Abstract
The fluid dynamics of microwater droplet transport in a parallel-plate electrowetting-on-dielectric (EWOD) device have been investigated via a numerical model. The transient governing equations are solved by a finite volume scheme with a two-step projection method on a fixed computational domain. The interface between liquid and gas is tracked by a coupled level set and volume-of-fluid method. A continuum surface force model is employed to evaluate surface tension at the interface. A simplified model is adopted for the viscous stresses exerted by the parallel plates at the gas–liquid interface in conjunction with contact angle hysteresis implemented as a crucial element in EWOD modeling. Excellent agreement has been achieved between the numerical and published experimental results. Special attention has been focused on some localized areas near the ON/OFF electrode border where the transport process is primarily influenced. A dimensionless curvature has been introduced and a critical value has been identified beyond which the droplet would split during the transport. A parametric study has been performed in which the effects of several crucial parameters including initial droplet shape, static contact angles, contact angle hysteresis, viscous stress, channel height and electrode size on the transport process have been revealed.
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References
Arzpeyma A, Bhaseen S, Dolatabadi A, Wood-Adams P (2008) A coupled electro-hydrodynamic numerical modeling of droplet actuation by electrowetting. Colloids Surf A 323(1):28–35. doi:10.1016/j.colsurfa.2007.12.025
Bahadur V, Garimella SV (2006) An energy-based model for electrowetting-induced droplet actuation. J Micromech Microeng 16(8):1494–1503. doi:10.1088/0960-1317/16/8/009
Baird ES, Mohseni K (2007) A unified velocity model for digital microfluidics. Nanoscale Microscale Thermophys 11(1–2):109–120. doi:10.1080/15567260701337514
Batchelor GK (2000) An introduction to fluid dynamics. Cambridge University Press, Cambridge
Berge B (1993) Electrocapillarité et mouillage de films isolants par l’eau. C R Acad Sci II 317(2):157–163
Berthier J (2012) Micro-drops and digital microfluidics. William Andrew, Norwich
Böhm S, Timmer B, Olthuis W, Bergveld P (2000) A closed-loop controlled electrochemically actuated micro-dosing system. J Micromech Microeng 10(4):498–504. doi:10.1088/0960-1317/10/4/303
Brackbill J, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100(2):335–354. doi:10.1016/0021-9991(92)90240-Y
Chang JH, Pak JJ (2012) Effect of contact angle hysteresis on electrowetting threshold for droplet transport. J Adhes Sci Technol 26(12–17):2105–2111. doi:10.1163/156856111X600136
Cho SK, Moon H, Kim C-J (2003) Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits. J Microelectromech Syst 12(1):70–80. doi:10.1109/JMEMS.2002.807467
Clime L, Brassard D, Veres T (2010) Numerical modeling of electrowetting transport processes for digital microfluidics. Microfluid Nanofluidics 8(5):599–608. doi:10.1007/s10404-009-0491-9
Darhuber AA, Valentino JP, Troian SM, Wagner S (2003) Thermocapillary actuation of droplets on chemically patterned surfaces by programmable microheater arrays. J Microelectromech Syst 12(6):873–879. doi:10.1109/JMEMS.2003.820267
Fair RB (2007) Digital microfluidics: is a true lab-on-a-chip possible? Microfluid Nanofluidics 3(3):245–281. doi:10.1007/s10404-007-0161-8
Gong J, Kim C-J (2008) All-electronic droplet generation on-chip with real-time feedback control for EWOD digital microfluidics. Lab Chip 8(6):898–906. doi:10.1039/B717417A
Guan Y, Tong AY (2015) A numerical study of droplet splitting and merging in a parallel-plate electrowetting-on-dielectric device. J Heat Transf 137(9):091016. doi:10.1115/1.4030229
Gupta R, Sheth DM, Boone TK, Sevilla AB, Frechette J (2011) Impact of pinning of the triple contact line on electrowetting performance. Langmuir 27(24):14923–14929. doi:10.1021/la203320g
Harlow F, Amsden A (1971) Fluid dynamics: a LASL monograph (mathematical solutions for problems in fluid dynamics). Technical report, LA-4700, Los Alamos National Laboratory
Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225. doi:10.1016/0021-9991(81)90145-5
Huh C, Scriven LE (1971) Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J Colloid Interface Sci 35(1):85–101. doi:10.1016/0021-9797(71)90188-3
Jang LS, Lin GH, Lin YL, Hsu CY, Kan WH, Chen CH (2007) Simulation and experimentation of a microfluidic device based on electrowetting on dielectric. Biomed Microdevices 9(6):777–786. doi:10.1007/s10544-007-9089-8
Jones TB, Gunji M, Washizu M, Feldman MJ (2001) Dielectrophoretic liquid actuation and nanodroplet formation. J Appl Phys 89(2):1441–1448. doi:10.1063/1.1332799
Keshavarz-Motamed Z, Kadem L, Dolatabadi A (2010) Effects of dynamic contact angle on numerical modeling of electrowetting in parallel plate microchannels. Microfluid Nanofluidics 8(1):47–56. doi:10.1007/s10404-009-0460-3
Kirby BJ (2010) Micro- and nanoscale fluid mechanics: transport in microfluidic devices. Cambridge University Press, Cambridge
Kothe DB, Mjolsness RC, Torrey MD (1991) RIPPLE: a computer program for incompressible flows with free surfaces. Technical report, LA-12007-MS, Los Alamos National Laboratory
Lu HW, Glasner K, Bertozzi AL, Kim C-J (2007) A diffuse-interface model for electrowetting drops in a Hele-Shaw cell. J Fluid Mech 590:411–435. doi:10.1017/S0022112007008154
Madou MJ (2002) Fundamentals of microfabrication: the science of miniaturization. CRC Press, Boca Raton
Meier M, Yadigaroglu G, Smith BL (2002) A novel technique for including surface tension in PLIC-VOF Methods. Eur J Mech B Fluids 21(1):61–73. doi:10.1016/S0997-7546(01)01161-X
Mohseni K, Arzpeyma A, Dolatabadi A (2006) Behaviour of a moving droplet under electrowetting actuation: Numerical simulation. Can J Chem Eng 84(1):17–21. doi:10.1002/cjce.5450840104
Moon H, Cho SK, Garrell RL (2002) Low voltage electrowetting-on-dielectric. J Appl Phys 92(7):4080–4087. doi:10.1063/1.1504171
Mugele F, Baret J-C (2005) Electrowetting: from basics to applications. J Phys Condens Matter 17(28):R705–R774. doi:10.1088/0953-8984/17/28/r01
Nguyen N-T, Ng KM, Huang X (2006) Manipulation of ferrofluid droplets using planar coils. Appl Phys Lett 89(5):052509. doi:10.1063/1.2335403
Pollack MG (2001) Electrowetting-based microactuation of droplets for digital microfluidics. Dissertation, Duke University
Pollack MG, Fair RB, Shenderov AD (2000) Electrowetting-based actuation of liquid droplets for microfluidic applications. Appl Phys Lett 77(11):1725–1726. doi:10.1063/1.1308534
Pollack MG, Shenderov AD, Fair RB (2002) Electrowetting-based actuation of droplets for integrated microfluidics. Lab Chip 2(2):96–101. doi:10.1039/B110474H
Ren H, Fair RB, Pollack MG, Shaughnessy EJ (2002) Dynamics of electro-wetting droplet transport. Sens Actuators B Chem 87(1):201–206. doi:10.1016/S0925-4005(02)00223-X
Renardy Y, Renardy M (2002) PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. J Comput Phys 183(2):400–421. doi:10.1006/jcph.2002.7190
Rudman M (1997) Volume-tracking methods for interfacial flow calculations. Int J Numer Methods Fluids 24(7):671–691. doi:10.1002/(SICI)1097-0363(19970415)24:7<671:AID-FLD508>3.0.CO;2-9
Rudman M (1998) A volume-tracking method for incompressible multifluid flows with large density variations. Int J Numer Methods Fluids 28(2):357–378. doi:10.1002/(SICI)1097-0363(19980815)28:2<357:AID-FLD750>3.0.CO;2-D
Sammarco TS, Burns MA (1999) Thermocapillary pumping of discrete drops in microfabricated analysis devices. AIChE J 45(2):350–366. doi:10.1002/aic.690450215
Scardovelli R, Zaleski S (1999) Direct numerical simulation of free-surface and interfacial flow. Annu Rev Fluid Mech 31(1):567–603. doi:10.1146/annurev.fluid.31.1.567
Son G, Hur N (2002) A coupled level set and volume-of-fluid method for the buoyancy-driven motion of fluid particles. Numer Heat Transf B Fundam 42(6):523–542. doi:10.1080/10407790190054067
Sussman M (2003) A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. J Comput Phys 187(1):110–136. doi:10.1016/S0021-9991(03)00087-1
Sussman M, Puckett EG (2000) A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J Comput Phys 162(2):301–337. doi:10.1006/jcph.2000.6537
Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 114(1):146–159. doi:10.1006/jcph.1994.1155
Tong AY, Wang Z (2007) A numerical method for capillarity-dominant free surface flows. J Comput Phys 221(2):506–523. doi:10.1016/j.jcp.2006.06.034
Walker SW, Shapiro B (2006) Modeling the fluid dynamics of electrowetting on dielectric (EWOD). J Microelectromech Syst 15(4):986–1000. doi:10.1109/JMEMS.2006.878876
Walker SW, Shapiro B, Nochetto RH (2009) Electrowetting with contact line pinning: computational modeling and comparisons with experiments. Phys Fluids 21(10):102103. doi:10.1063/1.3254022
Wang Z, Tong AY (2010) A sharp surface tension modeling method for two-phase incompressible interfacial flows. Int J Numer Methods Fluids 64(7):709–732. doi:10.1002/fld.2166
Wang W, Jones TB, Harding DR (2011) On-chip double emulsion droplet assembly using electrowetting-on-dielectric and dielectrophoresis. Fusion Sci Technol 59(1):240–249
Yaddessalage JB (2013) Study of the capabilities of electrowetting on dielectric digital microfluidics (EWOD DMF) towards the high efficient thin-film evaporative cooling platform. Dissertation, The University of Texas at Arlington
Yang X, James AJ, Lowengrub J, Zheng X, Cristini V (2006) An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. J Comput Phys 217(2):364–394. doi:10.1016/j.jcp.2006.01.007
Zeng J, Korsmeyer T (2004) Principles of droplet electrohydrodynamics for lab-on-a-chip. Lab Chip 4(4):265–277. doi:10.1039/B403082F
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Appendix: Grid refinement study
Appendix: Grid refinement study
Calculations of droplet transport have been conducted with three different mesh sizes for the grid convergence study. As shown in Fig. 23, the droplet shapes obtained from the three different grid sizes are very close, which indicates that grid convergence has been achieved. Based on the results of the grid refinement study, uniform square mesh of grid spacing of 0.05 mm is adopted for the present study.
Droplet transport with different grid sizes: 0.05 × 0.05 mm2, 0.025 × 0.025 mm2 and 0.0125 × 0.0125 mm2
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Guan, Y., Tong, A.Y. A numerical study of microfluidic droplet transport in a parallel-plate electrowetting-on-dielectric (EWOD) device. Microfluid Nanofluid 19, 1477–1495 (2015). https://doi.org/10.1007/s10404-015-1662-5
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DOI: https://doi.org/10.1007/s10404-015-1662-5