Surface Tension Flows inside Surfactant-Added Poly(dimethylsiloxane) Microstructures with Velocity-Dependent Contact Angles

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1 Micromachines 2014, 5, ; oi: /mi Article OPEN ACCESS micromachines ISSN X Surface Tension Flows insie Surfactant-Ae Poly(imethylsiloxane) Microstructures with Velocity-Depenent Contact Angles Jyh Jian Chen 1, *, Shih Chuan Liao 1, Mao Hsun Liu 2, Jenn Der Lin 3, Tsung Sheng Sheu 4 an Ming Miao Jr Department of Biomechatronics Engineering, National Pingtung University of Science an Technology, 1, Shuefu Roa, Neipu, Pingtung 91201, Taiwan; s: chaucer@love.url.com.tw (S.C.L.); clauiachen@gmail.com (M.M.) Department of Mechanical Engineering, National Chiao Tung University, 1001 University Roa, Hsinchu 30010, Taiwan; chaucer1114@gmail.com Department of Power Mechanical Engineering, National Formosa University, 64, Wunhua Roa, Huwei, Yunlin 63201, Taiwan; roni@ms13.url.com.tw Department of Mechanical Engineering, Chinese Military Acaemy, 1, Weiwu Roa, Fengshan, Kaohsiung 83059, Taiwan; chaucer.chenjj@msa.hinet.net * Author to whom corresponence shoul be aresse; chaucer@mail.npust.eu.tw; Tel.: (ext.7029); Fax: Receive: 6 January 2014; in revise form: 15 March 2014 / Accepte: 19 March 2014 / Publishe: 25 March 2014 Abstract: Filling of liqui samples is realize in a microfluiic evice with applications incluing analytical systems, biomeical evices, an systems for funamental research. The filling of a isk-shape polyimethylsiloxane (PDMS) microchamber by liqui is analyze with reference to microstructures with inlets an outlets. The microstructures are fabricate using a PDMS moling process with an SU-8 mol. During the filling, the motion of the gas-liqui interface is etermine by the competition among inertia, ahesion, an surface tension. A single ramp moel with velocity-epenent contact angles is implemente for the accurate calculation of surface tension forces in a three-imensional volume-of-flui base moel. The effects of the parameters of this functional form are investigate. The influences of non-imensional parameters, such as the Reynols number an the Weber number, both etermine by the inlet velocity, on the flow characteristics are also examine. An oxygen-plasma-treate PDMS substrate is utilize, an the microstructure is moifie to be hyrophilic. Flow experiments are conucte into both

2 Micromachines 2014, hyrophilic an hyrophobic PDMS microstructures. Uner a hyrophobic wall conition, numerical simulations with impose bounary conitions of static an ynamic contact angles can successfully preict the moving of the meniscus compare with experimental measurements. However, for a hyrophilic wall, accurate agreement between numerical an experimental results is obvious as the ynamic contact angles were implemente. Keywors: microfluiics; ynamic contact angle; gas-liqui interface; surface tension; filling process 1. Introuction During the last twenty years, microfluiic evices have been evelope for a broa range of applications in bio-analysis an chemical processing technologies. The original fabrication techniques of the microfluiic evices were erive from the semiconuctor inustry an most evices aopte silicon or glass as the substrates. These techniques were thought to be intricate an expensive. In recently years, polymeric materials have been extensively use for the fabrication of the microfluiic evices. Among these materials, poly(imethylsiloxane) (PDMS) receives a lot of attention ue to its optical transparency an biocompatibility an is utilize as the main substrate for various microfluiic systems. Liqui filling is commonly encountere in the operation of the microfluiic chip. Chips utilize lengthy microchannels to eliver liqui solution or air bubbles in liquis from one place to another or bring ifferent liqui fluis into microchambers [1]. Before using the microfluiic chips, the channels are usually washe via flushing through water or solvent, an then rie by hot air. When use, the inlet of the chip is connecte with a larger buffer liqui reservoir. The riving forces accompanie with surface tension will pull the liqui into the microchannels. Sometimes surface tension may be the sole riving force to help the liqui flow into the chip. Pressure, high electric fiels an gravity are usually exploite to rive the flow of liqui in microchannels. However, surface tension, which is typically negligible in macro-scale systems, is also a force responsible for a variety of physical phenomena involving small volumes of liqui. Molecules in the liqui state exert strong attractive forces on each other. Surface tension, a cohesive force, arises from attractive forces among the molecules in a flui, whereas an ahesive force to the wall acts on the flui interface at the contact point with the wall. Yang et al. [2] use the marching velocity or position of the meniscus front, which was riven by the capillary force an the gravitational effect, to measure the surface energy insie a parylene microchannel. They propose a one-imensional mathematical moel to evaluate the liqui-filling behavior in a straight microchannel. Kung et al. [3] emonstrate the balance among the inertial, surface tension, gravitational, an frictional forces of bloo flow characteristics in a glass microchannel. Trung et al. [4] use compresse air an air-sucking to loa the PCR sample into the microfluiic chip. The loaing rate of the sample results from the competition between the air pressure an the surface tension. They examine the epenence of the loaing rate of a PCR mixture on the thickness of the PDMS wall between the reaction chamber an the air jacket. The surface tension ominates the autonomous flui movement in a hyrophilic microchannel, e.g., glass or

3 Micromachines 2014, poly(methyl methacrylate) (PMMA) channels. However, because of the intrinsic hyrophobicity of PDMS or parylene, it is ifficult to move flui in a hyrophobic microchannel using only surface tension force. The avantages of utilizing the surface tension effect in microsystems inclue lower power consumption, ease of fabrication an no active fluiic component. A variety of applications for surface tension exist in microelectromechanical systems (MEMS), incluing hyrophobic valves [5], micro-injection moling [6], flow switches [7], liqui metering [8], surface tension-powere self assembly [9], microstructure formation [10], ink-jet printing [11], plasma extraction [12], an cell culture [13]. Experimental an numerical stuies of surface tension-riven flow in microchannels have been performe. Tseng et al. [14] stuie the process of a liqui slug, which was blown by an air flow moving in an out of the micro reservoir. They use the volume-of-flui (VOF) metho as a numerical scheme an consiere surface tension as a volumetric force. Results showe that the success of reservoir-filling strongly epens on the esigns of the hyrophilic wall surface an the wall shape/size of the flow network. Leu an Chang [15] presente the capillary stop valves an micro sample separator, which were using a pressure barrier. The pressure barrier of the stop valve esign coul be preicte well by utilizing the three-imensional meniscus metho. Jensen et al. [16] examine the quasi-static motion of wetting bubbles in microchannel contractions. The entire system close to equilibrium for all bubble positions was assume. Base on their analysis, they establishe three esign rules for reucing the pressure that is neee to push the bubbles out of the contraction. Chen et al. [17] examine the surface tension flow of open microchannels with turning angles from 45 to 135. It is shown that the turning angle plays a major role in the meniscus of liqui-gas interface shape. The simulation of surface tension-riven flow in microchannels has been attracting a lot of attention. Results were generate by assuming a constant value of the contact angle, which means that only the static contact angles were applie in all previous computational research. The contact angle is the angle between the free liqui surface an the confining wall, an is a result of the competition between surface tension an the ahesive force. When the competing forces are in balance, the contact line, i.e., the line where a soli meets the liqui-gas interface, oes not move an the matching contact angle is then calle static. If the forces are out of balance, the contact line will move towars its equilibrium position creating a ynamic contact angle. The velocity with which the contact line moves is calle the contact line velocity an is often moele as a function of the ynamic contact angle [18,19]. However, the static contact angle was still utilize to consier the moving meniscus qualitatively to euce some filling strategies in recent stuies. In numerical treatment of moving contact lines, contact angles are require an applie as a bounary conition at the contact line. However, the ynamic contact angle of the contact line epens on the velocity of the moving contact line. A mean-fiel free-energy lattice Boltzmann moel was use to solve the moving contact line problem of liqui-vapor interfaces an the ynamics of the wetting an movement of a three-phase contact line confine between two superhyrophobic surfaces [20,21]. The velocity fiels near the interface were in goo agreement with flui mechanics an molecular ynamics stuies. The ynamic contact angle in a microchannel coul be larger (avancing) or smaller (receing) than the static contact angle [22]. In all of the aforementione stuies, the effects of the relationship between the contact angle an the contact line velocity on the flow characteristics insie the

4 Micromachines 2014, microchannel or microchamber were not investigate. A computational moel with a simplifie linear relationship between the contact angle an the contact line velocity has been utilize in previous stuies. Baer et al. [23] evelope a finite element moving mesh moel in two sample problems: soli boy rotation of a flui an extrusion from a nozzle with a rectangular cross-section. Šikalo et al. [24] stuie the rop impact using a volume-of-flui base metho. The preicte time epenence of the rop-spreaing iameter an of the ynamic contact angle agrees well with the experimental ata for both the avancing an receing phases of the impact process. Afkhami an Bussmann utilize [25,26] three moels of contact angle variation with contact angle velocity on preictions of rop impact. The linear relationship between the contact angle an the contact line velocity is simple an can preict well the change of the ynamic contact angle. In our stuy, a generalize form with velocity-epenent contact angles is implemente for the calculation of surface tension forces in a volume-of-flui base moel. Unerstaning the liqui filling process is significant to esign microfluiic chips. Successful filling by the liqui flows of microchannels or microchambers is not as easy as that of a macro-scale system because the surface effects are significant [7]. Different geometry of microchannels or microchambers may result in ifferent filling behavior such as filling time or the possibility of entrapping an air bubble, etc. If the chip is poorly esigne, then air may easily become entrappe in the micro cavities, egraing the functions of the systems. In our previous stuy [27], the entrapment of air bubbles in the oval isk-shape chamber as a free surface move through the microstructure uring the filling process was examine. The two-imensional numerical results inicate linear relationships between the formation of the bubble an both the Weber number an the sum of the static contact angle an the change in the angle between the microchannels an the microchamber at the intersection. However, the flow front shapes iffere between numerical simulations an experimental interface locations, especially in regions in which the flow front entere the chamber after it passe aroun a sharp corner. Therefore, unerstaning the effects of surface tension, ahesion an inertia on flui flows with ynamic contact angles in microchannels or microchambers is of marke importance in the relate fiels of science, meicine an engineering. This work numerically establishes the filling processes of the liqui in the isk-shape microstructures by consiering microchambers with inlets an outlets fabricate using MEMS technologies. Three-imensional governing equations are aopte to simulate the flui flows insie the microfluiic evices. A general functional form with velocity-epenent contact angles is implemente for the accurate calculation of surface tension forces in a volume-of-flui base moel. The effects of the parameters of the functional form are investigate. Finally, the microfluiic evices are fabricate in PDMS substrates simply from a mol. Due to the hyrophobicity of the PDMS, the oxygen plasma treatment metho is use to moify the surface of PDMS microchannels to be hyrophilic. Flow experiments are conucte into both hyrophilic an hyrophobic PDMS microstructures an the results compare with those of numerical simulations. 2. Mathematical Moel an Numerical Methoology The liqui filling processes insie an oval or a circular isk-shape microchamber are accepte to be governe by the continuity an the Navier-Stokes equations subject to appropriate bounary an initial

5 Micromachines 2014, conitions. Numerical simulations are conucte to eluciate the motion of a liqui flow insie the microchannels an the oval isk-shape microchamber. Assuming that the flui obeys the linear Newtonian friction law an neglecting the compressibility, the governing equations comprise conservation of mass an momentum, an a scale function, F, of the liqui volume fraction insie a computational cell. The conservation equations of mass an momentum are solve to yiel the motion an the shape of the gas-liqui interface. The continuity equation can be expresse as follows: U 0 (1) where U is the flui velocity vector. The momentum equation for a continuum is the analogue of Newton s secon law for a point mass. The momentum principle states that the rate of change of linear momentum of material in a region equals the sum of the forces on that region. Two such forces may be inclue: boy forces, which act on the bulk of the material in the region, an surface forces, which act on the bounary surface. The momentum equation, i.e., the Navier Stokes Equation, is 2 U 1 1 U U P v U Fsv t (2) where t is time, ρ is the flui ensity, P is the static pressure, an v is the kinematic viscosity of the flui. The last term on the right han sie of Equation (2) is the volumetric surface tension, which can be calculate using the continuum surface force (CSF) moel. Surface tension-riven flows are source-term ominate, an convergent solutions become ifficult to obtain numerically. The orientation of the interface near the contact line reflects the contact angle, which is the angle between the normal to the liqui-soli interface an the normal to the soli surface at the contact line. A general correlation for the contact angle as a function of contact line velocity is not easy to be obtaine. van Mourik et al. [18] gave a brief summary about the contact angles moels. The theoretical stuies on the ynamic contact angle carrie out in the last few ecaes have le to numerous theoretical ynamic contact angle moels. In contrast with the theoretical analyses, ynamic contact angle moels have also been propose base on experimental measurements. The Blake s moel [28,29], which is base on molecular kinetics, is one of the most common use ynamic contact angle moels in numerical simulations. This moel has been examine for its success in escribing the experimentally observe behavior of the ynamic contact angle in many cases. The goo fit of the theoretical an experimental ata was avance as evience for accepting the propose theory. In the Blake's moel, the contact angle epens on the velocity. The relationship between ynamic contact angle an contact line velocity is essentially monotonic an is very similar to the hyperbolic tangent function. In a previous stuy [30], the hyperbolic functional form was also use to express the empirical moel for the ynamic contact angle. A single ramp moel with velocity-epenent contact angles [25] is implemente to moel the relationship between the contact angle an the contact line velocity in our stuy. The functional epenence an the require parameters are expresse in the following slope-intercept form, an shown in Figure 1.

6 Micromachines 2014, Figure 1. The slope-intercept form an the relationship between the contact angle an the contact line velocity. θ uc θ s θ lc Kvt s an max, min, lc uc (3) where θ is ynamic contact angle an v t is contact line velocity. K is the slope, an θ s, the static contact angle, can be interprete as the y-intercept of the line, the y-coorinate where the line intersects the y-axis. θ lc is the lower cutoff an θ uc is the upper cutoff of this functional form. The quaratic an the stretche hyperbolic tangent moels, shown in Figure 1, are also utilize to simulate the epenence of the contact angle on the local tangential spee of the liqui-gas interface, that is, contact line velocity. The functional epenence an the require parameters are for the quaratic moel an the stretche hyperbolic tangent moel expresse in the following Equations (4) an (5), respectively: 2 t a v bv c an t max, min, lc uc (4) an 3 2 tanha v bv cv (5) uc s t t t where a, b an c are constants. The 3 moels use to escribe the velocity epenency of the contact angle in our stuy have similar trens in the relationship between the contact angle an the contact line velocity, an are employe on preictions of the liqui filling processes in microchannels. The motions of a liqui flow insie the microchannels an the microchamber are compare among three moels. A finite volume approach is aopte using computational flui ynamics (CFD) software ESI-CFD (V2006, CFD Research Corporation, Huntsville, AL, USA) to moel the progress of a gas-liqui free

7 Micromachines 2014, surface. The metho is comprise of the volume-of-flui (VOF) metho [31], the interface tracking technique an the CSF surface tension moel [32]. The characterizing feature of the VOF approach is that the two fluis are consiere as one effective flui with a scalar variable F, calle the scalar function of the liqui volume fraction. F is a ratio of volume occupie by the liqui in a computational cell to the total cell volume. Given a flow fiel an an initial istribution of F over the gri, the evolution of the volume fraction istribution is etermine by solving the passive transport equation, U F 0 F t This equation must be solve together with Equations (1) an (2) to achieve computational coupling between the velocity fiel solution an the liqui istribution. In the numerical simulation, the surface tension at the free surface is moele with a localize volume force F in the framework of the continuum surface force (CSF) moel, which is ieally suite for the Eulerian interface of arbitrary topology [32,33]. In the Eulerian interface metho the gri mesh in the numerical computation is fixe an the flui an other objects flow across computational cells. The CSF moel eliminates the nee for etaile interface information an is commonly utilize in recent stuies. We can express F as the following: F sv F F F This volume force can then be incorporate into the momentum equations. Equation (6) must be solve together with Equations (1) an (2) to achieve computational coupling between the velocity fiel solution an the liqui istribution. The implementation of the bounary conition for the ynamic contact angle is incorporate within the framework of the CSF moel. Volumetric force applie at the soli walls is calculate with where n wall an t wall F n wall cos twall sin F represent outwar normal an tangential vectors for the walls, respectively. Therefore, F takes a unit value in cells that contain only liqui flui, an zero in cells that contain only gas. A cell that contains an interface woul have an F of between zero an unity. A three-imensional time-variant flui fiel is aopte to specify the flow characteristics of microsystems. The classification of the VOF metho as a volume tracking metho follows irectly from the use of F to escribe the istribution of liqui an to yiel the liqui volume evolution. One consequence of the purely volumetric representation of the phase istributions is that the interface between gas an liqui is not uniquely efine. Therefore, it must be ynamically reconstructe from the istribution of F. In this work, an upwin scheme with piecewise linear interface construction (PLIC) is aopte to etermine the flux of flui from one cell to the next an the curvatures of the surface. In the PLIC scheme, each cell has a unique surface normal that can be aopte to etermine the surface curvature from cell to cell, enabling the surface tension forces of the free surfaces to be calculate an ae. The etaile numerical methos were foun accoring to a previously reporte work [11]. sv sv (6) (7) (8)

8 Micromachines 2014, This work consiers a configuration of the flow systems. It comprises inlet/outlet microchannels an a circular or an oval isk-shape microchamber with an ahesive wall surface. The gri systems in the computational omain are selecte to ensure the orthogonality, the smoothness an the low aspect ratios that prevent numerical ivergence, shown in Figure 2. Poor orthogonality most irectly influences the accuracy of the flux calculations, whereas poor smoothness an high aspect ratios most irectly affect the accuracy of the surface reconstruction. Gri size sensitivity was analyze at the very beginning of the numerical simulations. Mesh ensity is increase continuously until it has minimal effects on the maximum velocity insie the system. Figure 3 shows the shapes of the liqui fronts at times of 0.02 s an 0.04 s at an inlet flow velocity of 0.1 m/s. The analyses of five mesh ensities ranging from to are use an the two finest meshes give a negligible relative ifference in their corresponing values which inicates they are mesh-inepenent. The values of maximum velocity insie the microchannel at two ifferent times for the five mesh ensities are also expresse in Table 1. Finally, the mesh ensity with has been chosen for further investigation since the maximum velocities insie the microchannel are almost the same an the numerical results are gri-inepenent. Figure 2. The gri systems of the computation omain for (a) oval an (b) circle isk-shape chambers.

9 Micromachines 2014, Figure 3. The shapes of the liqui fronts at times of (a) 0.02 s an (b) 0.04 s at an inlet flow velocity of 0.1 m/s at five mesh ensities. Gri1: , Gri2: , Gri3: , Gri4: , an Gri5: Number of noes Table 1. The analysis of the gri size inepenence. Maximum velocity at 0.02 s Relative ifference in maximum velocity at 0.02 s (%) Maximum velocity at 0.04 s Relative ifference in maximum velocity at 0.04 s (%) Gri1: Gri2: Gri3: Gri4: Gri5: Fabrication Process an Experimental Metho For the purpose of experimental characterization of the filling process of the microchamber, the microchannels an microchamber in poly(imethylsiloxane) (PDMS) substrate are covere with a PDMS or a glass plate. The flow evice from PDMS is fabricate by a replica moling metho. Initially, a silicon wafer is cleane an ehyrate on a hotplate. A thick film is fabricate by spin coating negative photoresist (SU-8) onto a silicon wafer. The resist is then soft bake on a level hotplate. The pattern is fabricate by photolithography using a photo mask. After evelopment, the master is washe an bake to fix the photoresist. A wafer with patterne SU-8 is then obtaine. Once the mol is complete, the wafer is rinse in eionize (DI) water an rie with nitrogen. The height of the positive

10 Micromachines 2014, patterns on the moling masters is 100 μm when measure with a surface profiler. The PDMS prepolymer mixture which is thoroughly mixe with the base solution an curing agent using a 10:1 weight ratio is egasse with a mechanical vacuum pump to remove air bubbles. After pouring the PDMS prepolymer mixture onto the wafer, micro-structures are fabricate using a PDMS replica moling process. The PDMS is then cure in an oven an the replicas are peele off from the mol. The inlet an outlet holes are then rille. Methanol is use as a surfactant to prevent two oxygen-plasma-treate PDMS replicas from being irreversibly bone when aligne improperly. A glass slie is also use to bon the PDMS replica. After O 2 plasma treatment an boning, the esigne microstructure, which consists of two microchannels an a microchamber has been fabricate. Due to the high hyrophobicity of PDMS, it is ifficult to transport aqueous flui on the PDMS surface without any external power. One of the avantages of fabricate PDMS microfluiic evices is easy visualization, so PDMS is still wiely use as the most important substrate for microfluiic systems. The O 2 plasma treatment metho is often use to moify the surface of PDMS microchannels to be hyrophilic [34]. Due to its instability, however, the oxiize PDMS surface slowly recovers its hyrophobicity after exposure to the ambient for a perio of time. Samples by the glass an PDMS surface moification are utilize to measure the contact angles an the results are shown in Figure 4. The mean value of the measurements at several measure times is use. The results emonstrate the wettability changes with the uration time of the glass (top sie) an PDMS (bottom sie) surfaces moifie with O 2 plasma. In this work, the time-epenent change of the contact angle can be observe clearly after surface treatment. The contact angle of unmoifie PDMS substrates remains at aroun from our measurements. Accoring to the literature, the contact angle of pure PDMS is greater than 105. However, the contact angle of PDMS with surface moification ecreases from 112 to 10. An it increases to 20 about 60 min after surface moification. Figure 4. The measurement of the static contact angle of water on the surface-moifie PDMS surfaces. 60 min 1440 min 60 min 1440 min

11 Micromachines 2014, The microchamber is esigne to stuy the effects of various forces such as inertia force, ahesion force an surface tension on the filling characteristics in a chamber. For the filling experiment in pressure-riven flows, flui is injecte into the microchannel using a syringe pump (Programmable Syringe Pump, KD Scientific, Holliston, MA, USA) at preset constant flow rates. The experimental setup for testing the performance of the fabricate microchamber is escribe as follows. One syringe is loae with DI water. The working flui first enters the inlet channel, flows through the microchamber, an finally exits through an outlet channel. Several experiments are performe with various flow rates for ifferent microchambers to investigate the effects of operational an geometrical parameters on filling performance. The filling patterns are ynamically recore using a computer system capture by a high-spee camera at a magnification of 40 with a graphic grabber system (VCD-Gear TV Plus) at rates of 125, 250, 500, an 1000 fps. The rate epens on the flow inlet velocity. 4. Results an Discussion In this section, two configurations of the flow network system are consiere. The microchannels are 100 μm wie, 100 μm eep, an the circular isk-shape microchamber has a iameter of 800 μm. These imensions correspon to angles between the microchannel an the microchamber at the intersection of The microchannels are 100 μm wie in the oval isk-shape microchamber for 700 μm an 250 μm of the semi-major an semi-minor axes. These imensions correspon to angles between the microchannel an the microchamber at the intersection of The chambers may have hyrophilic or hyrophobic surfaces. The contact angle of the air-water interface on the soli surface is specifie to simulate filling uner various surface conitions an to eluciate the mechanism by which the front changes in the chamber. In the following, the effects of the various parameters on the motion an the shape of the air-water interface in a circular isk-shape chamber are stuie first. Then, the comparisons between numerical an experimental results are shown. The above values of the parameters are use unless otherwise state. In an effort to unerstan the surface tension flows insie microfluiic chips, the changes in the shape of the liqui front are use to evaluate the liqui filling processes. Figures 5 an 6 plot the effects of various inlet velocities on the filling process for a microstructure. Weber numbers of an , an Reynols numbers of 50 an 10, are consiere, corresponing to inlet flow velocities of 0.5 an 0.1 m/s, respectively. The Weber number is the ratio of the inertia to the surface tension, an is given by 2 We U W. The Reynols number is the ratio of the inertia to the viscosity an is given by inlet Re U inlet W where U inlet is the inlet flow velocity an W is the with of the microchannel. ν an σ are the kinematic viscosity an the surface tension of the liqui, respectively. The static contact angle of the gas-liqui interface on a soli surface is use an taken to be 80. In Figure 5, the flui enters an inlet channel at a pumping velocity of 0.1 m/s. It presents the locations of the air-water interface as a function of time for t = , , , , , , , , , , an s, respectively. The liqui flows forwar an approaches the entrance of the chamber. Regaring the contact angle of 80, the liqui has a concave interface with air. When the interface reaches the sharp corner, the meniscus near this corner stops moving forwar an remains at this point until the bulk of the flow has avance sufficiently, allowing the meniscus to bulge sufficiently over the corner so that the contact angle at the ege reaches 80

12 Micromachines 2014, (marke by a blue otte circle). The ahesive force between the liqui an the soli wall is establishe to create a capillary pressure barrier that stops the flow. An abrupt enlargement in the cross-sectional area for the contact angle of 80 makes the pressure in the liqui become negative. Then, the capillary gating effect can be seen. At this point, the angle of the liqui meniscus must change to aopt the equilibrium contact angle at the slante walls. This sie of the meniscus escens own the sie of the chamber an along the surface. The other sie of the meniscus keeps moving forwar until it reaches the entrance of the chamber, because the wall of the inlet channel is tangential to the wall of the chamber an the inertia force continues to rive the liqui flow forwar. Then, the flow leaves the inlet channel, wetting the sie surface. This change in the angle between the microchannels an the microchamber at the intersection increases the gas-liqui area to more than the soli-liqui area for a given volume change, resulting in a negative opposing pressure. The surface tension of the meniscus an the liqui pumping force overcome this capillary pressure barrier that evelops when the cross section of the channel changes abruptly, establishing a positive pressure that pulls the liqui into the microchamber. We is equal to , so the surface tension ominates the flow mechanism. As the liqui flows into the chamber, the flow front becomes convex because of the inertia of the flui flow. The curvature of the wall of the chamber changes the shape of the front such that it becomes flat when the liqui occupies almost one-thir of the chamber volume. Then the shape becomes concave. The variations in the shape of the front are relate irectly to the inertia force an the properties of the wall. When the liqui meniscus reaches the outlet channel, one sie of the liqui meniscus reaches the sharp corner, an it stops moving forwar (marke by a re ashe circle). The other sie of the meniscus continues to flow through the chamber. When the angle of the liqui meniscus changes to the equilibrium contact angle at the sharp corner, the gas-liqui interface exits through the outlet channel. The results inicate that the change angles at the entrance an the exit of the chamber are closely relate to the flow progression when geometric changes occur at the connections between the chamber an the channels. Finally, the liqui completes the filling process. Figure 5. Filling process for inlet velocity of 0.1 m/s an θ s of 80. Re increases with the inlet velocity an the inertia force becomes ominant, as presente in Figure 6. An 80 static contact angle of the gas-liqui interface on a soli surface is use. The figure presents the results for t = , , , , an

13 Micromachines 2014, s, respectively, at an inlet velocity of 0.5 m/s. As the free surface reaches the sharp corner at the entrance of the chamber, the gas-liqui interface near this corner stops moving. The other sie of the free surface keeps moving. The inertial force causes the meniscus to move faster; it overcomes the flow resistance at the corner easily an rives the flui flowing into the chamber. The strong inertial force causes the interface to remain convex for almost two-thirs of the chamber volume. In Figure 6, the wave front shape is change from convex to flat an then to concave. When the flui flows into the outlet channel, inertia force pushes the free surface concave at one sie an convex at the other sie. Finally, the filling process is finishe without the entrapment of air bubbles. The competition between inertia an ahesion causes the shape to be linear insie the chamber for a long time. Figure 6. Filling process for inlet velocity of 0.5 m/s an θ s of 80. When the liqui flows through the microstructure, a precise agreement between simulate ata an experimental results is complicate [27]. Simulations are mostly generate by applying a static contact angle at the bounary conitions. However, the contact angle epens on the velocity of the moving contact line. The velocity-epenent contact angles must be realize for the accurate calculation of surface tension forces. Figure 7 shows the simulate velocity vectors as the liqui flows into the microstructure. We of an Re of 50 are use, corresponing to an inlet flow velocity of 0.5 m/s. The surface tension force ominates this case. Three ifferent moels of the contact angle variation with contact line velocity, v t, are employe on preictions of the liqui filling processes. The single ramp moel, the stretche hyperbolic tangent moel an the quaratic moel are utilize to compare these simulations, shown from left to right in Figure 7a c, respectively. Among these moels, θ s, static contact angle, is 80, θ lc, lower cutoff angle, is 45, an θ uc, upper cutoff angle, is 115. In the single ramp moel, K, the slope of the function, is 350 s/m. In the stretche hyperbolic tangent moel, a is 10 s 2 /m 2, b is 0 s/m, an c is 0. In the quaratic moel, a is 1750 s 3 /m 3, b is 350 s 2 /m 2, an c is 62.5 s/m. The functional epenences are shown in Figure 1. When the liqui-gas interface oes not move, i.e., v t equals 0 m/s, the static contact angle is use. The contact angle is consiere increase with the increasing of v t. From the top to the bottom in Figure 7, the results are present the results for t = , , , an s, respectively. The ifference is almost negligible at the four times. It means that the liqui filling processes insie our microstructures are approximately the same among three functional forms with specific parameters. The overall

14 Micromachines 2014, computational time for preicting the filling processes in our system by using the single ramp moel, the stretche hyperbolic tangent moel an the quaratic moel is about 36 h, 51 h, an 53 h per case, respectively, using a computer with Intel Core 2 Duo CPU T8300 an 2G RAM. However, the computational time for preicting the liqui filling process in our system is the shortest by using the single ramp moel. Thus the single ramp moel is chosen to prevent a lot of aitional computational time in the following simulations. Figure 7. Filling process for three moels: (a) single ramp moel; (b) stretche hyperbolic tangent moel; an (c) quaratic moel. Figure 8 plots the results concerning the motion of the gas-liqui interface at a velocity-epenent contact angle of a single ramp moel presente in Figure 7. In this case, K is equal to 350 s/m, θ s is 80, θ lc is 45, an θ uc is 115. It means that the contact angle increases linearly with v t from 80 to 115 while v t is uner 0.1 m/s, an the contact angle is invariant an equal to 115 while v t is greater than 0.1 m/s. When the gas-liqui interface reaches the sharp corner near the inlet or the outlet channel, the meniscus near this corner moves slowly an remains at the corners until the bulk of the flow has sufficiently avance. Concerning the wall ahesion properties, the wall is uner a hyrophilic conition (θ is less than 90 ) as v t is less than 0.03 m/s. The effect of a capillary pressure barrier oes not remain obvious; the flow front keeps moving into the chamber without stopping (marke by a blue otte circle). Compare with the results marke by a blue otte circle in Figure 5, the ahesive force between the liqui an the soli wall is establishe to create a capillary pressure barrier that stops the flow by regaring the static contact angle conition. Consiering the ynamic contact angle moel in Figure 8, the capillary pressure barrier near the sharp corner is negligible. From our previous results [27], the flow front shapes iffer between numerical an experimental ate in which the flow

15 Micromachines 2014, front enters the chamber after it passe aroun the sharp corner. It is foun that the flow front progresses into the chamber without stopping from visualize images. By utilizing the ynamic contact angle moel, the simulations compare with our experimental results [27] show a similar tren. When the liqui moves into the chamber an the cross-sectional area becomes large, the velocity of the gas-liqui interface starts to ecrease. With regar to the wall ahesion properties, the wall is uner a hyrophilic conition. The liqui moves along the circular chamber wall, an the flow is still riven by the inertia, so the meniscus bulges while entering the microchamber. Given a hyrophilic wall, the front is convex an then concave as the liqui flows through the chamber while wetting the sie surface. Figure 8. Filling process for the single ramp moel when K is 350 s/m, θ s is 80, θ lc is 45 an θ uc is 115. The effect of the parameters of the single ramp function at an inlet flow velocity of 0.25 m/s is stuie an emonstrate in Figure 9. We equals , an Re equals 25. When the liqui flows into the microstructure, the liqui/surface contact angle ranges between 50 an 85, 80 an 115, 110 an 145 for cases (a), (b), an (c), respectively. From the top to the bottom in Figure 9, the results are present the results for t = , , , , , an s, respectively. For a hyrophilic wall in case (a), the flow front keeps moving into the chamber without stopping because of surface tension an inertia. When the surface tension ominates, the flui flows into the chamber, wetting the sie surface, an the effect of a capillary pressure barrier oes not remain obvious. When the liqui moves into the chamber, the increase in the cross-sectional area of the chamber reuces the inertia. The interface stops moving at the sharp corner near the exit of the chamber an its angle changes to the contact angle. The interface retains its concave shape throughout the filling process. Given a hyrophobic wall for case (c), the front is convex as the liqui flows through the chamber without wetting the sie surface. After the meniscus reaches the sharp corner near the inlet or the outlet channel, it remains at the corners until the bulk of the flow has sufficiently avance. The liqui flow is still riven by the inertia, so the meniscus bulges over the whole chamber. The wave front becomes attache to the wall before the meniscus stretches across the whole chamber. The meniscus bulges sufficiently over the sharp corner near the outlet channel so the contact angle at the ege reaches impose conitions.

16 Micromachines 2014, Figure 9. Filling process for various θ s, θ lc an θ uc. (a) K is 350 s/m, θ s is 50, θ lc is 15 an θ uc is 85 ; (b) K is 350 s/m, θ s is 80, θ lc is 45 an θ uc is 115 ; an (c) K is 350 s/m, θ s is 110, θ lc is 75 an θ uc is 145. (a) (350, 50, 85, 15) (b) (350, 80, 115, 45) (c) (350, 110, 145, 75) From the previous work [18], it is presente that the contact angle increases with the increasing of the contact line velocity. For the single ramp function, K enotes the slope of the function. When K is large, the contact angle increases much as the contact line velocity becomes large. Figure 10 illustrates the results concerning the motion of the gas-liqui interface at various slopes of the single ramp function. In this case, θ s is 80, θ lc is 45, an θ uc is 115. K, the slope, is equal to 35 s/m, 350 s/m, an 1050 s/m, respectively, from left to right in Figure 10(a) to 10(c). It means that the contact angle increases linearly with the contact line velocity from 80 to 115 while v t is uner 1, 0.1, an m/s, an the contact angle is equal to 115 while v t is greater than 1, 0.1, an m/s, respectively. From the top to the bottom in Figure 10, the results are present the results for t = , , , , , an s, respectively. When K is 35 s/m, the microstructure for the liqui flow is generally uner a hyrophilic wall conition (the contact angle is

17 Micromachines 2014, less than 90 ) as v t is less than m/s. The flow front keeps moving into the chamber without stopping. The effect of a capillary pressure barrier oes not remain obvious. The interface stops moving at the sharp corner near the exit of the chamber an its angle changes to the contact angle. The same feature profile is use in Figure 10, but K is increase to 1050 s/m. A hyrophobic wall is generate (the contact angle is larger than 90 ) when v t is greater than m/s. The front is convex as the liqui flows through the chamber without wetting the sie surface. After the meniscus reaches the sharp corner near the inlet or the outlet channel, v t starts to ecrease. Then the contact angle ecreases an the walls become hyrophilic. The flow front keeps moving into the chamber or the outlet channel without stopping. The liqui flow is still riven by the inertia, so the meniscus bulges over the whole chamber. The interface escens along the outlet channel so air is almost entrappe. Finally, experimental an numerical stuies of surface tension-riven flow in our surface-moifie microstructures are performe. Because of the hyrophobicity of the PDMS, an oxygen plasma treatment is use to moify the surface of the PDMS substrate. Then the surface of PDMS microstructures can be moifie to be hyrophilic. Thus flow experiments are conucte into both hyrophilic an hyrophobic PDMS microstructures. In Figure 11, PDMS is use as a cover uner which the PDMS microstructure is fabricate using MEMS technology. The oxiize PDMS surface slowly recovers its hyrophobicity after exposure to the ambient after one ay. This PDMS is almost completely transparent in the visible spectrum. Flow experiments are conucte at least four times, uner the same conitions, to confirm repeatability. In each experiment, the total filling time is measure with a eviation of the orer of s. The experimental observations escribe below were repeatable. Figure 11 presents many experimental results obtaine in an oval microchamber an the microchannels are 100 μm wie an 100 μm eep with an inlet velocity of 0.02 m/s. One set of lengths of the semi-major an semi-minor axes of the oval isk-shape chamber are 700 μm/250 μm. From the top to the bottom in Figure 11, the results are present the results for t = , , , an s, respectively. The results are confirme by numerical simulation an experimental interface locations. The numerical results are also compare with experimental measurements an reveal similar filling processes. The parameters of the functional form of the ynamic contact angle for each case are (K, θ s, θ uc, θ lc ). A static contact angle is specific at the walls as K is equal to 0 s/m. The flow front shapes show similar results among case (a), (b), (c) an () experimental interface locations. The static contact angle of water on PDMS surface is about 105. For a pressure-riven flow, a flow hinrance effect with regar to the surface tension can be seen, so the range of the contact angle varies from 90 to 180 [2]. It means that the ynamic contact angles are still above 90 for a given hyrophobic conition. Results show that numerical simulations with impose bounary conitions of static an ynamic contact angles can successfully preict the moving of the meniscus compare with experimental measurements. A glass slie is also use to bon the PDMS replica. After O 2 plasma treatment an boning, the esigne microstructure has been fabricate. This chip is also almost completely transparent in the visible spectrum. Figure 12 presents many experimental results obtaine in similar conitions as those shown in Figure 11. The experiments are conucte aroun one hour after the PDMS surface moification. The static contact angle of water on the surface of glass-pdms boning microstructure is about 30, shown in Figure 4. From the top to the bottom in Figure 12, the results are present the results for t = , , , , an s, respectively. An it

18 Micromachines 2014, can be seen that the static contact angle remains the similar value at 40 min to 100 min after the oxygen treatment process. A flow hinrance effect with regar to the surface tension for a pressure-riven flow can cause the contact angle to range from 90 to 180. The assume hyrophilic an hyrophobic wall conitions for cases (a) an (b), respectively, cannot be use for accurate calculation of surface tension forces. The flow front shapes show similar results only between case (c) an () experimental interface locations. Results show that numerical simulations with a single ramp functional moel can successfully preict the moving of the meniscus compare with experimental measurements. Figure 10. Filling process for various K. (a) K is 35 s/m, θ s is 80, θ lc is 45 an θ uc is 115 ; (b) K is 350 s/m, θ s is 80, θ lc is 45 an θ uc is 115 ; an (c) K is 1050 s/m, θ s is 80, θ lc is 45 an θ uc is 115. (a) (35, 80, 115, 45) (b) (350, 80, 115, 45) (c) (1050, 80, 115, 45)

19 Micromachines 2014, Figure 11. Computational results corresponing to experimental measurements. (a) K is 0 s/m, θ s is 115, θ lc is 115 an θ uc is 115 ; (b) K is 0 s/m, θ s is 150, θ lc is 150 an θ uc is 150 ; an (c) K is 5000 s/m, θ s is 115, θ lc is 80 an θ uc is 150 ; () photographs of a microchannel evice showing liqui filling process. (a) (0, 115, 115, 115) (b) (0, 150, 150, 150) (c) (5000, 115, 150, 80) () Experimental results Figure 12. Computational results corresponing to experimental measurements. (a) K is 0 s/m, θ s is 30, θ lc is 30 an θ uc is 30 ; (b) K is 0 s/m, θ s is 150, θ lc is 150 an θ uc is 150 ; (c) K is 5000 s/m, θ s is 30, θ lc is 90 an θ uc is 150 ; () photographs of a microchannel evice showing liqui filling process. (a) (0, 30, 30, 30) (b) (0, 150, 150, 150) (c) (5000, 30, 150, 90) () Experimental results 1 2 3

20 Micromachines 2014, Figure 12. Cont Conclusions In this work, the filling processes of the liqui in a isk-shape microfluic evice are numerically stuie using microchambers with inlets an outlets fabricate by stanar MEMS technology. A three imensional computational moel is propose to trace the gas-liqui interface. Three ifferent moels of the contact angle variation with contact line velocity are employe on preictions of the liqui filling processes. The single ramp moel is chosen to prevent a lot of aitional computational time in our simulations. By utilizing the ynamic contact angle moel, the simulations compare with the previous experimental results [27] show a similar tren. The effect of the parameters of the single ramp function is emonstrate. The results specify the motion of the gas-liqui interface an the velocity vectors. Clearly, the wall ahesive conitions an the curve walls of the chamber significantly affect the shape of the gas-liqui interface uring filling, an the variations of the shape also epen on the Reynols number an the Weber number. Finally, the numerical results are compare with experimental measurements. The PDMS surface is treate with the oxygen plasma an the microstructure is moifie to be hyrophilic. Thus flow experiments are conucte into both hyrophilic an hyrophobic PDMS microstructures. The variant parameters of the functional form of the ynamic contact angle are investigate even with the experimental surface clearly hyrophobic or hyrophilic. Uner a hyrophobic wall conition, numerical simulations with impose bounary conitions of static an ynamic contact angles can successfully preict the moving of the meniscus compare with experimental measurements. However, for a hyrophilic wall, accurate agreement between numerical an experimental results is obvious as the ynamic contact angles were implemente. Acknowlegments The authors woul like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research uner Contract No. NSC B Daryl Switak is appreciate for his eitorial assistance.