Fluid filling into micro-fabricated reservoirs

Sensors and Actuators A 97±98 (2002) 131±138 Fluid ®lling into micro-fabricated reservoirs F.-G. Tsenga,*, I.-D. Yanga, K.-H. Linb, K.-T. Maa, M.-C. Lub, Y.-T. Tsenga, C.-C. Chienga a Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30043, Taiwan, ROC Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu 30043, Taiwan, ROC b Received 11 June 2001; received in revised form 5 November 2001; accepted 5 November 2001 Abstract This study reports that the success of reservoir-®lling strongly depends on the designs of the hydrophilic wall surface and the well shape/ size of the ¯ow network. The idea is illustrated both by experiments and numerical simulations: micro-particle-image-velocimetry (m-PIV) system is setup to monitor the process of a liquid slug moving in and out of the micro-reservoir and numerical computations are performed by solving ®rst principle equations to provide the details of the ¯ow process. The cross-check between measurements and computations validate the computations. Numerical computations solve conservation equations similar to homogenous ¯ow model used in two phase ¯ow calculation in cooperation with volume-of-¯uid (VOF) interface tracking methodology and continuum surface force (CSF) model. The simulations show that wall surface property as hydrophilic/hydrophobic is a dominating factor in ®lling processes of reservoirs of various shapes. A ¯ow system consisting of micro-channels and micro-wells is fabricated using MEMS technology to demonstrate the ®lling process and validate numerical simulation. The agreement between measurement and computation helps to fully understand the process. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Hydrophilic; Surface tension; Micro-reservoir; Computational model 1. Introduction Micro-¯uidic devices for bio-medical applications usually are combinations of passive and active parts, network of the micro-channels and micro-wells are the major passive components of the device. Micro-channels direct and distribute the bio-¯uids to micro-wells of which spaces for bio-reactions and processes. Successful ®lling of the micro-well is not as trivial as the ®lling in macro-scale system, which is resulted from the large ratio of surface area and volume. Surface properties have signi®cant effects on micro-scale ¯ow system (<1 mm) and have been demonstrated in many studies. Controlling liquid slug motion inside micro-channels is an interesting issue and the manipulation of the ¯ow based on patterning surface free energies is an example [1]. The fabrication of the ¯ow system is complicated, time-consuming and expensive. It is interested to have a reliable design tool to foresee the ®lling process. In the present study, ®lling processes of liquid slugs through three con®gurations of the ¯ow network are * Corresponding author. Tel.: ‡886-3-715131x4270; fax: ‡886-3-5720724. E-mail address: [email protected] (F.-G. Tseng). demonstrated either by experiments or numerical simulations, the wall surface property of hydrophilic/hydrophobic is the emphasis. Both approaches of experiments and numerical simulations should be able to reveal design features for complete ®lling, partial ®lling, or zero ®lling of the microreservoir. 2. Numerical simulation approach The approaches of numerical simulations are performed for the movement of a liquid mass inside ¯ow network. Since surface tension force is the major effect and the total surface force depends on the orientation and surface area of the liquid±gas interface, precise determination of the moving location and shape of the interface is the key issue of accurate computation. As a result, the numerical scheme for interface tracking must be robust with high resolution. Present study chooses volume-of-¯uid (VOF) method [2,3] for two phase homogenous ¯ow model [4] and the interface tracking technique in co-operation with CSF surface tension model [5], the ¯ow-®eld of gas phase as well as the liquid ¯ow-®eld must be calculated because the boundary of the liquid phase (liquid±gas interface) is part of the 0924-4247/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 ( 0 1 ) 0 0 8 2 6 - 3 132 F.-G. Tseng et al. / Sensors and Actuators A 97±98 (2002) 131±138 solution. Moreover, transient histories of the gas±liquid interface shape can be obtained. The governing equations consist of equations for a scale function F of liquid volume fraction inside a computational cell, and conservation equations of mass and momentum. The averaged value of F represents the phase state and fraction in the cell, i.e. F ˆ 1 if computational cell is fully occupied by the liquid, F ˆ 0 if the cell is fully occupied by the gas, and F is between 1 and 0 at the cell containing an interface. Under the assumption of incompressibility, the volume fraction F obeys the continuity equation: @F ~ ‡ Um
rF ˆ 0 @t (1) where Um is the velocity of the liquid±gas mixture. Solving volume fraction equation accurately is the key preserving the sharpness of interface. However, due to the topology and numerical consideration, Eq. (1) is integrated R with control volume, V F ˆ F dV, then integrated Eq. (1) can be discretized in time as follows: Z X ~m † dV F dV F;n ˆ dt r
U (2) V F;n‡1 V F;n ‡ ~m
AF dt, estimated from the The volume ¯uxes, dV F ˆ U geometry of control volume, is the main feature of the VOF. The conservation equations of mass and momentum are the basic equations to be solved, and they must be incorporated with PLIC±VOF interface tracking methodology to capture the interface. The equations can be expressed as follows: @rm ~m † ˆ 0 ‡ r
rm U @t continuity equation† (3) into three regions by the interface Eq. (7): 8 r0 behind interface > < > 0 for~ ~ n c ˆ 0 for~ r0 on interface r0
~ > : < 0 for~ r0 front interface The unit normal vector, estimated from volume fraction gradient ~ n ˆ rF=jrFj, is the important key for the accuracy of interface tracking algorithm. The least square gradient that minimize the sum of square Taylor serial expansion of volume fraction minus other neighborhood P volume fraction, min‰ nb FPTS Fnb †2 Š, is applied to achieve second-order accuracy of calculating rF in space. For a given constant c, the truncation volume that the fraction of cell volume truncated by interface can be derived from the interface equation (Eq. (6)) by a complicate geometric manipulation. However, the constant c is approximated by equivalent the truncation volume to the volume fraction of the cell. An iteration procedure of c is required for resolving the interface location that reconstructed the interface from the volume fraction of the cell. Once the interface is depicted, the volume ¯uxes and the integrated of volume fraction in Eq. (2) can be calculated with the time marching technique. Recently, Wang and coworkers [6] robust the PLIC±VOF method by separating the pressure gradient term for an interface cell into liquid and gas components so that the non-physical ``parasitic current'' can be eliminated. 3. Experimental approach Use of micro-particle-image-velocimetry (m-PIV) is very attractive due to its capability of visualization without ~m @rm U ~m U ~m † ‡ r
rm U @t ~m † ‡ ~ ˆ rP ‡ rm~ g ‡ r mm r U Fsv momentum equation† (4) ~ Fsv in Eq. (4) is the volumetric surface tension force which can be calculated by continuum surface force (CSF) model: ~ Fsv ˆ ~ fsv ds and ~ fsv ˆ sk~ n ‡ rs s (5) where ~ fsv is the surface tension per unit interfacial area, ds the surface data function, s the surface tension coef®cient, k ˆ r
~ n the curvature of interface, and ~ n is the unit normal vector. 2.1. PLIC±VOF interface tracking methodology The interface equation of each computational cell is given by [2,3] ~ r
~ n cˆ0 (6) where ~ r is the locus of the interface and c the constant prescribing the interface. At any point,~ r0 , in the cell is sorted (7) Fig. 1. Schematic diagram of m-PIV setup. F.-G. Tseng et al. / Sensors and Actuators A 97±98 (2002) 131±138 133 Fig. 2. SEM pictures of the fabricated micro-channel and reservoir of the third configuration. disrupting the ¯ow-®eld. Our micro-¯ow visualization system is setup based on TSI Inc.'s PIV components, collocating the Nikon inverted ¯uorescent microscope and the syringe pump (Fig. 1). In order to achieve the micro-scale resolution, the seeding particles in PIV must be: (1) small enough to follow the ¯uid ¯ow faithfully, but not interfering the ¯ow-®eld and obstructing the micro-channel; (2) large enough to restrain the effect of Brownian motion and producing necessarily large images. In this experiment, polystyrene ¯uorescence-tagged particles with diameter 1 mm and speci®c gravity of r ˆ 1:055 is chosen. The ¯uorescent dye can absorb green light (wavelength, l  535 nm) and emits red light (wavelength, l  575 nm). In order to eliminate the error due to Brownian motion [7], the beads in micron scale and 7.6 particles (in average) per interrogation spots of 10:3 mm  10:3 mm  4 mm are chosen [8] in this experiment. For the measurement, pulsed Nd-YAG laser is used to illuminate ¯uorescent particles inside the ¯ow-®eld in very short exposure time. After absorbing the laser light (l  532 nm), the ¯uorescent dye on particles emits the red light. Then images can be recorded by a cooled CCD camera with resolution of 1280  1204 pixels, 12 bit per pixel. By the frame-straddling technique and cross-correlation methodology, the ¯ow-®eld is obtained. The ®rst laser pulse synchronizer is triggered at the very end of the ®rst image after a pulse delay time of 252 ns, then the second laser pulse is triggered after pulse separation time dT which Fig. 3. Fabrication process of micro-channel/reservoir for the third configuration. 134 F.-G. Tseng et al. / Sensors and Actuators A 97±98 (2002) 131±138 depends on the image displacement. In the current experiments, dT ˆ 500 ms is chosen as the pulse separation time. These recorded images are processed by TSI, Inc.'s PIV analyzing software ``INSIGHTTM'' to obtain the detailed ¯ow-®eld in the picture. Flow systems have been designed and fabricated to visualize the ¯uid ®lling. The sizes of the micro-well and micro-channels are of 200 mm  200 mm and 100 mm 71 mm, respectively (Fig. 2). The cross-section of the channel is formed as a V-groove by anisotropic etching in KOH. Over etching in KOH is performed so that an inclined plane interconnecting channels and wells is obtained to ease the ¯uid ¯owing into the reservoir. Hydrophilic surface inside the ¯ow device is designed. 4. Fabrication process Fig. 4. (a) Configuration of flow network. (b) The grid system of the computation domain, for reservoir first configuration. upstream the inclined well initially. For the three cases of different contact angles, completely different ®llings are observed with same ¯ow system geometry and same Reynolds number (0.02 based on liquid). Fig. 5a not only show The ¯ow network device was fabricated by micro-machining technology as shown in Fig. 2. (1) LPCVD silicon nitride masking layers was deposited on both sides of (1 0 0) silicon wafers. (2) Photoresist (AZ5214) was spun on the rear side of the wafer. (3) Patterned for the de®nition of backside ¯uid entrance holes. (4) After RIE opening Si3N4 window, the wafer was etched by KOH (30%, 75 8C) until the formation of through holes. (5±7). The second anisentropic etching was then performed to form channels and wells on wafer front side. (8) After silicon nitride layer stripped, the wafer was dipped into HNO3 (30%) to generate a thin native silicon oxide for forming hydryphilic surface. (9) Finally, Pyrex glass was anodically bonded to the silicon substrate at 1000 V and 450 8C, which ®nished the process. The fabricated micro-wells and micro-channels have the sizes of 200 mm (width)  200 mm (length) and 100 mm (width)  71 mm (depth), respectively (Fig. 3). Time controlled KOH etching was performed to fabricate an inclined plane interconnecting channels and wells for helping ¯uid ¯ow from channels to wells. 5. Flow network configuration and filling process There are three different con®gurations of the ¯ow network system. The ®rst two con®gurations consist of 1 mm diameter micro-channels and a rectangular (Fig. 4) or a 458 inclined wall (Fig. 6) reservoir with the hydrophilic/hydrophobic surface. Contact angles of liquid±gas interface on solid surface as 30, 120, and 908 representing hydrophilic, hydrophobic surfaces, and in between, are implemented to survey the mechanism causing liquid trapped in the well. Fig. 4a is the con®guration of a square channel with a rectangular well embedded. A grid system of 135  10 5 nodes for the square micro-channel and 20  10  5 nodes for the rectangular well is shown in Fig. 4b. The blowing air velocity is set to be 0.1 m/s, with outlet pressure as 1 atm. A 4 mm long liquid slug (0.004 cm3) is placed motionless Fig. 5. Filling processes for various contact angles of (a) 308, (b) 1208, (c) 908, for reservoir first configuration (liquid region in gray and air region in black). F.-G. Tseng et al. / Sensors and Actuators A 97±98 (2002) 131±138 135 Fig. 6. (a) Configuration of flow network. (b) The grid system of the computation domain, for reservoir with 458 inclined wall, second configuration. the successful ®lling process through the micro-well, but the shape changing of the liquid slug. In this paper, gray color region represents liquid occupancy and black represents air for all the ®gures showing the computed ®lling process. Fig. 8. (a) Schematic diagram. (b) Grid system of computation domain, for flow network third configuration. Fig. 7. Filling processes for various contact angles of (a) 308, (b) 1208, (c) 908, for reservoir with 458 inclined wall, second configuration. Fig. 5b shows that the ®lling is completely failed and no liquid is left in the well if the wall surface is hydrophobic. Fig. 5c indicates that only a portion of the liquid left in the well if the wall surface is nearly hydrophobic. In order to prove that the importance of the hydrophilic nature, a 458 inclined wall is embedded to direct the liquid entering reservoir. Fig. 6a is the con®guration of a square channel with a 458 inclined well embedded. A grid system of 100  10  5 nodes for the square micro-channel and 20  10  5 nodes for the inclined well is employed for second con®guration (Fig. 6b). Trend as complete ®lling, failed ®lling, or almost-failed ®lling is obtained for different contact angles (Fig. 7a±c). It implies that the inclined wall helps very little on successful ®lling if the wall surface is hydrophobic, i.e. hydrophilic/hydrophobic nature of the wall surfaces is a key issue for liquid ®lling into micro-reservoirs if the channel/reservoir size is in 1 mm range. For the third con®guration of the ¯ow network, the ¯ow surfaces of the channel and reservoir are hydrophilic, but the channel size is reduced to 100 mm with side views of the channel and reservoir as trapezoidal (Fig. 8a) instead of rectangular. The grid systems of 82  12  14 nodes and 28  22  14 nodes are employed for the ¯ow channel and the micro-reservoir, respectively (Fig. 8b). The detailed ¯ow-®eld is obtained by numerical computation and Fig. 9 shows the ®lling process on bottom, middle, and top planes of the ¯ow network as well as the velocity vectors. It is found that a large bubble is entrapped inside the micro-reservoir 136 F.-G. Tseng et al. / Sensors and Actuators A 97±98 (2002) 131±138 Fig. 9. The filling process with water velocity of 1 m/s and Reynolds number of 100 for flow network third configuration. Fig. 10. Measured velocity vector plot of flow filling in the fabricated well for flow network third configuration. F.-G. Tseng et al. / Sensors and Actuators A 97±98 (2002) 131±138 and dif®cult to be removed. The water velocity is 1 m/s with Reynolds number of 100 in this case. The failure of the reservoir-®lling and the formation of the bubble are caused by the strong surface tension evolution inside the micro-size channel. This study fabricates a ¯ow network device of the third con®guration similar as the above-mentioned, so that the ®lling process can be visualized by m-PIV system and compared with the process from numerical simulation. The water is directed into the micro-channel by the syringe pump and the surface tension drives the water slug ¯owing into the system quickly. The image of the ¯ow-®eld is recorded as the water slug passing over the reservoir. Fig. 10 is the detailed velocity vector plot as the water reaching the reservoir. The big empty bubble inside the vectors means that no liquid in this region, which implies the ®lling of the reservoir is not completed. The Reynolds number based on liquid is of the order of 0.02. The experiments imply that the complete ®lling of the reservoir via the manufactured ¯ow network device is failed, which is consistent with the computational results (Fig. 9). 6. Concluding remarks Computational model solving ®rst principle equation as well as m-PIV is a very effective tool to investigate detailed ¯ow phenomena. Both experimental and computational models suggest that nature of ¯ow channel/reservoir wall surface plays important role of the ®lling reservoirs as well as size/shape design of micro-scale ¯ow network system. As the size of the micro-channel is reduced to millimeter range, surface tension is the dominating force driving the liquid ¯ow and hydrophilic nature can ease the liquid entering micro-reservoir completely. However, the complete ®lling becomes dif®cult even the wall surface is hydrophilic if the size of the ¯ow system is down to 100 mm. Therefore, effective ®lling of the reservoir needs extensive study for good ¯ow network system design. Acknowledgements This study was sponsored by the contract numbers NSC 89-2323-007-007, NSC 89-2323-007-008, and NSC 892323-007-009 from National Science Council, Republic of China. References [1] B. Zhao, J.S. Moore, D.J. Beebe, Surface-directed liquid flow inside micro-channels, Science 291 (2001) 1023±1026. [2] D.B. Kothe, W.J. Rider, S.J. Mosso, J.S. Brock, J.I. Hochstein, Volume tracking of interfaces having surface tension in two and three dimensions, in: Proceedings of the 34th Aerospace Science Meeting and Exhibit, 1996, AIAA Paper 96±0859. 137 [3] W.J. Rider, D.B. Kothe, Stretching and tearing interface tracking methods, in: Proceedings of the 12th AIAA Computational Fluid Dynamic Conference, 1995, Technical Report AIAA-95-1717. [4] M. Ishii, Thermo-fluid Dynamic Theory of Two-phase Flow, Eyrolles, Paris, 1975, pp. 202±233. [5] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, J. Computat. Phys. 100 (1992) 335± 354. [6] S.A. Bayyuk, D.M. Wang, S.A. Lowry, A self-consistent, higher-order accurate scheme for the VOF methodology for multi-phase flows, in: Proceedings of the International Congress of Theoretical and Applied Mechanics, Chicago, USA, 29 August 2001, Paper GK-10. [7] J.G. Santiago, S.T. Wereley, C.D. Meinhart, D.J. Beebe, R.J. Adrian, A particle image velocimetry system for micro-fluidics, Exp. Fluids 25 (1998) 316±319. [8] C.D. Meinhart, S.T. Wereley, J.G. Santiago, PIV measurements of a micro-channel flow, Exp. Fluids 27 (1999) 414±419. Biographies Fan-Gang Tseng was born in 1967 in Taichung, Taiwan, ROC. He received the BS degree from the Department of Power Mechanical Engineering, National Tsing Hua University, Taiwan, ROC in 1989, and the MS degree from the Institute of Applied Mechanics, National Taiwan University, Taiwan, ROC in 1991. In 1998, he received his PhD degree in mechanical engineering from the University of California, Los Angeles, USA, with an emphasis on MEMS technology. His PhD dissertation was on the design, fabrication and applications of a novel micro-droplet injector system. This novel system is currently under technology transfer for commercialization. After 1 year staying with USC/Information Science Institute as a senior engineer working on a new micro-fabrication process, EFAB, he has been an assistant professor with Engineering and System Science Department of National Tsing Hua University, Taiwan, ROC since August 1999. His interests are in the fields of bio-MEMS and micro-fluidics. He received five patents, wrote one chapter in MEMS Handbook by CRC Press, published more than 40 technical papers in MEMS, bio-MEMS, and fluid mechanics related fields, and co-chaired in the technique sessions of IS3M, HK in 2000, and Transducers'01, Munich, Germany in 2001. He has consulted more than four US-based and three Taiwan-based companies, as well as three Taiwan-based organizations. I-Da Yang was born in 1974 in YunLin, Taiwan, ROC. He received the BS degree from the Department of Naval Architecture and Marine Engineering, National Cheng Kung University, Taiwan, ROC in 1996, and the MS degree from the Institute of Engineering Science, National Cheng Kung University, Taiwan, ROC in 1999. Now, he is the PhD candidate in the Department of Engineering and System Science, National Tsing Hua University, Taiwan, ROC, with an emphasis on MEMS technology. His interests are in the fields of bio-MEMS, optical-MEMS, and microfluidics, especially in micro-flow-field visualization with micro-PIV. Kuo-Tong Ma received the PhD degree from the Department of Engineering and System Science, National Tsing Hua University, Taiwan, ROC in 1999. He received the MS degree from Nuclear Engineering Department of National Tsing Hua University, Taiwan, ROC in 1990 and the BS degree from Aeronautical Engineering Department of National Cheng Kung University, Taiwan, ROC in 1981. He has worked in the following fields: the jet propulsion system design and analysis, especially, the S-shape inlet duct that is successful applied in the navy missile; the three-dimensional numerical simulation of thermal±hydraulic system for nuclear power plant, the simulation results are utilized for the locating corrosion/erosion position in steam pipe system and the safety analysis of the nuclear reactor pressure vessel under pipe broken accident; the study of the high heat flux nucleate boiling heat transfer mechanism for his PhD dissertation; the micro-fluidics design, analysis and numerical simulation 138 F.-G. Tseng et al. / Sensors and Actuators A 97±98 (2002) 131±138 for bio-MEMS. The relative published papers are more than 15 in the versatile fields. Ming-Chang Lu has been a MS student in the Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan, ROC since he obtained his BS from the same department in 2000. His research interests are molecular dynamic simulation and computational heat transfer and fluid flow. Kwan-Hua Lin has been a MS student in the Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan, ROC since he obtained his BS from the same department in 2000. His research interests are MEMS technology and micro-fluidics. Yuan-Tai Tseng has a MS student in the Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan, ROC since he obtained his BS from the same department in 2000. His research interest is micro-fluidics. Ching-Chang Chieng has been a professor in the department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan, ROC since 1981 and her major emphasis of research is microscale heat transfer and fluid flow in recent years. Her specialties include numerical scheme developments and applications for turbulent flow computations, in both macro- and micro-scales. She obtained her PhD in aerospace and ocean engineering from Virginia Polytechnic Institute and State University in 1974. She is also an associate fellow of AIAA.