Microparticle Influenced Electroosmotic Flow

Transcription

1 Brigham Young University BYU ScholarsArchive All Theses and Dissertations Microparticle Influenced Electroosmotic Flow John M. Young Brigham Young University - Provo Follow this and additional works at: Part of the Mechanical Engineering Commons BYU ScholarsArchive Citation Young, John M., "Microparticle Influenced Electroosmotic Flow" (2005). All Theses and Dissertations This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact scholarsarchive@byu.edu, ellen_amatangelo@byu.edu.

2 MICROPARTICLE INFLUENCED ELECTROOSMOTIC FLOW by John M. Young A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical Engineering Brigham Young University August 2005

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4 COPYRIGHT 2005 John M. Young All Rights Reserved

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6 BRIGHAM YOUNG UNIVERSITY GRADUATE COMMITTEE APPROVAL of a thesis submitted by John M. Young This thesis has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory. Date R. Daniel Maynes, Chair Date Brent W. Webb Date Jeffrey P. Bons

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8 BRIGHAM YOUNG UNIVERSITY As chair of the candidate s graduate committee, I have read the thesis of John M. Young in its final form and have found that (1) its format, citations, and bibliographical style are consistent and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the graduate committee and is ready for submission to the university library. Date R. Daniel Maynes Chair, Graduate Committee Accepted for the Department Matthew R. Jones Graduate Coordinator Accepted for the College Alan R. Parkinson Dean, Ira A. Fulton College of Engineering and Technology

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10 ABSTRACT MICROPARTICLE INFLUENCED ELECTROOSMOTIC FLOW John M. Young Department of Mechanical Engineering Master of Science The influence of microparticles on electroosmotic flow was investigated experimentally and numerically. Experiments were conducted using four different particle types of varying chemical composition, surface charge and polarity. Each particle type was tested at five different volume fractions ranging from φ = With a constant applied electric field, positively charged particles enhanced the electroosmotic flow by as much as 850%. The enhancement depended on particle composition, size and concentration. For negatively charged particles, the bulk electroosmotic flow was retarded with the largest reductions being 35%. This occurred for the greatest negative paricle concentration studied. A final experimental study utilizing a single volume fraction and particle type was conducted using microtube inner diameters of µm. It was found that the effective electroosmotic mobility decreases with increasing microtube diameter.

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12 A numerical study of microparticle influenced electroosmotic flow was also conducted for positively and negatively charged particles. A Galilean transformation was employed in which the particles were held stationary. A moving wall model was utilized to account for the particle velocity and the wall-induced electroosmotic flow. The particle-induced electroosmotic flow was also accounted for. A range of particle velocities were imposed in order to study the flow physics for a range of potential flows. Scenarios were run for a single tube diameter of 100 µm and a single particle diameter of 1.7 µm. Volume fractions of φ = 0.001, φ = and φ = were tested for both positively and negatively charged particles. At least two particle charges were studied for each volume fraction and polarity. Comparisons of the trends in the numerical model are qualitatively compared with the trends in the experimental data. The numerical and experimental data demonstrated similar trends. For positively charged particles, an increase in volume fraction showed a nonlinear increase in the average bulk flow velocity. For negatively charged particles an increase in volume fraction showed a nonlinear decrease in the average bulk flow velocity.

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14 ACKNOWLEDGEMENTS I would like to acknowledge and thank my beautiful wife who always believes in me even when I don t believe in myself. You inspire me everyday with your support and love for me. Without you, this would have been near impossible. I would also like to acknowledge my beautiful little girls. Your love and your smiles lift me up when life gets me down. Also, thank you to my parents. You always expected me to do my best and you helped me with loving hearts and hands to do just that. I would like to thank Dr. Maynes and Dr. Webb for the opportunity to work on this project. Your countless hours, especially these last few months, have been priceless. Thank you for all of the help and encouragement. It kept me going when I needed it the most. Finally, a special thanks to everyone in the lab, past and present. Thank you for your willingness to share your vast knowledge and for the laughter when the going got tough. You are and will continue to be an inspiration.

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16 TABLE OF CONTENTS TITLE PAGE...I COPYRIGHT...III SIGNATURE PAGES... V ABSTRACT...IX ACKNOWLEDGEMENTS...XIII TABLE OF CONTENTS...XV LIST OF FIGURES... XIX LIST OF TABLES...XXV LIST OF SYMBOLS... XXIX 1 INTRODUCTION INTRODUCTION TO ELECTROKINETICS Electroosmosis Electrophoresis MOTIVATION AND DEFINITION OF PROBLEM LITERATURE REVIEW PREVIOUS WORK CONTRIBUTION OF THIS WORK EXPERIMENTAL METHOD AND RESULTS EXPERIMENTAL SETUP AND METHOD Experimental Setup Definitions of Terminology Data Acquisition Method Particle Types and Concentrations Description of Tests Completed UNCERTAINTY ANALYSIS RESULTS AND DISCUSSION OF RESULTS Definition of Relative Velocity and Relative Mobility Particle Placement Tests Increased Conductivity with Particle Addition Concentration Tests Tube Diameter Tests MODEL DEVELOPMENT AND RESULTS NEED FOR A NUMERICAL SOLUTION DEVELOPMENT OF THE NUMERICAL SOLUTION Description of Physics and Transformation The Numerical Model Method and Description of Simulations Completed Model Approximations xv

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18 4.3 RESULTS AND DISCUSSION Positively Charged Particles Negatively Charged Particles QUALITATIVE COMPARISON OF EXPERIMENTAL AND NUMERICAL RESULTS CONCLUSIONS AND RECOMMENDATIONS OBJECTIVE SUMMARY RECOMMENDATIONS REFERENCES APPENDIX A EXPERIMENTAL DATA SHEETS A-1 PARTICLE PLACEMENT TESTS A-2 CONCENTRATION TESTS A-3 TUBE DIAMETER TESTS APPENDIX B USER DEFINED FUNCTION APPENDIX C HEAT TRANSFER ANALYSIS xvii

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20 LIST OF FIGURES Figure 1-1: Diagram showing the characteristics of the Electric Double Layer for silica water... 2 Figure 1-2: Diagram showing the characteristics of electroosmotic flow Figure 1-3: A silica particle flowing through water with an EDL... 7 Figure 1-4: Depiction of a relaxed electric double layer... 8 Figure 3-1: A diagram of the apparatus used to obtain the experimental data Figure 3-2: Diagram of the complete circuit including the apparatus Figure 3-3: A flow chart showing the layout and processes of a test Figure 3-4: Plot of the calibration data for the high voltage probe multimeter with accompanying linear curve fit and R 2 value Figure 3-5: Schematics for the response of positively and negatively charged solutions Figure 3-6: Relative velocity and mobility from particle placement tests on the MIN-U-SIL 5 particle type with the conditions: E z ~ 250,000 V/m, φ = 0.01, d micro = 100 µm and L micro = 10 cm Figure 3-7: Relative velocity and mobility results from particle placement tests of the GL-0258 particle type with the conditions: E z ~ 250,000 V/m, E z,both ~ 150,000 V/m, φ = 0.01, d micro = 100 µm, L micro = 10 cm Figure 3-8: Relative velocity and mobility results from particle placement tests of the HGS particle type with the conditions: E z ~ 250,000 V/m, φ = 0.01, d micro = 100 µm, L micro = 10 cm Figure 3-9: Relative velocity and mobility results from particle placement tests of the GL-0191 particle type with the conditions: Ez ~ 100,000 V/m, φ = 0.01, d micro = 100 µm, L micro = 10 cm Figure 3-10: Adjusted velocity and mobility results from concentration tests of MIN-U-SIL 5 with the conditions: dv/dl ~ 250,000 V/m, Particles in the Small Tank only, d micro = 100 µm, L micro = 10 cm Figure 3-11: Relative velocity and mobility for concentration tests of the GL-0258 particle type with the conditions: Particles in the Large Tank only, d micro =100 µm, L micro =10 cm. E z varies as follows: ,000 V/m; ,000 V/m; ,000 V/m; ,000 V/m; ,000 V/m Figure 3-12: Relative velocity and mobility results from concentration tests of the HGS particle type with the conditions: E z ~ 250,000 V/m, particles in the Large Tank only, d micro = 100 µm, L micro = 10 cm Figure 3-13: Adjusted velocity and mobility results for concentration tests of GL-0191 with the conditions: Particles in the Large Tank only, xix

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22 d micro =100 µm, L micro =10 cm. E z varies as follows: ,000 V/m; ,000 V/m; ,000 V/m; ,000 V/m; ,000 V/m Figure 3-14: The change in the relative mobility with volume fraction for the four particle types Figure 3-15: Relative velocity and mobility from tubes diameter tests of the GL-0191 particle type with the conditions: φ = 0.01, L micro =10 cm, Particles in the Large Tank only. E z varies as follows: 100 µm 120,000 V/m; 150 µm 95,000 V/m; 250 µm 60,000 V/m; 320 µm 50,000 V/m Figure 4-1: A depiction of the general physical phenomena present in microparticle influenced electroosmotic flow with negatively charged particles Figure 4-2: A depiction of the general physical phenomena present in microparticle influenced electroosmotic flow with positively charged particles Figure 4-3: Depiction of the actual scenario contrasted with the transformed scenario Figure 4-4: Front and side views of the tube geometry and the boundary conditions used for computational simplification Figure 4-5: 60 degree wedges of a six micron slice of a 100 micron diameter tube, showing volume fractions of (left) and (right) Figure 4-6: Charge potential distribution around a sphere as solved by Fluent Figure 4-7: Variation of the relative mobility with the arbitrarily imposed particle velocity for three volume fractions of positively charged particles (ζ = 90 mv) Figure 4-8: Variation of the relative mobility with the arbitrarily imposed particle velocity for three volume fractions of positively charged particles (ζ = 60 mv) Figure 4-9: Dependence of the relative mobility on the particle zeta potential for positively charged particles Figure 4-10: Variation in the relative mobility with the arbitrarily imposed particle velocity for positively charged particles ( φ = 0.001) Figure 4-11: Variation in the relative mobility with the arbitrarily imposed particle velocity for positively charged particles ( φ = ) Figure 4-12: Variation in the relative mobility with the arbitrarily imposed particle velocity for positively charged particles ( f = 0.025) Figure 4-13: Variation of the relative mobility with the arbitrarily imposed particle velocity for three volume fractions of negatively charged particles (ζ = 90 mv) Figure 4-14: Variation of the relative mobility with the arbitrarily imposed particle velocity for three volume fractions of negatively charged particles (ζ = 60 mv) Figure 4-15: Variation in the relative mobility with the arbitrarily imposed particle velocity for negatively charged particles ( φ = 0.001) Figure 4-16: Variation in the relative mobility with the arbitrarily imposed particle velocity for negatively charged particles ( φ = ) Figure 4-17: Variation in the relative mobility with the arbitrarily imposed particle xxi

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24 velocity for negatively charged particles ( φ = 0.025) Figure 4-18: Comparison of the results for the negatively charged particle model and the MIN-U-SIL 5 particle type Figure A-1: Plots for Small Tank tests of MIN-U-SIL Figure A-2: Plots for Large Tank tests of MIN-U-SIL Figure A-3: Plots for Both Tank tests of MIN-U-SIL Figure A-4: Plots for Small Tank tests of GL Figure A-5: Plots for Large Tank tests of GL Figure A-6: Plots for Both Tank tests of GL Figure A-7: Plots for Small Tank tests of HGS Figure A-8: Plots for Large Tank tests of HGS Figure A-9: Plots for Both Tank tests of HGS Figure A-10: Plots for Small Tank tests of GL Figure A-11: Plots for Large Tank tests of GL Figure A-12: Plots for Both Tank tests of GL Figure A-13: Plots for MIN-U-SIL 5 at a volume fraction of Figure A-14: Plots for MIN-U-SIL 5 at a volume fraction of Figure A-15: Plots for MIN-U-SIL 5 at a volume fraction of Figure A-16: Plots for MIN-U-SIL 5 at a volume fraction of Figure A-17: Plots for MIN-U-SIL 5 at a volume fraction of Figure A-18: Plots for GL-0258 at a volume fraction of Figure A-19: Plots for GL-0258 at a volume fraction of Figure A-20: Plots for GL-0258 at a volume fraction of Figure A-21: Plots for GL-0258 at a volume fraction of Figure A-22: Plots for GL-0258 at a volume fraction of Figure A-23: Plots for HGS at a volume fraction of Figure A-24: Plots for HGS at a volume fraction of Figure A-25: Plots for HGS at a volume fraction of Figure A-26: Plots for HGS at a volume fraction of Figure A-27: Plots for HGS at a volume fraction of Figure A-28: Plots for GL-0191 at a volume fraction of Figure A-29: Plots for GL-0191 at a volume fraction of Figure A-30: Plots for GL-0191 at a volume fraction of Figure A-31: Plots for GL-0191 at a volume fraction of Figure A-32: Plots for GL-0191 at a volume fraction of Figure A-33: Plots for GL-0191 in a 100 micron tube Figure A-34: Plots for GL-0191 in a 150 micron tube Figure A-35: Plots for GL-0191 in a 250 micron tube Figure A-36: Plots for GL-0191 in a 320 micron tube Figure C-1: Schematics for the energy balance performed on the microtube xxiii

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26 LIST OF TABLES Table 3-1: Statistical information for the particle types used in the experimentation Table 3-2: The concentration and mass for each volume fraction tested Table 3-3: Number of tests run and the type of test Table 3-4: Tabulated values for the uncertainty of each measured variable Table 4-1: Number of particles in a 60 degree wedge of a six micron slice of a 100 micron diameter tube at three volume fractions Table 4-2: Wall velocities entered into Fluent for positively and negatively charged particles and a zeta potential magnitude of 90 mv Table A-1: Particle Placement data for MIN-U-SIL 5 in the Small Tank (2/10/04) Table A-2: Particle Placement data results for MIN-U-SIL 5 in the Small Tank (3/13/04) Table A-3: Particle Placement data for MIN-U-SIL 5 in the Large Tank (2/11/04) Table A-4: Particle Placement data for MIN-U-SIL 5 in the Large Tank (3/13/04) Table A-5: Particle Placement data for MIN-U-SIL 5 in Both Tanks (2/12/04) Table A-6: Particle Placement data for MIN-U-SIL in Both Tanks (3/16/04) Table A-7: Particle Placement data for GL-0258 in the Small Tank (2/13/04) Table A-8: Particle Placement data for GL-0258 in the Large Tank (3/23/04) Table A-9: Particle Placement data for GL-0258 in the Large Tank (3/26/04) Table A-10: Particle Placement data for GL-0258 in Both Tanks (3/26/04) Table A-11: Particle Placement data for GL-0258 in Both Tanks (3/30/04) Table A-12: Particle Placement data for HGS in the Small Tank (2/24/04) Table A-13: Particle Placement data for HGS in the Small Tank (2/28/04) Table A-14: Particle Placement data for HGS in the Large Tank (3/8/04) Table A-15: Particle Placement data for HGS in Both Tanks (3/9/04) Table A-16: Particle Placement data of GL-0191 in the Small Tank (7/21/04 a) Table A-17: Particle Placement test data for GL-0191 in the Small Tank (7/21/04 b) Table A-18: Particle Placement data of GL-0191 in the Large Tank (7/19/04) Table A-19: Particle Placement data for GL-0191 in the Large Tank (7/20/04) Table A-20: Particle Placement data for GL-0191 in the Large Tank (3/4/05) Table A-21: Particle Placement data for GL-0191 in Both Tanks (7/21/04) Table A-22: Particle Placement data for GL-0191 in Both Tanks (3/7/05) Table A-23: Concentration data for MIN-U-SIL 5 at φ = (4/26/2004) Table A-24: Concentration data for MIN-U-SIL 5 at φ = (5/10/2004) Table A-25: Concentration data for MIN-U-SIL 5 at φ = (5/11/2004) Table A-26: Concentration data for MIN-U-SIL 5 at φ = (6/16/2004) Table A-27: Concentration data for MIN-U-SIL 5 at φ = (8/2/2004) Table A-28: Concentration data for MIN-U-SIL 5 at φ = 0.01 (2/10/2004) Table A-29: Concentration data for MIN-U-SIL 5 at φ = 0.01 (3/13/2004) Table A-30: Concentration data for MIN-U-SIL 5 at φ = (5/3/2004) xxv

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28 Table A-31: Concentration data for GL-0258 at φ = (5/14/2004) Table A-32: Concentration data for GL-0258 at φ = (5/17/2004) Table A-33: Concentration test data for GL-0258 at φ = (5/24/2004) Table A-34: Concentration data for GL-0258 at φ = (7/2/2004) Table A-35: Concentration data for GL-0258 at φ = (7/6/2004) Table A-36: Concentration data for GL-0258 at φ = (7/7/2004 a) Table A-37: Concentration data for GL-0258 at φ = (7/7/2004 b) Table A-38: Concentration data for GL-0258 at φ = 0.01 (7/7/2004) Table A-39: Concentration data for GL-0258 at φ = 0.01 (7/9/2004) Table A-40: Concentration data for GL-0258 at φ = (7/9/2004) Table A-41: Concentration data for HGS at φ = (5/31/2004) Table A-42: Concentration data for HGS at φ = (6/9/2004) Table A-43: Concentration data for HGS at φ = (6/3/2004) Table A-44: Concentration data for HGS at φ = (6/9/2004) Table A-45: Concentration data for HGS at φ = (6/14/2004 a) Table A-46: Concentration data for HGS at φ = (6/14/04 b) Table A-47: Concentration data for HGS at φ = 0.01 (3/8/2004) Table A-48: Concentration data for HGS at φ = 0.01 (6/2/2004) Table A-49: Concentration data for HGS at φ = 0.01 (6/11/2004) Table A-50: Concentration data for HGS at φ = (6/15/2004 a) Table A-51: Concentration data for HGS at φ = (6/15/2004 b) Table A-52: Concentration data for GL-0191 at φ = (7/26/04) Table A-53: Concentration data for GL-0191 at φ = (7/28/04) Table A-54: Concentration data for GL-0191 at φ = (7/26/04) Table A-55: Concentration data for GL-0191 at φ = (7/28/04) Table A-56: Concentration data for GL-0191 at φ = (7/26/04) Table A-57: Concentration data for GL-0191 at φ = (7/29/04) Table A-58: Concentration data for GL-0191 at φ = 0.01 (7/30/04 b) Table A-59: Concentration data for GL-0191 at φ = 0.01 (7/30/04 a) Table A-60: Concentration data for GL-0191 at φ = (7/28/04) Table A-61: Concentration data for GL-0191 at φ = (7/30/04) Table A-62: Tube Size data for GL-0191 at d=100 µm (7/30/04 a) Table A-63: Tube Size data for GL-0191 at d=100 µm (7/30/04 b) Table A-64: Tube Size data for GL-0191 at d=150 µm (7/19/04) Table A-65: Tube Size data for GL-0191 at d=150 µm (7/20/04) Table A-66: Tube Size data for GL-0191 at d=250 µm (8/3/04) Table A-67: Tube Size data for GL-0191 at d=250 µm (8/5/04) Table A-68: Tube Size data for GL-0191 at d=320 µm (8/4/04) Table A-69: Tube Size data for GL-0191 at d=320 µm (8/6/04) xxvii

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30 LIST OF SYMBOLS Acronym EDL EHD UDF UDS Acronyms Definition Electric Double Layer Electrohydrodynamics User Defined Function User Defined Scalar Roman Symbols Symbol Unit(s) Definition a m Particle radius a 0 V Least Squares Fit Coefficient a 1 V/V Least Squares Fit Coefficient A a m 2 Surface area of the microtube exposed to air A i m 2 Inner surface area of the microtube A r m 2 Radiative surface area of the microtube exposed to air A w m 2 Surface area of the microtube exposed to water c 0 mol/m 3 Electrolyte concentration far from the wall d m Microtube inner diameter d o m Microtube outer diameter D m Particle diameter D meas m Measuring tube inner diameter D micro µm Microtube inner diameter e C Elementary charge E z V/m Applied Electric Field E & gen W Rate of energy generated in the microtube E & W Rate of energy transferred to the microtube in E & W Rate of energy transferred from the microtube out F C/mol Faraday s constant; C/mol g m/s 2 Gravitational constant h a W/m 2 K Average heat transfer coefficient for air xxix

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32 h w W/m 2 K Average heat transfer coefficient for water h W/m 2 K Heat transfer coefficient for the inner surface of the microtube i h r W/m 2 K Radiative heat transfer coefficient I A Electric current k B J/K Boltzmann s constant; 1.38x10-23 J/K k s W/mK Thermal conductivity of silica k w W/mK Thermal conductivity of water L micro cm Microtube length L a m Length of the microtube exposed to air L w m Length of the microtube exposed to water m g Mass of particles n 1/m 3 Ionic strength of the fluid N Number of data points for Least Squares Fit N u D Average Nusselt number based on microtube inner diameter P Atmospheric pressure Pr Prandtl number r m Radial spatial coordinate R kj/kgk Universal gas constant; kj/kgk R 2 Quality of the least squares fit Ra D Rayleigh Number based on diameter S V/m 2 Momentum source term S ψ V/m 2 Potential source term t s Time T K Absolute temperature T K Absolute temperature of the surroundings T m K Absolute mean temperature in the microtube T i K Absolute temperature of the microtube inner surface T o K Absolute temperature of the microtube outer surface u m/s x-direction velocity U m/s Velocity U w m/s Moving wall model wall velocity U p m/s Particle Velocity U eo m/s Wall-induced electroosmotic velocity Ū m/s Average Velocity Ū eof m/s Average of pure electroosmotic run velocities xxxi

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34 V m V Measured voltage from the multimeter V s V Voltage measured from the source V p m/s Baseline Particle velocity V in V Voltage produced by the source V out V Voltage measured at the exit of the experimental apparatus V applied V Applied Voltage V solid m 3 Volume of the particulate material V total m 3 Total volume of the solution x cm Location of the fluid meniscus in the measuring tube x Streamwise coordinate y Wall-normal coordinate z Axial coordinate z Charge number Greek Symbols Symbol Unit(s) Definition ε C/Vm Permittivity of the liquid φ Volume fraction λ D m Debye length µ m 2 /Vs Electroosmotic mobility and effective electroosmotic mobility µ eof m 2 /Vs Average of pure electroosmotic run mobilities η kg/ms Fluid viscosity ρ kg/m 3 Fluid density ρ e C/m 3 Charge density σ W/m 2 K 4 Stefan-Boltzmann Constant, 5.67x10-8 W/m 2 K 4 σ m Uncertainty in the measuring tube diameter D meas σ m Uncertainty in the microtube diameter D micro σ V Uncertainty in the curve fit for the source voltage fit σ m Uncertainty in the microtube length L micro σ V Uncertainty in the accuracy of the source voltage dial source σ V Uncertainty in the accuracy of the voltmeter voltmeter σ V Uncertainty in the measuring the applied voltage V applied σ m Uncertainty in the change of location of the meniscus. x σ s Uncertainty in the change in time required to travel x t σ m 2 /Vs Uncertainty in the mobility µ xxxiii

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36 ψ V Electric Potential ζ V Zeta potential Symbol Unit(s) Mathematical Symbols Definition x 1/m First derivative in the x direction 2 2 x 1/m 2 Second derivative in the x direction 2 2 y 1/m 2 Second derivative in the y direction xxxv

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38 1 INTRODUCTION 1.1 INTRODUCTION TO ELECTROKINETICS The various phenomena present in electrokinetics have been recognized and studied for over a hundred years [1]. Electrokinetics defines those processes where a charged fluid-solid interface reacts to external influences. Electrokinetics is often categorized into four distinct phenomena. Two of these phenomena, streaming potential and sedimentation potential, are concerned with the generation of an electric field due to forced fluid or solid motions, where charged fluid-solid interfaces are present. These phenomena are not the focus of this research and the interested reader should seek elsewhere for more in-depth treatment of these occurrences [2,3]. The remaining two electrokinetic phenomena, electroosmosis and electrophoresis, are of significance to the research herein described. Electroosmosis is the motion of a fluid relative to a stationary charged surface under the influence of an applied electric field. Electrophoresis is the opposite, namely, motion of a charged surface, or particle, relative to a stationary liquid under the influence of an applied electric field. This thesis is concerned with the effects of combined electrophoretic particulate motion and induced electroosmotic flow. When an aqueous medium comes into contact with most surfaces, natural chemical reactions take place. These reactions result in the surface acquiring a charge. Counter-ions in the fluid are attracted to the surface in order to obtain charge equilibrium. 1

39 Potential 0.63ζ Diffuse Layer ζ Stern Layer Surface of Surface (Silica) Shear Figure 1-1: Diagram showing the characteristics of the Electric Double Layer for silica-water. Depending on the polarity of the surface charge, a predominantly positive or predominantly negative charge near the surface will exist. This accumulation is known as the Electric Double Layer, or EDL. A visual representation of the EDL for a silica-water interface is shown in Figure 1-1. The EDL is named for its two characteristic layers: the stern layer and the diffuse layer. The stern layer is a single layer of immobile ions adsorbed to the surface. This layer of ions partially equilibrates the charge of the wall. Therefore, the charge on the outer surface of the stern layer will be smaller in magnitude than the wall potential. The stern layer and the diffuse layer are divided by an imaginary plane known as the surface of shear, this plane is considered the location of zero velocity. The potential at this layer is known as the zeta potential, denoted ζ. The zeta potential is used as a boundary condition for the potential at the point of zero velocity and is thus essential in calculations of electrokinetic flows. The diffuse layer is a characteristic layer of mobile ions between the plane of shear and sixty three percent, or e -1, of the zeta potential. It consists predominantly of ions of opposite charge from that on the surface. The bulk motion of this layer, in 2

40 response to an applied electric field, is responsible for electroosmotic flow as will be discussed in Section The EDL is characteristically defined by the Debye length, or Debye shielding distance, denoted by λ D. The Debye length is an estimate of the approximate thickness of the EDL. It is derived from the Poisson equation and is shown symbolically as Equation 1-1: k B εt λ D = (1-1) 2 e n where k B is Boltzmann s constant, ε is the permittivity of the fluid, T is the absolute temperature of the fluid, e is the elementary charge and n is the ionic strength of the fluid. The size of this layer relative to the characteristic length of the flow geometry is an important parameter to determine the influence of electroosmosis. This is due to the fact that typical Debye lengths are on the order of one micron or less. Thus, the double layer becomes increasingly important as the characteristic length decreases. The potential in the electric double layer is analyzed using Poisson s equation with the Boltzmann distribution defining the ion concentration. This result is shown in Equation 1-2, a nonlinear equation for the potential [2]. 2 d ψ = 2 dx zfc ε 2 0 sinh zfψ RT (1-2) 3

41 1.1.1 Electroosmosis As defined previously, Electroosmosis is the motion of a fluid relative to a stationary charged surface as a result of an applied electric field. Consider a scenario in which distilled water is contained within a silica microtube and where the Debye length is small relative to the tube diameter. In this scenario, the silica obtains a negative charge. Thus, the EDL along the surface of the tube is positively charged. When an electric field is applied to the system, the ions in the diffuse layer of the EDL begin to flow towards the negative electrode. The ions exert a viscous drag body force on the surrounding fluid which causes bulk fluid motion. Figure 1-2 shows the simplified mechanics of electroosmosis for the scenario described above. The bulk fluid motion is governed by the ratio of the tube diameter to Debye length as well as the pressure and the applied electric field. In the case of large tube diameter to Debye length (d/λ D ), and in the absence of pressure gradients, the body force on the bulk fluid is concentrated near the walls and results in plug flow profiles. In the case of small d/λ D, the body force is no longer concentrated only near the walls, but can act across the entire tube cross section. However, as d increases, the relative magnitudes y z Figure 1-2: Diagram showing the characteristics of electroosmotic flow. 4

42 of the induced body force near the wall with respect to the total fluid volume diminishes. Consequently, the flow is much more influenced by small pressure gradients than by applied electric fields. Thus, electroosmosis exerts influence in flows through channels with diameters less than a few hundred microns. As discussed above, electroosmosis is the result of the induced body force due to the non-uniform charge distribution in the fluid. This body force is the product of the charge density and the electric field. The charge density may be determined from a solution of Poisson s equation [2]. Assuming steady, fully developed flow with no pressure gradients, the result is the simplified form of the z-momentum Navier-Stokes equation shown in Equation 1-3. η 1 u r = ee z r r r ρ ε ρ e = r r r ψ r η u r r r r ε ψ = r r r r E z (1-3) In the above equations, η is the fluid viscosity, u is the z component of velocity, r is the radial spatial coordinate, ε is the permittivity of the fluid, and ψ is the electric potential. ρ e E z is the body force term, where ρ e is the charge density and E z is the applied voltage gradient in the z direction. Equation 1-3 is solved using the conditions of zero gradients as r/λ D >> 1 and that ψ is equal to ζ at the point of zero velocity. In the limiting case of 5

43 large channel diameter to Debye length ratios, the resulting solution for electroosmotic velocity is shown as Equation 1-4. U εζ = E z (1-4) η The grouping of permittivity, zeta potential and viscosity is often referred to as the electroosmotic mobility, µ. Thus, the product of the mobility and the electric field yields the nearly one-dimensional velocity. Mobility is an important parameter and is only a function of the fluid and solid properties. It is constant for ideal fluid-solid interfaces. The overall magnitude of electroosmosis is affected by the fluid type and purity, the material of the tube or channel and the value of the applied electric field. Therefore, for a given set of conditions there is only one possible flow velocity and mobility. In order to vary these values, the conditions must be altered. It should also be noted that electroosmosis primarily occurs in dielectric fluids. As current is able to flow, the strength of the electric field decreases, and the flow diminishes. Also, as previously stated, electroosmotic flow is limited to fine channels Electrophoresis Electrophoresis is the motion of a charged surface, or particle, relative to a stationary fluid as a result of an applied electric field. The particulate becomes charged due to the same natural surface charging mechanism responsible for the development of the EDL. Electrophoresis occurs because the charged surface is free to move and is acted on by the applied electric field. The force experienced by the particle due to the electric 6

44 field is the predominant force in electrophoresis. There are other forces which arise due to the formation of the double layer and particulate motion. These forces have been termed [2]: Electrophoretic retardation Surface Conductance Relaxation Particle interactions Electrophoretic retardation, as illustrated in Figure 1-3 for a silica particle moving through water, results from electroosmotic flow around the particle. The applied electric field causes the negatively charged silica particle to flow towards the positive electrode. However, the EDL around the particle is positively charged and thus the liquid is acted on by a body force and flows towards the negative electrode. This electroosmotic flow around the particle impedes its motion and is termed electrophoretic retardation. Surface conductance arises due to an absence of charge neutrality in the EDL. This absence causes a local increase in conductivity which lowers the applied field as seen by the particle. This effect can typically be neglected in solutions with small particle Debye lengths relative to particle diameter (λ D /a <<1) [2,3]. Figure 1-3: A silica particle flowing through water with an EDL. 7

45 Figure 1-4: Depiction of a relaxed electric double layer. Relaxation takes into account the time required for the EDL around a mobile particle to adjust and develop as the particle moves through the fluid. The center of the EDL is offset from the center of the particle, which sets up a much smaller electric field behind the particle. This additional electric field results in a smaller net force experienced by the particle. Figure 1-4 shows this effect. This effect has been shown to be negligible for zeta potentials less than 25 mv, and for Debye length ratios (a/λ D ) greater than 300 or smaller than 0.1 [2]. Particle motion is also affected by particle-particle interactions as well as particle interactions with walls. It has been shown that solutions of particulate interact with each other and are impeded in their motion [4-6]. 1.2 MOTIVATION AND DEFINITION OF PROBLEM There is a desire to better understand electrokinetic phenomena due to the number of current and potential applications of electroosmosis, electrophoresis and combined systems. These applications range from separation processes which are used in the analysis of colloids and proteins to microcooling and micropumping devices. In most 8

46 microscale applications, both electroosmosis and electrophoresis will be significant and will impact each other. In many current separation applications, great effort is used to eliminate electroosmotic flow effects [7-9]. A better understanding of the interactions between electroosmosis and electrophoresis could yield a more desirable approach. Also, since electroosmosis is dependent only on fluid type and applied voltage, a method for varying the flow with particulate has potential benefit in situations where these parameters are fixed. Potential situations exist where the fluid used in an electroosmotic flow will contain particulate. Thus, there are many applications where a better understanding of the electrokinetic interactions and resulting total electroosmotic flow is of practical interest. The focus of this work will characterize for the first time the influence of particle type and concentration on the gross electroosmotic flow for flow through capillaries. This thesis will be focused in two directions. First, experimental data will be shown that provides a picture of the actual effects of dilute and concentrated solutions. Second, a mathematical model will be presented which accounts for the influence in combined flows. 9

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48 2 LITERATURE REVIEW 2.1 PREVIOUS WORK Due to its present and future applicability, much previous research has addressed the physics and modeling of microscale pumping. These pumps come in many forms, from mechanical to chemical. A thorough review of all of these techniques for micropumping, including strengths and weaknesses, has been written by Singhal et al. [10]. A method of electrokinetic pumping that has received considerable attention is known as electrohydrodynamic pumping or EHD. EHD is characterized by either traveling electric waves or ion injection from a point electrode. Most of the research in EHD has been done for macroscopic applications [11-12]. There has also been some research done on microscale EHD [13-14]. These microscale EHD flows show promise for high velocity electrokinetic flows. However, they require microscale fabrication of ion emitting and collecting electrodes. Electroosmosis does not require point emitters or collectors and thus avoids the problems of electrode microfabrication. Fundamental research into electroosmosis has led to understanding the parameters involved in the phenomena and in modeling their behavior. A summary of current understanding of the parameters involved and of the models primarily used in the literature can be found in a text by Probstein [2]. Experimental research has investigated various fluid types used to generate flow and the values of the wall zeta potential 11

49 associated with those fluids [15]. Recent research has been focused in many directions. One direction is the improvement of velocity measuring techniques [16-18]. Research is also being conducted on how to obtain the maximum zeta potential with surface treating [19]. Other research has been conducted to investigate the heat transfer involved in electroosmotic flows [20]. Recently work has been done to simplify the analysis of electroosmotic channel flows by introducing a moving wall model [21]. Fundamental research in electrophoresis has been primarily concerned with separation techniques, sedimentation and particle interactions. Information on the development of the electric double layer on both particulate and flat surfaces can be found in most texts which discuss colloid hydrodynamics or the chemistry of surfaces. A two volume set edited by Bier [22] describes the modeling and research done on particle electrophoresis. The first chapter of this work is concerned with the derivation of a model for particle velocity which considers all forces acting on a single particle in a stationary fluid. A text by Michov [23] also provides a good summary of different approaches to modeling single particle motion in a stationary fluid under the influence of an electric field. Two texts, one by Hunter [24] and one by Shaw [3], discuss in detail the phenomena of electrokinetics associated with electrophoresis. Both Hunter and Shaw present a discussion of the physics involved with two particles interacting. Shaw also presents a discussion of how electrophoretic measurements can be made in a close-ended tube. He discusses that these measurements are difficult to make due to recirculation created by electroosmosis and how measurements need to be made in region where electroosmosis can be neglected. He offers no discussion on how the particle motion and electroosmotic motion influence each other in these situations. None of the above authors 12

50 present a discussion of combined electroosmotic and electrophoretic flows in open ended channels. A number of studies have been conducted to investigate particle-particle and particle-surface interactions in electrophoretic flows including the texts of Hunter, Shaw and Van de Ven [25]. Anderson [4] derived a relationship between concentration and electrophoretic mobility. This was followed by other studies on the effects of concentration, both dilute [5,26-27] and concentrated [6,28-29] suspensions. Chen and Keh [5] investigated dilute solutions and concluded that for particles of equal zeta potential, the only factor influencing mean velocity is the volume fraction of the particles. Johnson and Davis [6] investigated the effect in concentrated suspensions. They showed that as the volume fraction increases, so also does the conductivity. This was confirmed in experimental work done for this thesis. All of the above studies investigate the electrophoretic mobility of single particles or clouds of particles and the associated conductivity of the solutions in unbounded fluids with no externally imposed fluid motion. There has been very little research done to show the combined effects of electrophoresis and electroosmosis. Ye and Li [30] created a model exploring the influence of gravity and settling effects on microparticle-influenced electroosmotic flows. Their research focused on the effects of gravity on individual particles. They considered that the particle was moving through an electroosmotically induced flow field but did not consider that this flow field would be affected by the particle motion. Their model also assumes that the particle zeta potentials would be limited to small potentials (<25 mv). In a recent paper [31], Ye and Li numerically investigate particle-particle interactions in a 13

51 rectangular channel. To do this they investigated two particles of various size and charge. Their paper also discusses the influence of a charged particle on the electric field. In summary, extensive research has gone into examining the electrophoretic mobility of single particles in unbounded, stationary fluids. Extensive research has also been conducted on how two particles interact with each other when brought into contact. Studies conducted on dilute and concentrated suspensions of particles have focused on how particle-particle interactions affect the overall electrophoretic mobility of the particles and do not consider the influence of an externally imposed electroosmotic flow. All of these studies focused on particle motion in unbounded stationary fluids. Very few studies have been conducted on particle motion in flows bounded by channel walls. These studies have considered only individual particles and have focused on the individual particle mobilities and not on the bulk fluid motion. Other studies involving channels have investigated eliminating electroosmosis by coating the channel walls. These studies do not discuss the effects of electroosmotic flow from the channel and its effects on the particle motion or on the bulk fluid motion. No previous work has considered the effects of combined electroosmosis and electrophoresis on the bulk motion of fluids through microchannels. There have also been no reports in the literature of measurements made of particulate solutions in uncoated capillaries. 2.2 CONTRIBUTION OF THIS WORK As stated above, there have been no experimental measurements reported in the literature for combined electroosmotic and electrophoretic systems. This work will 14

52 provide data for four distinct particle types, both positively and negatively charged, in silica capillaries with inner diameters between 100 and 320 micrometers. Data is provided for each of these particle types at five concentrations from dilute to concentrated. There is also no mathematical model provided in the literature which characterizes the bulk fluid motion generated by particulate solutions in electroosmosis generating capillaries. This work will provide a model for solutions of particles in microchannels containing electroosmotic flow. Therefore, this work is focused in two parts: A mathematical simulation of positively and negatively charged particles at five concentrations in a capillary producing an electroosmotic body force. Experimental measurements of bulk fluid motion under the influence of electrophoresis and electroosmosis. Measurements will be made with four different particle types at various concentrations and in various tube sizes. 15

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54 3 EXPERIMENTAL METHOD AND RESULTS 3.1 EXPERIMENTAL SETUP AND METHOD Average electrokinetic velocity measurements were taken in microscale flows involving different particle types, particle concentrations, and tube sizes. This was done to observe the physical dependence of each of these variables on the flow physics. The following sections describe the apparatus and method used to obtain average velocity data Experimental Setup A diagram of the apparatus which was used to obtain data is shown in Figure 3-1. It consists of two Lexan tanks, a large tank, which holds 1350 ml, and a small tank which holds 100 ml. The tanks are connected by a capillary microtube (Polymicro Technologies) which is fixed to the tanks by the use of vespel ferrules and Swagelok Meniscus Measuring Tube Large Tank cm Flow Small Tank Microtube Figure 3-1: A diagram of the apparatus used to obtain the experimental data. 17

55 fittings. The connections employ silicon sealant to prohibit flow of either fluid mass or electrical current. A one millimeter inside diameter tube (Polymicro Technologies) is also connected to the top of the small tank. This tube is referred to as the measuring tube. It runs parallel to the microtube and is mounted on a length scale. Hence, it can be used to allow measurement of the distance traveled by a liquid meniscus over time. Once the tanks are filled, they are brought into equilibrium by allowing the fluid to flow between them until the fluid levels in the large tank and the measuring tube are in equilibrium. This is accomplished with the use of connecting valves (not shown) in both tanks. Placed in each tank is a platinum electrode connected to a voltage source (Spellman CZE1000PN30) capable of producing up to 30 kv with either positive or negative polarity. Positive polarity is shown in the figure and was used in all experiments. Two multimeters (Fluke 87III, HP E2377A) were included in the circuit to measure both the exact applied voltage as well as the voltage drop across the microtube. This circuit is shown in Figure 3-2. The figure shows that the input and output voltages are measured before and after the apparatus. The applied voltage (V in ) is measured using a high voltage test probe V s V in V out Apparatus Figure 3-2: Diagram of the complete circuit including the apparatus. 18

56 (Simpson 0508). The 25 kv test probe contains a 500 MΩ resistor which allows a normal multimeter (HP E2377A), to be used to make measurements of V in. The current flowing through the apparatus is obtained by measuring the voltage (V out ) across a kω resistor and applying Ohm s law Definitions of Terminology In the following discussions of data acquisition, reference will be made to runs, data sets and tests. These terms are used throughout the remainder of this thesis and will be defined here. A test is a comparison of pure electroosmotic flow and microparticle influenced electroosmotic flow for a given set of conditions. A test is comprised of four data sets and a data set contains a number of runs, typically two. It is conducted with the same microtube and is completed in a two to three hour period. The first three data sets are pure electroosmotic flow (they contain no particles). Between each data set, the method of adding particles is followed to ensure that the process of particle addition does not affect the results. In this way, the first three data sets establish a control group for the fourth set which contains the particles. In summary: A Test is a comparison of electroosmotic flow and microparticle influenced electroosmotic flow for a given set of conditions. A Data Set is a portion of a test between which the particle addition process is followed. 19

57 A Run is a portion of a data set in which the meniscus travels along the measuring tube in a certain amount of time Data Acquisition Method Special care was taken to ensure that only the particles, not the process used to add the particles, affected the flow. As discussed in section 3.1.2, each test consisted of four data sets. Between each data set the process used to add particles was followed exactly. The first two times that the particle addition process was followed, no particles were added. Therefore, the results of the first three data sets reveal any effects of the process used to add particles and acts as a control group for comparison with the fourth data set, in which particles were added. The layout of a test is shown in Figure 3-3. As an example of how this process is carried out, consider a test in which particles are to be placed in the large tank only. To begin, distilled water is placed in the tanks and the fluid level is equalized. The outside of the apparatus is then thoroughly dried to eliminate potential current leaks. The voltage supply is attached to the electrodes and is turned on. The fluid moves through the microtube and into the small tank, this forces fluid up into the measuring tube where the velocity of the meniscus is measured using the Data Set One Pure EOF Typically Two Runs Particle Addition Process No Particles added Data Set Two Pure EOF Typically Two Runs Particle Addition Process No Particles added Data Set Three Pure EOF Typically Two Runs Particle Addition Process Particles added Data Set Four EOF with Particles Typically Six Runs Figure 3-3: A flow chart showing the layout and processes of a test. 20

58 attached ruler and a stop watch. This velocity measurement is defined as a run and is conducted twice. These two measurements comprise a data set. Once the data set is complete, the voltage supply is disconnected and the large tank is opened. The water is poured into a clean container. The water from the container is then poured back into the large tank, the tank is resealed and the fluid levels are then re-equalized. This same method is then repeated for the remaining data sets. After the third data set is completed, a measured mass of particles is placed in the clean container before the tank is emptied into it. The water is poured into the container and the particle solution is well stirred. This solution is then poured into the large tank, the fluid levels are equalized and the voltage supply is attached. For the fourth data set, six runs, or velocity measurements, are made. Both tanks are then emptied, and the tanks and container are washed with soap and rinsed well with distilled water in preparation for the next test. Also, a new microtube was used for each test. Therefore, a new microtube was then inserted for use in the next test. Generally speaking, this method is the same for all tests whether the particles were placed in the large tank, the small tank or both tanks, with the appropriate tanks being emptied and filled. For each run the following values were recorded: Distance traveled by the meniscus in the measuring tube Time needed for the meniscus to travel the measured distance The time averaged applied voltage from the source The time averaged voltage drop across the microtube 21

59 Once these values were recorded, the velocity and the bulk fluid mobility were calculated. The velocity in the microtube was found from the velocity in the measuring tube using conservation of mass as shown in Equation 3-1: U D = D meas micro 2 x t (3-1) where U is the average fluid velocity in the microtube, D meas is the measuring tube inner diameter, D micro is the microtube inner diameter, x is the distance traveled by the meniscus and t is the time required for the meniscus to travel the distance x. As discussed in Chapter 1, the bulk fluid mobility is defined as the velocity divided by the voltage gradient as shown in Equation 3-2: U E meas micro µ = = (3-2) z D D micro 2 x L t V applied where µ is the electroosmotic mobility, U is the average velocity, E z is the electric field, L micro is the total length of the microtube and V applied is the applied voltage. For a number of scenarios, multiple tests were conducted with the same conditions. This was done for two reasons. First, it was desired that the data could be shown to be repeatable. Ideally, a given fluid-solid interface such as silica-water should always yield the same velocity and mobility. In reality a number of factors influence the 22

60 magnitude of the electroosmotic flow and the microparticle influenced electroosmotic flows. These factors include the: Purity of the distilled water. Chargeable sites on a given silica surface. Temperature of the fluid or solution. Impurities in the particle solution. Therefore, a number of tests were conducted to obtain average values for a given set of conditions Particle Types and Concentrations Four particle types were selected based on size, density and chemical composition. These particles, as identified by their manufacturer, are: MIN-U-SIL 5 GL-0258 Sphericel 110P8 HGS GL-0191 The first particle, identified as MIN-U-SIL 5 by its manufacturer, was selected due to its similar composition with fused silica microtubes. The other particles were selected at varying amounts of silica composition as well as the amounts of other 23

61 Table 3-1: Statistical information for the particle types used in the experimentation. Particle Name Composition Size A particles /A wall Vendor MIN-U-SIL 5 SiO % < 10 µm φ = U.S. Silica Al 2 O 3 1.1% Median 1.7 µm φ = Fe 2 O 3, CaO, < 0.06% φ = TiO 2,MgO, φ = Na 2 O, K 2 O φ = Sphericel 110P8 HGS SiO 2 B 2 O 3 Na 2 O K 2 O Al 2 O % 7-13% 4-8% 4-8% 2-7% 4 21 µm Median 11.7 µm φ = φ = φ = φ = φ = Potters Industries Inc. GL-0258 SiO 2 Al 2 O 3 CaO B 2 O 3 MgO Fe 2 O 3 Na 2 O 45-65% 10-20% 10-25% 5-15% 0-8% < 2% < 1.5% <12µm Median 4 µm φ = φ = φ = φ = φ = Mo Sci Specialty Products GL-0191 SiO 2 Al 2 O 3 CaO MgO Na 2 O Fe 2 O % 0-5% 6-15% 1-5% 10-20% < 0.8% <12 µm Median 4 µm φ = φ = φ = φ = φ = Mo Sci Specialty Products elements. Table 3-1 shows the particles selected, their individual compositions, and their sizes. The particle sizes are as reported by the manufacturer. The mean particle diameter was not confirmed by separate measurement. As will be discussed in the next section, it was desired to test five concentrations for each of these particles. The concentrations were to cover the range from very dilute to relatively concentrated. Concentrations for particle solutions are often measured using what is known as a volume fraction. The volume fraction used in this research is defined as the ratio of the volume of solid material to the total volume as shown in Equation

62 V solid φ = (3-3) V Total φ represents the volume fraction, V solid is the volume of the solid material and V total is the total volume of the solution. A dilute concentration is considered to be φ<<1. A volume fraction of was selected as a dilute solution and was selected as a relatively concentrated solution. The remaining three fractions were selected at convenient amounts between those values. Once the volume fractions had been selected, the corresponding concentrations, in particles per cubic micrometer, were found. Using these concentrations the number of particles and the density of the particles were used to calculate the total mass of particles required to obtain the given volume fraction. Measuring the particles by mass eliminated the problems associated with measuring by volume, such as accounting for the air pockets between the particles. Table 3-2 shows the mass of particles required to obtain the desired volume fractions for a given particle type Description of Tests Completed Tests were completed to quantify the influence of particulate on electroosmotic flow when particles were placed in varying tanks at distinct concentrations and in different tube sizes. As tests were run, it was discovered that for the GL-0258 and GL particle types, at higher volume fractions, there was a maximum applied voltage which could be applied before electrical instability occurred. Therefore, as the volume fraction increased for these particle types, the applied voltage was decreased from the desired gradient of 250,000 V/m until a stable flow was acquired. A detailed discussion of this instability is found in Section

63 Table 3-2: The concentration and mass for each volume fraction tested. Total Volume Small Tank 100 ml Large Tank 1350 ml MIN-U-SIL 5 Properties Desired Concentration Small Tank Large Tank Both Tanks ρ [g/cm 3 ] φ particles/mm 3 m [g] m [g] m [g] x D [µm] x x m [g] x E x GL-0258 Properties Desired Concentration Small Tank Large Tank Both Tanks ρ [g/cm 3 ] φ particles/mm 3 m [g] m [g] m [g] x D [µm] x x m [g] x E x HGS Properties Desired Concentration Small Tank Large Tank Both Tanks ρ [g/cm 3 ] φ particles/mm 3 m [g] m [g] m [g] x D [µm] x x m [g] x E x GL-0191 Properties Desired Concentration Small Tank Large Tank Both Tanks ρ [g/cm 3 ] φ particles/µm 3 m [g] m [g] m [g] x D [µm] x x m [g] x E x

64 Table 3-3: Number of tests run and the type of test. Particle Placement Tests Particle Type Tank MIN-U-SIL 5 GL-0258 HGS GL-0191 Small Large Both Particle Concentration Tests Particle Type Vol. Fraction MIN-U-SIL 5 GL-0258 HGS GL Tube Inner Diameter Tests Particle Type Diameter MIN-U-SIL 5 GL-0258 HGS GL The particle placement tests were completed to determine whether the particles were positively or negatively charged. The varying concentration studies examined the influence of the overall particle concentration on the electroosmotic flow. Lastly, the tube diameter studies investigated the influence of varying the inner diameter of the tube. As discussed at the end of Section 3.1.3, multiple tests were completed for many of the scenarios. Table 3-3 shows the test scenarios and the number of tests completed. For example, for Particle placement tests with particles placed only in the small tank, two tests were completed for the MIN-U-SIL 5, HGS and GL-0191 particles types and one test was completed for the GL-0258 particle type. Not all tests were repeated due to the agreement of the results with what was expected. For example, for the particle GL-0258 placed in the small tank, one test 27

65 showed no effect, thus repeating it was unnecessary. Some tests were repeated more than once in order to obtain clarification if the repeatability of the results seemed unclear. 3.2 UNCERTAINTY ANALYSIS An uncertainty analysis was performed to quantify the amount of experimental uncertainty that exists. This was done for each run and experiment. The uncertainty was found in the electroosmotic mobility or, if particles were included, in the effective electroosmotic mobility. The electroosmotic mobility was defined in Equation 3-2. The uncertainty in Equation 3-2 is found using Equation σ D 2σ D σ x σ σ σ V meas micro t Lmicro applied σ µ = (3-4) Dmeas Dmicro x t Lmicro Vapplied 2 2 Where σ denotes the uncertainty in the subscript variable and the other variables have been defined previously. Using Equation 3-4, the uncertainty in the overall magnitude for every run was calculated and found to be in the range of ±12-17% depending on the test parameters. The primary source of this error is in the uncertainty associated with the microtube and measuring tube inner diameter. For a fixed tube, the uncertainty in the average velocity measurements would be much smaller than the ±12-17% values. Therefore, when comparing data for tests in a given microtube, the uncertainty would be much smaller. For this research, the goal was to understand the overall flow physics and the impact of the particle concentration and tube diameter on the flow. Thus obtaining exact values for the average velocity is not essential. 28

66 Table 3-4: Tabulated values for the uncertainty of each measured variable. Uncertainties U Lmicro [mm] 0.5 U Dmicro (100 µm) [µm] 6 U Dx [mm] 0.5 U Dmicro (150 µm) [µm] 6 U Dt [s] 0.5 U Dmicro (250 µm) [µm] 12 U Vapplied [V] U Dmicro (320 µm) [µm] 12 U Dmeas [µm] 50 The uncertainty of each variable is shown in Table 3-4. The uncertainties for the microtube length, x and t are all half the least count of the measuring devices. The uncertainties for the measuring and microtube diameters are those values reported by the manufacturer, Polymicro Technologies. The uncertainty in the applied voltage was derived from the calibration of the high voltage probe and the accompanying multimeter. The voltage supply has an analogdial which allows application of 30,000 volts in increments of 1000 volts. Voltage measurements from the multimeter were taken at each 1000 volt demarcation, these points were then fit with a least squares fit shown in Figure 3-4. The uncertainty in the linear curve fit was calculated using Equation 3-5 [32], N ( Vs [ a0 + a1v m ]) 2 i= 1 σ fit = (3-5) N 2 where σ fit is the uncertainty in the curve fit, N is the number of data points being fit, a 0 and a 1 are coefficients determined in the fit, V s is the source voltage and V m is the measured voltage from the high voltage probe. There was also a least count uncertainty from the voltage source and a least count uncertainty in the multimeter. The total 29

67 High Voltage Probe Calibration Source Voltage [V] V s = V m R 2 = Measured Voltage [V] Figure 3-4: Plot of the calibration data for the high voltage probe multimeter with accompanying linear curve fit and R 2 value. uncertainty in the voltage source was therefore the square root of the sum of these three uncertainties squared as shown in Equation 3-6 [32]. V applied 2 fit 2 source 2 voltmeter σ = σ + σ + σ (3-6) The uncertainty from the curve fit is volts. The uncertainty of the source is 500 volts and the uncertainty of the voltmeter is 0.5 volts. Therefore, the overall uncertainty, as shown in Table 3-4, is volts. 3.3 RESULTS AND DISCUSSION OF RESULTS Definition of Relative Velocity and Relative Mobility In all of the results presented hereafter, the average bulk velocity and the average bulk mobility are shown comparatively. As discussed earlier, some variation in the magnitude of electroosmotic flow velocities exists, dependent on solution purity and 30

68 other conditions. Therefore, in order to make meaningful comparisons, the measured average bulk fluid velocity data for each scenario is compared to the measured particlefree electroosmotic flow that exists. This is done by considering the relative change in the magnitude of the bulk flow velocity from the particle-free electroosmotic velocity. All of the data is thus presented in terms of the relative velocity, defined as (U Ū eof ) / Ū eof, where Ū eof is found by averaging the particle-free electroosmotic flow data points for that specific test. Therefore, the control runs all show values for the relative velocity of approximately zero. The values are not exactly zero due to the averaging involved in finding Ū eof. The presentation of velocity data in terms of the relative velocity, allows for meaningful comparison of trends. For all of the data presented, the relative velocity plots are accompanied by figures illustrating the effective bulk flow mobility. As discussed in Chapter 1, the net electroosmotic mobility in a particle free system is only a function of the properties of the microtube fluid-solid interface and is thus independent of the applied field and the velocity. The relative mobility is a measure of the mobility of particle-laden solutions and is a function of the fluid-solid interface of the microtube as well as the particle motion and the fluid-solid interfaces of the particles. The relative mobility is also independent of the applied electric field and the bulk flow velocity. The mobility is presented in a similar manner as described above for velocity as ( µ µ eof ) / µ eof. µ eof is found by averaging the mobility for the particle-free electroosmotic flow runs of the specific test shown. The magnitudes for Ū eof and µ eof for each test are shown in the figure legends. For the concentration tests of the GL-0258 and GL-0191 particle types illustrated in Section 31

69 3.3.3, the applied voltage was not constant. The values of the applied potential for each volume fraction are shown in the figure captions Particle Placement Tests The purpose of the particle placement tests was to determine both the surface charge sign (positive of negative) on the particles, as well as the best location for particle addition in the concentration and tube diameter tests. As discussed in Section 3.1.1, the electrode in the large tank was positively charged for all tests. This causes the electroosmotic flow, in a silica-water system where the walls of the tube are negatively charged, to flow from the large tank towards the small tank. Thus, the expected result for particles placed in the large tank and exhibiting a positive surface charge, is an increase in the average velocity relative to the particle-free electroosmotic velocity. In a similar manner, if the particles were placed in the small tank and exhibited a net negative charge, the average bulk fluid velocity is expected to decrease. Figure 3-5 illustrates these Negatively Charged Particle Solution No Particle Motion No Particles Positively Charged Particle Solution Particle Motion No Particles Electroosmotic Flow Direction Electroosmotic Flow Direction No Particles Particle Motion Negatively Charged Particle Solution No Particles No Particle Motion Positively Charged Particle Solution Electroosmotic Flow Direction Electroosmotic Flow Direction Figure 3-5: Schematics for the response of positively and negatively charged solutions. 32

70 expected responses to an applied electric field for both positively and negatively charged particle solutions. As can be seen in the figure, if a particle solution is negatively charged and is placed in the small tank only, it would be attracted to the positive electrode in the large tank and would cause a decrease in velocity relative to the particle-free electroosmotic velocity. Likewise, if the negatively charged particles were placed in the large tank only, the particles would not flow through the microtube at all and thus should not affect the flow. The opposite is true for positively charged particles. The bulk fluid velocity should increase when particles are placed in the large tank and is not affected when they are placed in the small tank. Figures 3-6 through 3-9 show the particle placement test results for the four particle types discussed. The particle placement tests were all conducted with a volume fraction of The applied electric field for the tests of particle placement, for all particle types except the GL-0191 particle type, was a constant magnitude of 250,000 volts per meter. The tube diameter used for these tests was 100 micrometers for all particle types except GL The GL-0191 particle type was tested using an applied electric field of 100,000 volts per meter and tube diameters of 150 micrometers. Results from the particle placement tests for the MIN-U-SIL 5 particle type are shown in Figure 3-6. The MIN-U-SIL 5 particle type has a similar chemical composition to silica microtubes, thus the particles are expected to have a net negative charge. These particles placed only in the small (negatively charged) tank, showed a decrease in the measured average fluid velocity relative to the pure electroosmotic velocity. This decrease is due to the negatively charged particles moving away from the negatively 33

71 No Particles Particles 0 ( U - U eof ) / U eof Small Tank Large Tank Both Tanks U eof = 1.89 cm / s U eof = 2.32 cm / s U eof = 2.64 cm / s Run No Particles Particles 0 ( µ - µ eof ) / µ eof Small Tank Large Tank Both Tanks µ eof = m 2 / Vs µ eof = m 2 / Vs µ eof = m 2 / Vs Run Figure 3-6: Relative velocity and mobility from particle placement tests on the MIN-U-SIL 5 particle type with the conditions: E z ~ 250,000 V/m, φ = 0.01, d micro = 100 µm and L micro = 10 cm. 34

72 charged electrode, through the microtube, in the opposite direction as the wall-induced electroosmotic flow. Thus, the bulk flow velocity is decreased and confirms the negative charge of the particles. The magnitude of the decrease measured nominally 7 millimeters per second, a decrease of 37%, from the particle-free electroosmotic velocity. MIN-U-SIL 5 particles placed only in the large tank initially had a negligible effect. However, as time elapsed, a noticeable change was observed as data collection proceeded. The average velocity was observed to decrease slightly and after 700 seconds the average velocity measured 2.5 millimeters per second lower than the average particlefree electroosmotic velocity, an 11% change. This change in velocity is contrary to the expected result for negative particles placed in a positively charged tank. The behavior is likely due to particle migration from the tank into the microtube over time. It could also be due to some particles being pulled into the microtube by the electroosmotic flow. Such particles provide additional flow resistance to the solution and would result in a decrease of the measured average velocity. When MIN-U-SIL 5 particles were placed in both tanks, the effect was similar to that of a combination of particles placed in the small and large tanks only. The decrease in average velocity for the both tank tests averaged 6.4 millimeters per second, a 24% change. The results of average velocity and relative mobility for Both Tank tests for all of the particle types will be discussed in greater detail below. The relative mobility results for the MIN-U-SIL 5 particle type are shown in the lower panel of Figure 3-6. The results show trends similar to the average velocity results. This is due to the fact that the relative mobility is calculated by dividing velocity by the applied potential. The potential is a constant and thus the result is a similar trend. 35

73 2 1.5 Small Tank Large Tank Both Tanks U eof = 2.69 cm / s U eof = 2.36 cm / s U eof = 2.36 cm / s 1 ( U - U eof ) / U eof No Particles Particles Run Small Tank Large Tank Both Tanks µ eof = m 2 / Vs µ eof = m 2 / Vs µ eof = m 2 / Vs ( µ - µ eof ) / µ eof No Particles Particles Run Figure 3-7: Relative velocity and mobility results from particle placement tests of the GL-0258 particle type with the conditions: E z ~ 250,000 V/m, E z,both ~ 150,000 V/m, φ = 0.01, d micro = 100 µm, L micro = 10 cm. 36

74 Results from the GL-0258 particle type show that when particles are placed in the large tank only, the flow is enhanced (Figure 3-7). This suggests that the GL-0258 particles exhibit a net positive surface charge. The positive particles move away from the positively charged large tank towards the negatively charged small tank. This is the same direction as the electroosmotic flow of the microtube and thus the bulk flow rate is enhanced. For the Large Tank only tests, the average velocity increased by nominally 2.8 centimeters per second relative to the pure electroosmotic velocity, a change of 119%. When particles were placed in the small tank only, there was no significant change in the flow velocity, confirming the conclusion that the particles are positively charged. The magnitude of the relative average velocity change is much larger for the GL particle type than for the MIN-U-SIL 5 particle type, measuring in centimeters per second as opposed to millimeters per second. This is most likely due to: (1) the magnitude of the surface charge on the particles; and (2) the fact that these particles have a much larger diameter. The MIN-U-SIL 5 particle type has a mean diameter of 1.7 micrometers and the GL-0259 particle type has a mean diameter of 4 micrometers. These differences could result in a greater influence on the average velocity results. The relative mobility results for particle placement in the small tank and the large tank for the GL-0258 particle type, show trends similar to the average velocity results. This occurs for the same reason as it did for the MIN-U-SIL 5 particle type. The velocity results are divided by a constant applied electric field. The relative mobility result for the test of both tanks did not follow the trend in the result for both tanks. Instead of following the velocity trend with a decrease from the control runs, the observed mobility result showed a negligible change from the particle-free mobility. This discrepancy is due to a 37

75 natural decrease in the applied voltage with increasing conductivity for this particle type. When the particles were placed in the large tank, the conductivity of the solution increased and the applied voltage decreased from 250,000 volts per meter to 150,000 volts per meter. However, this decrease in the applied electric field does not account for the decrease in the bulk flow velocity relative to the particle-free electroosmotic runs. Even at a lower applied voltage, the positively charged particles should enhance the flow. This unexpected velocity result is discussed in greater detail below. When particles are placed in both tanks, the expected result is a summation of the average velocity results from tests with particles placed in the large tank and the small tank only. This expected result was seen in the Both Tank test results for the MIN-U-SIL 5 particle type as well as for the HGS particle type (Figure 3-6 and Figure 3-8). For the MIN-U-SIL 5 particle type, the negatively charged particles in the small tank flow towards the positively charged electrode in the large tank, while the particles in the large tank remain in the large tank. The same is true for the HGS particle type. The positive particles in the large tank flow towards the negative electrode in the small tank, while those particles in the small tank remain in the small tank. This is the behavior expected for all of the particle types. However, for Both Tank tests with the GL-0258 and GL-0191 particle types (Figure 3-7 and Figure 3-9), the expected result described above did not occur. Instead, the observed phenomenon was an observed decrease of the average velocity. The expected result for both of these particle types was an enhancement similar to that seen in the Large Tank only tests. This phenomenon of decreased velocity is repeatable and at present unexplainable. 38

76 1.5 1 Small Tank Large Tank Both Tanks U eof = 2.24 cm / s U eof = 1.95 cm / s U eof = 1.87 cm / s ( U - U eof ) / U eof No Particles Particles Run Small Tank Large Tank Both Tanks µ eof = m 2 / Vs µ eof = m 2 / Vs µ eof = m 2 / Vs ( µ - µ eof ) / µ eof No Particles Particles Run Figure 3-8: Relative velocity and mobility results from particle placement tests of the HGS particle type with the conditions: E z ~ 250,000 V/m, φ = 0.01, d micro = 100 µm, L micro = 10 cm. 39

77 Although perplexing, the unexpected result of the both tank tests of these two particle types does not affect the objective of this research. The particle placement tests were done primarily to determine the polarity of the particle surface charge and to find locations for the particle placement of the particles for tests of concentration and tube size. The results from the Particle placement test of the HGS particle type are shown in Figure 3-8. When HGS particles were placed in the large tank only, the flow velocity was enhanced by 1.8 centimeters per second relative to the pure electroosmotic velocity, an increase of 92%. When they were placed in the small tank only, there was a negligible change in the measured velocity. This implies that the particles are positively charged. As stated above, HGS particles placed in both tanks showed the expected effect of increasing the flow rate similar to the results when particles were placed in the large tank only. The average velocity for the test of particles placed in both tanks resulted in a 1.7 centimeter per second (91%) increase over the pure electroosmotic velocity. As expected, the trends in the relative mobility results for the HGS particle type are similar to the trends of the average velocity results. The average velocity and relative mobility results for the GL-0191 particle type are shown in Figure 3-9. The GL-0191 particles are also positively charged in that they enhance the flow when placed only in the large tank and have a negligible influence on the average velocity when placed only in the small tank. The results are very similar to those for GL The velocity was increased by 2.1 centimeters per second (304%) when particles were placed in the large tank only. GL-0191 Particles placed in both tanks provided the same perplexing phenomenon as the GL-0258 particle type discussed 40

78 6 5 4 Small Tank Large Tank Both Tanks U eof = 0.59 cm / s U eof = 0.69 cm / s U eof = 0.75 cm / s ( U - U eof ) / U eof No Particles Particles Run 6 Small Tank Large Tank Both Tanks µ eof = m 2 / Vs µ eof = m 2 / Vs µ eof = m 2 / Vs ( µ - µ eof ) / µ eof No Particles Particles Run Figure 3-9: Relative velocity and mobility results from particle placement tests of the GL-0191 particle type with the conditions: Ez ~ 100,000 V/m, φ = 0.01, d micro = 100 µm, L micro = 10 cm. 41

79 previously. The mobility for the GL-0191 particles showed similar trends to the average velocity measurements. After the Particle placement tests were completed, it was found that one particle type, MIN-U-SIL 5, had a negative surface charge and that the remaining particle types were positively charged. For the positively charged particles, the GL-0191 particle type showed the greatest enhancement of the bulk flow velocity. The HGS particle type showed the smallest enhancement of the bulk flow. For the concentration and tube size tests, the particles were placed in either the small or large tank only depending on their charge, as determined from the Particle placement tests. The particle types were placed as follows for the Concentration and Tube size tests: MIN-U-SIL 5 Small Tank GL-0258 Large Tank HGS Large Tank GL-0191 Large Tank Increased Conductivity with Particle Addition For all of the particle types, when the particles were introduced, the electrical conductivity of the solution increased from that of the particle-free distilled water. For the MIN-U-SIL 5 and HGS particle types, the current increased from 0.25 µa for pure distilled water to the range of 5.5 µa to 30 µa when particles were present. This is an increase of as much as 120 times. For the GL-0258 and GL-0191 particle types, the increase was much larger. The current increased to the range of 72 µa to 150 µa, an increase of as much as 600 times. This large increase in the current for the GL-0258 and 42

80 GL-0191 particle types was accompanied by regions of vapor appearing in the microtube. These vapor regions created unsteady flow conditions as they traveled along the microtube and exited/discharged into the small tank. It was assumed that these vapor regions were created by a bulk temperature increase in the solution due to joule heating. Therefore, the microtube was analyzed with an energy balance to determine the bulk temperature of the fluid for all of the scenarios tested. The analysis considered convective and radiative heat transfer from the microtube. Actual measurements of the voltage drop across the tube and the current flowing through the tube were used to calculate the magnitude of the joule heating. The analysis was completed using a number of assumptions. The flow through the microtube was assumed to be steady and fully developed. The inner and outer surfaces of the microtube were considered to have constant surface temperatures and the surrounding room and air was assumed to have a constant temperature of 23 degrees Celsius. Regions of the tube covered by Swageloks and sealant were assumed to be perfectly insulated. Regions of the outer surface of the tube in the large and small tanks were assumed to be in contact with water at a temperature of 23 degrees. The properties of the polymide coating on the microtubes are unknown; therefore, the polymide was replaced in the energy balance with an equal thickness of silica. The thermal conductivity and the emissivity of silica were assumed to be constant with values of 1.38 W/mC [33] and 0.75 respectively. This value of the emissivity is lower than the reported value [33] but was chosen in order to have a conservative solution. Properties of water in the microtube and of the air around the microtube were considered temperature dependent. The heat generation in the microtube was assumed to be constant throughout and was calculated 43

81 by multiplying the voltage drop across the microtube by the current. With these assumptions, the highest bulk solution temperature in the microtube was found to be 34 degrees Celsius, well below the boiling point of water. The equations and values used for the energy balance can be found in Appendix C. From this analysis, it is concluded that these large increases in current does not raise the bulk fluid temperature enough to create the vapor regions. Therefore, the assumption is made that the increase in current creates localized regions of boiling, while the bulk solution remains well below the boiling temperature. Experimental evidence for this conclusion was seen as the vapor regions developed at seemingly random locations along the length of the microtube. A possible nucleation site for the regions of localized boiling could be in clumps of particles found in the flow. Air pockets could be trapped in the particle clumps which would provide a nucleation site for the boiling to begin. As mentioned, these vapor regions created unsteady and unstable flow characteristics. Therefore, in order to measure the greatest possible average velocity for the given particle type and volume fraction in a stable operating regime, the applied voltage was of necessity lowered as the particle concentration was increased. The voltage was reduced at each volume fraction until vapor regions no longer appeared in the microtube. It could be seen that vapor regions no longer appeared when the flow and the applied voltage measurements became steady. This new lower voltage was then utilized for both the control runs as well as the runs containing particle solutions for that volume fraction. The lower applied voltage did not create such large increases in current and, according to the energy balance described above, kept the temperature in the fluid at values only slightly higher than 23 degrees Celsius. The bulk temperature in the fluid 44

82 increased by only approximately 10 degrees Celsius for the highest measured current flow Concentration Tests Tests were run to determine the overall effect of particle concentration on the physical interaction between electroosmosis and electrophoresis, and the overall impact on the maximum stable average velocity. All tests were conducted using 100 micrometer diameter microtubes. For the MIN-U-SIL 5 and HGS particle types, the applied electric field was a constant 250,000 volts per meter. The applied electric field for all concentration tests of the GL-0258 and GL-0191 particle types varied with volume fraction. The reason for this variation was discussed in Section The results for the tests of concentration are shown in Figure 3-10 through Figure Figure 3-10 shows the results for the MIN-U-SIL 5 particle type. Generally speaking as the concentration of this particle type increases, the average velocity decreases. This is as expected. Negatively charged particles move opposite the tubeinduced electroosmotic flow, exerting a drag force on the fluid resulting in an overall reduction in the bulk fluid velocity. Each particle also induces an electroosmotic flow in the same direction as the tube-induced flow. As the concentration increases, the flow hindering drag force and the flow enhancing particle-induced electroosmotic flow increase. The presence of the particle-induced electroosmotic flow results in a nonlinear change in the bulk average velocity with increasing volume fraction. The velocity is decreased by an average of 3.2 millimeters per second relative to pure electroosmotic flow for the φ = volume fraction. This is a decrease of 16%. 45

83 0.2 No Particles Particles 0 ( U - U eof ) / U eof φ = U = 1.95 cm / s eof φ = U = 1.79 cm / s eof φ = U = 1.76 cm / s eof φ = 0.01 U = 1.92 cm / s eof φ = U = 2.57 cm / s eof Run No Particles Particles 0 ( µ - µ eof ) / µ eof -0.5 φ = φ = µ eof = m 2 / Vs µ eof = m 2 / Vs φ = µ eof = m 2 / Vs -1 φ = 0.01 φ = µ eof = m 2 / Vs µ eof = m 2 / Vs Run Figure 3-10: Adjusted velocity and mobility results from concentration tests of MIN-U-SIL 5 with the conditions: dv/dl ~ 250,000 V/m, Particles in the Small Tank only, d micro = 100 µm, L micro = 10 cm. 46

84 ( U - U eof ) / U eof φ = U = 1.89 cm / s eof φ = U = 1.22 cm / s eof φ = U = 1.02 cm / s eof φ = 0.01 U = 0.84 cm / s eof φ = U = 0.56 cm / s eof 0 No Particles Particles Run φ = φ = µ eof = m 2 / Vs µ eof = m 2 / Vs 10 φ = µ eof = m 2 / Vs ( µ - µ eof ) / µ eof φ = 0.01 φ = µ eof = m 2 / Vs µ eof = m 2 / Vs 2 0 No Particles Particles Run Figure 3-11: Relative velocity and mobility for concentration tests of the GL-0258 particle type with the conditions: Particles in the Large Tank only, d micro =100 µm, L micro =10 cm. E z varies as follows: ,000 V/m; ,000 V/m; ,000 V/m; ,000 V/m; ,000 V/m. 47

85 When the volume fraction is increased to φ = 0.025, the average velocity decreases by 9 millimeters per second (35%). As expected, due to the constant applied electric field, the relative mobility results show the same trends as the velocity results. Average velocity comparisons between volume fractions can be conducted for the GL-0258 particle type (Figure 3-11) despite the decrease in the applied voltage with increasing volume fraction. These are comparisons of the maximum stable average velocity. The maximum stable average velocity shows an increase between volume fractions of φ = and φ = to 5.19 centimeters per second, a 425% increase from Ū eof. After this point the velocity decreases with increasing volume fraction to 2.43 centimeters per second, a 434% change from Ū eof. This increase in average velocity followed by a decrease is likely due to the drop in the applied voltage with increasing volume fraction. For this particle type, comparisons of the relative mobility between volume fractions are more meaningful. This is due to the fact that the mobility is independent of the applied electric field. It is interesting to note that for this particle type the relative mobility worked out to roughly the same magnitude for the four highest volume fractions. This is due to the fact that as the applied electric field is decreased, the particle motion and induced electroosmotic velocities on the tube wall and on the particles, is also decreased. The relative mobility is calculated by dividing the measured average velocity by the electric field, both of which decrease in magnitude. Therefore effective mobilities of nominally the same value imply a comparable decrease in the velocity with the electric field for this particle type. The results for the HGS particle type are shown in Figure As stated previously, the applied voltage for this particle type was constant 250,000 volts per 48

86 ( U - U eof ) / U eof φ = U = 1.85 cm / s eof φ = U = 1.85 cm / s eof φ = U = 1.86 cm / s eof φ = 0.01 U = 1.89 cm / s eof φ = U = 2.08 cm / s eof No Particles Particles Run 8 φ = φ = µ eof = m 2 / Vs µ eof = m 2 / Vs 6 φ = µ eof = m 2 / Vs ( µ - µ eof ) / µ eof 4 φ = 0.01 φ = µ eof = m 2 / Vs µ eof = m 2 / Vs 2 0 No Particles Particles Run Figure 3-12: Relative velocity and mobility results from concentration tests of the HGS particle type with the conditions: E z ~ 250,000 V/m, particles in the Large Tank only, d micro = 100 µm, L micro = 10 cm. 49

87 meter. It can be seen that as the concentration increases, so does the velocity. This is as expected. The positive particles flow in the same direction as the wall-induced electroosmotic flow. Thus, the average bulk flow velocity is increased. This increase is due to the drag force that the particles exert on the fluid. As the number of particles increases, so does the drag force and thereby the average measured velocity. The increase is nonlinear due to the particle-induced electroosmotic flow which flows opposite the wall-induced flow. The lowest concentration has no significant influence on the measured flow velocity. As the concentration is increased, the change in the average velocity between the volume fractions also increases. The highest concentration shows a nominal velocity increase of 4.9 centimeters per second, an increase of 236% from particle-free electroosmotic velocity. At a volume fraction of φ = 0.01, the velocity increase is 1.2 centimeters per second, an increase of 63%.For the GL-0191 particle type (Figure 3-13), as with the GL-0258 particle type discussed previously, it is important to remember that the comparisons being made are for the maximum stable average velocities. This is due to the decrease in applied potential with increased volume fraction. For the GL-0191 particle type, the maximum average velocity reached approximately the same value at high volume fractions, an increase of 850%. This is likely due to the fact that the drop in applied voltage causes the velocities to drop in a manner such that the resulting average velocities come out to approximately the same value. Due to the variable applied voltage, an investigation of the relative mobility reveals an understanding of the flow physics. The effective mobilities for this particle type increase as the concentration increases. Therefore, as expected, for a constant applied potential, the bulk average velocity would increase with increasing concentration 50

88 ( U - U eof ) / U eof φ = U = 1.42 cm / s eof φ = U = 1.10 cm / s eof φ = U = 0.86 cm / s eof φ = 0.01 U = 0.59 cm / s eof φ = U = 0.56 cm / s eof 0 No Particles Particles Run φ = φ = µ eof = m 2 / Vs µ eof = m 2 / Vs ( µ - µ eof ) / µ eof φ = µ = m 2 / Vs eof φ = 0.01 µ = m 2 / Vs eof φ = µ = m 2 / Vs eof 4 0 No Particles Particles Run Figure 3-13: Adjusted velocity and mobility results for concentration tests of GL-0191 with the conditions: Particles in the Large Tank only, d micro =100 µm, L micro =10 cm. dv/dl varies as follows: ,000 V/m; ,000 V/m; ,000 V/m; ,000 V/m; ,000 V/m. 51

89 10 8 MIN-U-SIL 5 GL-0258 HGS GL ( µ - µ eof ) / µ eof φ Figure 3-14: The change in the relative mobility with volume fraction for the four particle types. meter. It can be seen that as the concentration increases, so does the velocity. This is as instead of leveling off. As the number of particles increases, the velocity produced by the drag force exerted by these particles also increases. Figure 3-14 illustrates the change in the relative mobility with volume fraction for the four particle types tested. Each data point is an average of the runs containing particles for that particle type and volume fraction. The lines shown on the plot are trend lines and are shown only for ease in visualizing the results. Generally speaking, as the volume fraction increased, the magnitude of the relative mobility also increased. Generally speaking, the GL-0191 particle type has the greatest increase in relative mobility with volume fraction and HGS has the smallest increase with volume fraction. The relative mobility of the GL-0258 particle type reveals an unexpected behavior. The 52

90 relative mobility increases with increasing volume fraction until the φ = 0.01 volume fraction. At this concentration there is a large decrease in the relative mobility. The reason for this behavior is unknown but is repeatable Tube Diameter Tests The tube diameter tests were conducted to investigate the effects of the microtube diameter on the combined electroosmotic and electrophoretic flow. The maximum stable average velocity and relative mobility results for these tests can be seen in Figure The Tube diameter tests were conducted using only the GL-0191 particle type at a volume fraction of As discussed in Section 3.3.3, the applied voltage was decreased as the microtube diameter increased. A decrease in the applied voltage was necessary due to the increase in the amount of current which can flow as the diameter increased. This increased current flow could cause vapor regions and unstable flow. Therefore, the applied voltage is decreased to obtain the maximum average velocity with stable flow. As with the concentrations test results for the GL-0191 particle type, it is important to note for comparison purposes, that the average velocity at each tube size is the maximum possible in the stable flow regime. As the diameter increases, the maximum average velocity measured through the microtube decreases. This is due to the fact that as the applied voltage is decreased, the force on the particles and ions in the solution decreases. These factors cause a decrease in the average flow velocity. Because of the varying applied voltage between the tube diameters, the relative mobility is meaningful for understanding the flow physics. As the 53

91 d = 100 µm d = 150 µm d = 250 µm d = 320 µm U = 0.69 cm / s eof U = 0.69 cm / s eof U = 0.41 cm / s eof U = 0.13 cm / s eof ( U - U eof ) / U eof No Particles Particles Run 24 d = 100 µm µ eof = m 2 / Vs 20 d = 150 µm µ eof = m 2 / Vs ( µ - µ eof ) / µ eof d = 250 µm d = 320 µm µ = m 2 / Vs eof µ = m 2 / Vs eof 4 0 No Particles Particles Run Figure 3-15: Relative velocity and mobility from tubes diameter tests of the GL-0191 particle type with the conditions: φ = 0.01, L micro =10 cm, Particles in the Large Tank only. E z varies as follows: 100 µm 120,000 V/m; 150 µm 95,000 V/m; 250 µm 60,000 V/m; 320 µm 50,000 V/m. 54

92 diameter increases, the relative mobility decreases. Thus, as the tube diameter increases, the amount of velocity produced by a single imposed applied potential would also decrease. Due to the change in applied voltage with tube diameter, a more meaningful analysis is completed by investigating the trends in the relative mobility. Generally speaking, as the diameter increases, the relative mobility decreases. This decrease reveals that higher velocities will be obtained with smaller tube diameters. This is likely due to the relative influence of the tube-induced electroosmotic flow on the average bulk velocity. There is a greater influence of the tube-induced flow with smaller diameter. 55

93 56

94 4 MODEL DEVELOPMENT AND RESULTS 4.1 NEED FOR A NUMERICAL SOLUTION As was shown in the experimental results of Chapter 3, microparticles in solution have a profound effect on electroosmotic flows. The influence of the electroosmotic flow induced at the wall on the bulk fluid is affected by the presence of the electrophoretically active particles. In like manner, the particle motion is affected by the bulk fluid motion generated by the electroosmotic body force at the wall. Therefore, analysis of these flows requires knowledge of the relative velocity of the particles or of the relative velocity of the bulk fluid. These velocities are not known and are dependent on each other. The problem of microparticle influenced electroosmotic flow is complex, and is thus modeled numerically. 4.2 DEVELOPMENT OF THE NUMERICAL SOLUTION Description of Physics and Transformation Consider a particle-laden solution in an infinitely long tube of material and diameter such that the charge on the tube and the charge on the particles is negative as shown in Figure 4-1. As the water comes into contact with the particle and wall surfaces, positively charged electric double layers develop. When the electric field is applied, electroosmotic flow develops around each particle as well as along the walls of the tube. 57

95 Combined Velocity Pure EOF Figure 4-1: A depiction of the general physical phenomena present in microparticle influenced electroosmotic flow with negatively charged particles. The applied electric field also exerts a force on the unrestrained charged particles causing them to move. In this scenario, the particles are moving opposite the wallinduced electroosmotic flow and thus, the flow velocity will be reduced as shown in the figure. It should be noted that while a slug profile is often expected (with small Debye length) in pure electroosmotic flow, it is not expected in combined flow and the slug profile as shown illustrates only qualitatively the change in magnitude of the flow. Figure 4-2 depicts positively charged particles which augment the electroosmotic flow velocity. Combined Velocity Pure EOF Figure 4-2: A depiction of the general physical phenomena present in microparticle influenced electroosmotic flow with positively charged particles. 58

96 Due to the complex nature of the combined electroosmotic/electrophoretic flow, the flow was modeled numerically. In order to model these physics directly, polydisperse spherical particles would move through a fluid domain, while an electroosmotic body force acts on the fluid at the tube and particle surfaces. While the body force can be numerically accounted for, a transformation in which the physics are analyzed from the perspective of stationary particles was adopted. Figure 4-3 shows the actual physical scenario contrasted with the transformed scenario. In the actual physical case, the fluid near the tube wall is acted on by the electroosmotic body force, resulting in a fluid velocity, U eo. A transformation is employed here in which the particles are assumed to be stationary, and the walls and fluid move with some relative velocity. Thus, in the transformed case, the electroosmotic velocity, or the velocity at the tube walls, is to be transformed by the particle velocity. The change of reference frame, therefore, changes the body force-induced electroosmotic velocity on the tube walls to a moving wall velocity. For thin Debye length, a wall velocity can be utilized for U eo without affecting the accuracy of the results. This was investigated by Tenny [21] who showed that electroosmotic flow can, in cases of small Debye layer thickness (d > 200λ D ), be appropriately modeled with a moving wall U eo U eo +U p U p U p U p U p Ū Ū+U p Up Up U eo U eo +U p Figure 4-3: Depiction of the actual scenario contrasted with the transformed scenario. 59

97 analogy. The magnitude of the body force-induced electroosmotic velocity is computed from Equation 1-4. This velocity is then summed with the particle velocity to obtain the required relative velocity at which the wall should be translated. Details of this transformation are described in Section After reaching a solution, the average fluid velocity through the tube cross section is transformed back relative to the particle velocity by subtracting the magnitude of the particle velocity. The result is the average fluid velocity in the microtube The Numerical Model The numerical solution for this study employed the computational fluid dynamics package Fluent. A three-dimensional geometry was created using Gambit. The threedimensional geometry allows for representation of electroosmotic flow around each particle. In order to decrease computation time, symmetry of the flow domain was exploited by creating a 60º wedge of the microtube section. This angle was arbitrarily selected. Periodic upstream/downstream boundary conditions were used to simulate an infinitely long tube. Figure 4-4 shows the microtube geometry and the boundary conditions utilized. A front and a side view of the tube section is presented showing the 60º wedge and the boundary conditions. For simplification purposes, it was assumed that the particles are monodisperse with a particle mean diameter of 1.7 micrometers and that they are uniformly spatially distributed. 1.7 micrometers is the mean diameter of the MIN-U-SIL 5 particle type, which was chosen arbitrarily. The purpose of this model is to examine trends for conditions representative of those explored experimentally. With 60

98 Front View Side View Symmetry Boundaries Periodic Boundaries Wall Figure 4-4: Front and side views of the tube geometry and the boundary conditions used for computational simplification. these assumptions, an analysis of the number of particles needed to obtain uniform particle dispersion in a given section of tube was completed for three volume fractions varying from dilute to concentrated. The number of particles needed in a 60 degree wedge of a six micron slice of tube to simulate the desired particle volume fractions are shown in Table 4-1. After the tube geometry was created, the appropriate number of spheres, as shown in Table 4-1, were placed in the tube section. The spheres were placed as uniformly as possible, accounting for spacing between the spheres in all directions including upstream and downstream. These spherical volumes represent the stationary particles. Examples of the geometry, including particles, in a 60 degree wedge are shown in Figure 4-5 for volume fractions of and Table 4-1: Number of particles in a 60 degree wedge of a six micron slice of a 100 micron diameter tube at three volume fractions. VOLUME FRACTION PARTICLE d = 1.7 µm

99 Figure 4-5: 60 degree wedges of a six micron slice of a 100 micron diameter tube, showing volume fractions of (left) and (right). In order to model the reference frame transformation illustrated schematically in Figure 4-3, an electroosmotic body force is present in the fluid surrounding each charged particle. The body force arises due to the presence of the EDL. As discussed in Chapter 1, the EDL is a charge accumulation near a surface which decays exponentially with distance from the surface. In Fluent, this electric potential distribution is created using what Fluent defines as a User Defined Function, or UDF. The UDF allows the creation of a User Defined Scalar (UDS) which can be solved in Fluent similar to velocity or temperature. A UDF was written which stores a source term for a scalar transport equation which calculates the charge potential throughout the domain. The scalar equation solved in this case is shown in Equation