures at the inner and outer RTD versus thermal power input. Measured evaporation rates and measured temperature for the inner and outer annular RTDs show good agreement with the numerial model. Figure 6.15 shows transient temperature histories for transient evaporation with the onditions of 10Hz 30% duty yle and 34mW power input. In Figure 6.15, numerial alulations of inside RTD temperature profile is indiated with a solid line, and experimental measurements of inside RTD temperature is indiated with a dotted line. Table 6.10 shows the inner and outer RTD temperature ranged from 37 o C to 49 o C and 33 o C to 42 o C. Evaporation rates ranged from 130µg/se to 167µg/se. Both the experimental and numerial energy balanes indiate that approximately 68% to 75% of the power dissipated in the resistane heater is onduted out through the silion membrane. Only 25% to 32% of the power is arried away by the latent heat of evaporation. Figure 6.16 shows numerial results for transient operation at a frequeny of 10Hz and duty yle of 10% for thermal power inputs of 34, 44, and 57mW. No experimental results are presented for a frequeny of 10Hz and duty yle of 10%. Figure 6.16 (a) shows alulated evaporation rates versus thermal power input. Figure 6.16 (b) shows alulated temperatures at the inner and outer RTD versus thermal power input. In Figure 6.16, a numerial alulation of inside RTD temperature profile is indiated with a solid line. Table 6.11 shows the inner and outer RTD temperature ranged from 38 o C to 51 o C and 34 o C to 44 o C. Evaporation rates ranged from 130µg/se to 167µg/se. 159

179 () Numerial Evaporation (d) Numerial Temperature Figure 6.16 Numerial Evaporation rate and temperature: Tapered hannel 40 x 5~80, 10Hz frequeny 10% duty yle with various power inputs 160

180 Table 6.11 Numerial Energy balanes: Tapered hannel 40 x 5~80, 10Hz frequeny 10% duty yle with various power inputs The numerial energy balanes indiate that approximately 67% to 74% of the power dissipated in the resistane heater is onduted out through the silion membrane. Only 26% to 33% of the power is arried away by the latent heat of evaporation. Figure 6.17 shows numerial and experimental results for the tapered miro-hannel evaporator operated at a frequeny of 20Hz and a duty yle of 50% for thermal power inputs of 34, 44, and 57mW (see Appendix C). Again, the numerial alulations are indiated with lines, and the experimental results are indiated with symbols. Figure 6.17 (a) shows alulated evaporation rates versus thermal power input. Figure 6.17 (b) shows alulated temperatures at the inner and outer RTDs versus thermal power input. Measured evaporation rates and measured temperatures for the inner and outer annular RTD show good agreement with the numerial model. Figure 6.18 shows transient temperature histories for transient evaporation with the onditions of 20Hz 50% duty yle and 34mW power input. In Figure 6.18, numerial alulations of inside RTD temperature profile is indiated with a solid line, and experimental measurements of inside RTD temperature is indiated with a dotted line. 161

181 (a) Numerial and Experimental Evaporation (b) Numerial and Experimental Temperature Figure 6.17 Numerial and Experimental Evaporation rate and Temperature: Tapered hannel 40 x 5~80, 20Hz frequeny 50% duty yle with various power inputs 162

182 Figure 6.18 Numerial and Experimental Temperature History: Tapered hannel 40 x 5~80, 20Hz frequeny 50% duty yle with 34mW power input Table 6.12 Numerial and Experimental Energy balanes: Tapered hannel 40 x 5~80, 20Hz frequeny 50% duty yle with various power inputs 163

183 Table 6.12 shows the inner and outer RTD temperature ranged from 35 o C to 45 o C and 31 o C to 40 o C. Evaporation rates ranged from 122µg/se to 147µg/se. Both experimental and numerial energy balane indiate that approximately 70% to 78% of the power dissipated in the resistane heater is onduted out through the silion membrane, while 22% to 30% of power is arried away by the latent heat of evaporation. Figure 6.19 shows numerial and experimental results for transient operation at a frequeny of 20Hz and a duty yle of 30% for thermal power inputs of 34, 44, and 57mW (see Appendix C). Figure 6.19 (a) shows alulated evaporation rates versus thermal power input. Figure 6.19 (b) shows alulated temperatures at the inner and outer RTD versus thermal power input. Measured evaporation rates and measured temperature for the inner and outer annular RTDs show good agreement with the numerial model. Figure 6.20 shows transient temperature histories for transient evaporation with the onditions of 20Hz 30% duty yle and 34mW power input. In Figure 6.20, numerial alulations of inside RTD temperature profile is indiated with a solid line, and experimental measurements of inside RTD temperature is indiated with a dotted line. Table 6.13 shows the inner and outer RTDs temperature ranged from 35 o C to 48 o C and 32 o C to 41 o C. The evaporation rate ranged from 127µg/se to 168µg/se. Both experimental and numerial energy balane indiates that approximately 69% to 76% of the power dissipated in the resistane heater is onduted out through the silion membrane, while 24% to 31% of power is arried away by the latent heat of evaporation. Figure 6.21 shows numerial results for transient operation at a frequeny of 20Hz and duty yle of 10% for thermal power inputs of 34, 44, and 57mW. No experimental results are presented for a frequeny of 20Hz and duty yle of 10%. Figure 6.21 (a) shows alulated evaporation rates versus thermal power input. 164

184 (a) Numerial and Experimental Evaporation (b) Numerial and Experimental Temperature Figure 6.19 Numerial and Experimental Evaporation rate and Temperature: Tapered hannel 40 x 5~80, 20Hz frequeny 30% duty yle with various power inputs 165

185 Figure 6.20 Numerial and Experimental Temperature History: Tapered hannel 40 x 5~80, 20Hz frequeny 30% duty yle with 34mW power input Table 6.13 Numerial and Experimental Energy balanes: Tapered hannel 40 x 5~80, 20Hz frequeny 30% duty yle with various power inputs 166

186 (a) Numerial Evaporation (b) Numerial Temperature Figure 6.21 Numerial Evaporation rate and Temperature: Tapered hannel 40 x 5~80, 20Hz frequeny 10% duty yle with various power inputs 167

187 Table 6.14 Numerial Energy balanes: Tapered hannel 40 x 5~80, 20Hz frequeny 10% duty yle with various power inputs Figure 6.21 (b) shows alulated temperatures at the inner and outer RTD versus thermal power input. In Figure 6.21, a numerial alulation of inside RTD temperature profile is indiated with a solid line. Table 6.14 shows the inner and outer RTD temperature ranged from 37 o C to 50 o C and 33 o C to 41 o C. Evaporation rates ranged from 130µg/se to 167µg/se. The numerial energy balanes indiate that approximately 67% to 75% of the power dissipated in the resistane heater is onduted out through the silion membrane. Only 25% to 33% of the power is arried away by the latent heat of evaporation. In all ases the transient results show that the effiienies of the miro-hannel evaporators dereased as thermal power input to the miro-hannel evaporator inreased, just as for the steady state results. The transient results also show that effiienies of the evaporator inreased as duty yle dereased and as operating frequeny inreased. 168

188 6.7 TRANSIENT TEST RESULTS (Tapered Miro-hannel: SiNx) A seond set of tapered miro-hannels was fabriated on 300nm thik Silion Nitride membranes. Silion Nitride membranes were used for two reasons. First, the thermal ondutivity of Silion Nitride is muh lower than Silion: 15W/mK vs.148 W/mK. Seond Silion Nitride membranes an be fabriated to be muh thinner than silion membranes: 300nm vs. 2µm. The tapered miro-hannels were idential to the tapered miro-hannels fabriated on Silion membranes as shown in Figure 6.4. As before the tapered miro-hannels were 40µm deep with hannel widths that tapered from 80µm at their outer radius to 5µm at their inner radius. Likewise hannel wall thikness tapered from 80µm down to 5µm. Numerial results presented in this hapter are for the silion nitride membrane with wiking wall dimensions of 40µm deep and tapered hannel 5µm to 80µm wide. Figure 6.22 shows transient temperature histories for the transient operation at a frequeny 10Hz and a duty yle 50% for power input of 11mW power input with the fixed boundary ondition of 22.8 o C. In Figure 6.22, numerial alulations of inside RTD temperature profile is indiated with a solid line, and numerial alulations of outside RTD temperature is indiated with a dotted line. Unlike the transient simulation with silion membrane, no waveform was observed from the transient simulation with silion nitride membrane. Table 6.15 shows the inner and outer RTD temperature was 40.6 o C and 25.2 o C. The evaporation rate was 117µg/se. Numerial energy balanes indiate that approximately 12% of the power dissipated in the resistane heater is onduted out through the silion membrane, while 88% the power is arried away by the latent heat of evaporation. 169

189 Figure 6.22 Numerial Temperature History: Tapered hannel 40 x 5~80, 10Hz frequeny 50% duty yle with 11mW power input Table 6.15 Numerial Energy balanes: Tapered hannel 40 x 5~80, 10Hz frequeny 50% duty yle with 11mW power inputs 170

190 6.8 EFFECT OF HEAT INPUT AREA (a) Numerial Evaporation (b) Numerial Temperature Figure 6.23 Numerial Evaporation rate and Temperature: 171

191 Table 6.16 Numerial Energy balanes Steady state evaporation from open top tapered miro-hannels is simulated for thermal power input of 34, 44, and 58mW. The thermal input is applied to entire bottom surfae of miro-hannel evaporator. Dimensions of tapered miro-hannels are 40µm deep and their width is 80µm at the outer radius of the miro-hannel. Eah mirohannel width tapers down to 5µm at the inner radius of the miro-hannel. The walls dividing miro-hannels also are 80µm wide at their outer radius and taper down to a width of 5µm at their inner radius. The numerial results are indiated with lines. Figure 6.23 shows numerial results for tapered miro-hannels with thermal power inputs of. 34, 44, and 57mW. Figure 6.23 (a) shows evaporation rates. Figure 6.23 (b) shows temperatures at the inner (solid line) and outer (dotted line) annular RTDs versus thermal power inputs. Table 6.16 shows that for the tapered miro-hannel (40µm deep with 5µm to 80µm tapered width) the inner and outer RTD temperature ranged from 33 o C to 44 o C and 29 o C to 35 o C. The evaporation rate ranged from 103.3µg/se to 135.6µg/se. Both experimental and numerial energy balanes indiates that approximately 70% to 80% of the power dissipated in the resistane heater is onduted out through the silion membrane, while 20% to 30% of power is arried away by the latent heat of evaporation. 172

192 CHAPTER 7 CONCLUSIONS 7.1 CONCLUSIONS The first goal of the present study is to find the most effiient wiking struture by determining the overall effiienies of the miro-hannel evaporator with varying wik dimensions. The seond goal of this study is to build an effetive design tool for the development of effiient miro-hannel evaporator. Channels with dimensions from ten to one hundred mirons are used in this study. To find the overall most effetive wik geometry and dimensions, the steady state evaporation test and transient evaporation test are performed with silion-based membranes and silion-nitride-based membranes. Evaporative heat transfer rates and evaporation rates from various SU8 miro-hannels have been experimentally measured. A numerial model of sensible heat transfer and evaporation from the miro-hannel evaporator has been developed. Results from the experimental measurements and numerial alulations shows no signifiant differene between the different dimensions and designs of the miro-wiking hannels for the steady state evaporation ondition with silion-based membranes. For onstant ross setion retangular hannels, the liquid thiknesses of miro-hannels are estimated by omparison of the experimental measurements and numerial alulations from various liquid thiknesses. Suh a omparison of the numerial alulations and experimental measurements yields onsistent estimates of liquid thikness for the mirohannels within about ±5µm. For tapered (wiking wall dimensions of 40µm deep and tapered hannel 5µm to 80µm wide) hannels, the fore balane equations are introdued 173

193 and inluded in the numerial model to eliminate estimating the liquid thikness. The updated numerial model and experimental results are ompared to validate the model. A omparison of the numerial alulations and experimental measurements shows good agreement. Silion based membrane steady state evaporation shows that both the experimental and numerial energy balanes indiates that approximately 70%~80% of the power dissipated in the resistane heater is by ondution through the membrane, while 20%~30% of power is arried away by the latent heat of evaporation. Results also show wik effiienies are dereased as power inputs are inreased for all silion-based membrane steady state evaporation test ases. Sine muh work is ompleted for the steady state evaporation test, the transient tests are performed with silion-based membranes to see how the performane of the evaporator hanges at transient operations. A number of resonant operation onditions and a number of duty yles are used to perform both experimental tests and numerial alulations. A omparison of the numerial alulations and experimental measurements shows good agreement. The results are ompared with the steady state evaporation results, and the results from transient operations show no signifiant improvement in the wik effiienies. Again, results show wik effiienies are dereased as power inputs are inreased for all silion-based membrane steady state evaporation ases. In the same resonant operation ondition, the results show that wik effiienies are inreased as duty yles are dereased. Silion-nitride based membranes are used in the evaporation test sine the silion-based membrane evaporation test does not show effetive wik effiienies. Changing the membrane material from the high ondutivity material to the low ondutivity material 174

194 shows signifiant improvement in the wik effiienies beause the low ondutivity material signifiantly dereases the heat loss from the radial ondution heat transfer. The experimental measurements and the numerial preditions presented in this dissertation shows that the latent heat by evaporation of the heat added to the onentri heater at the enter of the membrane ranged from roughly 18%-26% for silion based membranes and 82%-86% for silion nitride based membranes. 175

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207 APPENDIX A 1. Cylindrial ondution equation Figure A1 Cylindrial oordinates The heat transfer, q, by Fourier s law is set at equation A1-1. dt q ka dr = (A1-1) where A= 2πrL (A1-2) so 188

208 dt q k( 2πr) dr = (A1-3) Using the energy balane equation and Taylor expansion, the equation is rewritten as equation A1-4. q r qr + dr dt dt dt = k( 2 rl) + k(2πrl) d k(2πrl) = 0 dr dr dr π (A1-4) By using equation A1-5 from equation A1-4, equation A1-6 is set up. dt dt onstatnt C r = ons tan t = = (A5) dr dr r r T ( r) = C1 lnr+ C2 (A6) By applying the boundary onditions, T=T 1 where r=r 1 and T=T 2 where r=r 2, to equation A1-2, onstants C 1 and C 2 is determined as shown equation A1-7 and equation A1-8. T1 T2 C 1 = (A1-7) r1 ln r 2 189

209 ln ln r r r T T T C = (A1-8) The final ylindrial ondution equation is formed as equation A1-9 by substituting equation A1-6 to equation A1-3. = ln 2 r r T T LK q π (A1-9)

210 2. 2-D Flow Analysis in miro-hannel P+dP τ τ dx X 0 dy -w +w Y P Figure A2 2-Dimensional Flow From Figure A2, the x-diretion of the fore balane is set as equation A2-1. F x = Pdy Pdy dpdy 2dx τ = 0 (A2-1) wher p is pressure, x is distane along with the hannel, y is the distane of width of hannel. The fore balane equation of flow is derived as followed. 191

211 dpdy 2 τ dx = 0 (A2-2) dpdy = 2τdx (A2-3) dp 2τ = (A2-4) dx dy 2 dp d u = 2µ (A2-5) dy 2 dx From the boundary onditions, equation A2-5 an be solved as follows. 2-D B.C: (a) u=0, where y=±w (b) du/dy=0, where y=0 From equation A2-5, du/dy and u is du dy = 1 dp 2µ dx y+ C 1 (A2-6) 1 4µ dp dx 2 u = y + C1y+ C 2 (A2-7) From the boundary ondition, C 1 =0 and C 2 = 1 dp 2 w. 4µ dx Finally, Flow veloity of the 2D flow an be written as follows. 192

212 dp u = ( y 4µ dx w ) (A2-8) 3. Derivation of menisus Figure A3 Menisus surfae The menisus is tending to be form a irular shape. The irular shape in menisus an be desribed by using following mathematial alulations. dθ p =γ (A3-1) ds pi o pi o p = ρ g( Z H ) (A3-2) dz ds = sinθ (A3-3) dθ γ = ρg( Z H ) (A3-4) ds 193

213 Multiply dz/ds to both side of equation A3-4, and rewritten the equation A3-4. dθ dz dz γ = ρg( Z H ) (A3-5) ds ds ds The equation A3-5 beomes equation A3-6 with using equation A3-3. dθ dz γ sinθ =ρg( Z H ) (A3-6) ds ds γ sinθd θ = ρg( Z H ) dz (A3-7) Equation A3-7 is solved with boundary onditions of θ=0 at Z=H, then equation A3-7 is beomes equation A Z ρgh ρg ρghz+ γ osθ + γ = 0 (A3-8) 2 2 Using solution of seond polynomial equation solves the equation A3-8. 2γ Z = H ± (1 osθ ) (A3-9) ρg Sine the solution Z is the funtion of osine, the shape of menisus should be forms a irular shape. 194

214 APPENDIX B 1. CALIBRATION TEST RESULTS Figure B.1 Detailed dimensions of wik and hannel strutures The experiment proedures of alibration tests are presented in setion 3.3. The separate alibration tests are performed every time even though the testing membrane has the same wik strutures, if the different testing membrane is used in the evaporation test. Calibration result for eah wik dimension that used in this work is presented in previous setion 5.3. First, a simple feature of 10 x 10 x 10 (10µm high SU8 wall, 10µm wide hannel, and 10µm thik SU wall) wiking struture membrane with dual RTD is alibrated to validate the simple numerial alulation. The alibration results of 10 x 10 x 10 wiking struture membrane are shown in Figure B.2. The dimensions of 10 x 10 x 10 are SU8 wall height, hannel width, and wall thikness in unit of mirons (µm) as shown in Figure B.1. The silion material membrane is used in this alibration. 195

215 Figure B.2 Calibration test results of 10 x 10 x 10 wiking struture membrane The voltage and temperature data are olleted in a range of water bath temperatures from 30 o C to 40 o C, and the linear relationships of voltage and temperature are determined for the inside RTD and the outside RTD. The y is referred temperature and the x is referred voltage in the linear relationship equations. This alibration results has the R 2 value of 0.99, and this value is show that how well the atual experiment data is fitted in the linear urve. The R 2 value of 0.99 is possible and desired beause the platinum has the linear relationship between the temperature value and the resistane value. The dual RTD alibration test results of 40µm high SU8 wall and 5µm wide wiking wall dimensions with 35µm, 50µm, and 70µm wide miro-hannels are shown in Figure B.3, Figure B.4, and Figure B.5 respetively. The silion material membrane is used in these alibration tests. 196

216 Figure B.3 Calibration test results of 40 x 35 x 5 wiking struture membrane The voltage and temperature data are olleted in a range of water bath temperatures from at 20 o C to 42 o C in these alibration tests. Again, the linear relationship is determined from these test data. The results also show the R 2 value of 0.99 for all test ases. The Figure B.6 shows the triple RTD alibration test results of the retangular mirowik hannel that has the dimensions of 40 x 70 x 5. The details of the triple RTD dimension are previously explained in setion 3.2. The edge RTD shows in the Figure B.6 is the third RTD explained in setion 3.2. The silion material membrane is used. The alibration results are reorded between the water bath temperatures of 24 o C and 42 o C, and these results are used to establish the linear relationships between the temperature and voltage data. The R 2 value of 0.99 is obtained for all three RTDs. 197

217 Figure B.4 Calibration test results of 40 x 50 x 5 wiking struture membrane Figure B.5 Calibration test results of 40 x 70 x 5 wiking struture membrane 198

218 Figure B.6 Triple RTD alibration test results for 40 x 70 x 5 wiking struture membrane Figure B.7 Triple RTD alibration test results for 40 x 5~80 wiking struture (Si) 199

219 Figure B.8 Triple RTD alibration test results for 40 x 5~80 wiking struture (SiNx) The triple RTD alibration test results of the 40µm high SU8 wall with the 80µm narrow to 5µm wide tapered hannels and SU8 walls are presented in Figure B.7 and Figure B.8. The details of the triple RTD designs are previously explained previously in setion 3.2, and the third RTD refers to the edge RTD in the hapter 5. The silion material membrane is used. The wiking struture membrane is alibrated with temperatures ranging from 22 o C to 40 o C. The equations in Figure B.7 shows the voltage to temperature relationship and the R 2 shows the auray fit between the linear urve and the data. The R 2 value of 0.99 is obtained. The silion nitride material membrane (SiNx) is used in the alibration test results shown in Figure B.8, and the dimensions of wiking struture and hannels are the 40µm high SU8 wall with the 80µm narrow to 5µm wide tapered hannels and SU8 walls. The 200

220 R 2 value of 0.99 is obtained between the experimental data and the alibrated linear urve. The linear relationships of the temperature and voltage are established and shown in equation forms as shown in Figure B.8. These alibration test results are used to onvert voltage hange to the temperature, thus a temperature profile aross the membrane an be measured in the evaporation experiments. 201

221 APPENDIX C 1. STEADY STATE EXPERIMENTAL TEST RESULTS Table C.1 40 x 35 x 5 onstant ross setion retangular miro-hannel evaporator: Si Table C.2 40 x 35 x 5 onstant ross setion retangular miro-hannel evaporator: Si Table C.3 40 x 50 x 5 onstant ross setion retangular miro-hannel evaporator: Si 202

222 Table C.4 40 x 50 x 5 onstant ross setion retangular miro-hannel evaporator: Si Table C.5 40 x 50 x 5 onstant ross setion retangular miro-hannel evaporator: Si Table C.6 40 x 50 x 5 onstant ross setion retangular miro-hannel evaporator: Si Table C.7 40 x 70 x 5 onstant ross setion retangular miro-hannel evaporator: Si 203