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Numerical and theoretical analyses of the dynamics of droplets driven by electrowetting on dielectric in a Hele-Shaw cell

Published online by Cambridge University Press:  01 February 2018

Yasufumi Yamamoto Open the ORCID record for Yasufumi Yamamoto [Opens in a new window] ,
Takahiro Ito ,
Tatsuro Wakimoto  and
Kenji Katoh
Yasufumi Yamamoto*
Affiliation:
Department of Mechanical Engineering, Kansai University, 3-35, Yamate-cho 3-chome, Suita, Osaka, 564-8680, Japan
Takahiro Ito
Affiliation:
Department of Energy Engineering and Science, Nagoya University, Furo-cho Chikusa-ku, Nagoya, 464-8603, Japan
Tatsuro Wakimoto
Affiliation:
Department of Mechanical Engineering, Osaka City University, 3-3-138, Sumiyoshi-ku Sugimoto, Osaka, 558-8585, Japan
Kenji Katoh
Affiliation:
Department of Mechanical Engineering, Osaka City University, 3-3-138, Sumiyoshi-ku Sugimoto, Osaka, 558-8585, Japan
*
†Email address for correspondence: [email protected]
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Abstract

Droplet movement by electrowetting on dielectric (EWOD) in a Hele-Shaw cell is analysed theoretically and numerically. We propose a simple theoretical model for the motion, which describes well the voltage dependency of droplet speed below the saturation voltage as measured experimentally. The simulation method for numerical analyses is constructed by using the Young–Lippmann equation to represent EWOD and the generalised Navier boundary condition to represent the moving contact line in the context of the front-tracking method. With an adjusted slip parameter, the present full three-dimensional numerical simulation reproduces well the shape evolution and movement speed of droplets as observed experimentally. We verify the proposed theoretical model in numerical experiments with various shapes and voltages. Furthermore, we analyse theoretically the behaviour of the contact line at the onset of droplet motion as observed in the simulation and experiment, and we are able to estimate very well the time scale on which the contact angle changes.

JFM classification

Interfacial Flows (free surface): Capillary flows Drops and Bubbles: Drops Interfacial Flows (free surface): Contact lines
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , pp. 468 - 488
Copyright
© 2018 Cambridge University Press 

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References

Afkhami, S., Zaleski, S. & Bussmann, M. 2009 A mesh-dependent model for applying dynamic contact angles to VOF simulations. J. Comput. Phys. 228, 5370–5389.Google Scholar
Berthier, J., Clementz, Ph., Raccurt, O., Jary, D., Claustre, P., Peponnet, C. & Fouillet, Y. 2006 Computer aided design of an EWOD microdevice. Sensors Actuators A 127, 283–294.Google Scholar
Blake, T. D., Clarke, A. & Stattersfield, E. H. 2000 An investigation of electrostatic assist in dynamic wetting. Langmuir 16, 2928–2935.Google Scholar
Brakke, K. A. 1992 The surface evolver. Exp. Math. 1, 141–165.Google Scholar
Chen, L. & Bonaccurso, E. 2014 Electrowetting – from statics to dynamics. Adv. Colloid Interface Sci. 210, 2–12.Google Scholar
Cho, S. K., 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, 70–80.Google Scholar
Cox, R. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169–194.Google Scholar
Darhuber, A. A. & Troian, S. M. 2005 Principles of microfluidic actuation by modulation of surface stresses. Annu. Rev. Fluid Mech. 37, 425–455.Google Scholar
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.Google Scholar
Dupont, J. -B. & Legendre, D. 2010 Numerical simulation of static and sliding drop with contact angle hysteresis. J. Comput. Phys. 229, 2453–2478.Google Scholar
Fair, R. B. 2007 Digital microfluidics: is a true lab-on-a-chip possible? Microfluid. Nanofluid. 3, 245–281.Google Scholar
Fontelos, M. A., Grün, G., Kindelán, U. & Klingbeil, F. 2012 Numerical simulation of static and dynamic electrowetting. J. Adhes. Sci. Technol. 26, 1805–1824.Google Scholar
Katoh, K, Azuma, T., Higashine, M. & Miyamoto, Y. 2006 On the sliding down of liquid drops on inclined plates (1st report, critical inclination angles of plates). Trans. Japan Soc. Mech. Engng B 72, 1287–1294 (in Japanese).Google Scholar
Kistler, S. F. 1993 Hydrodynamics of wetting. In Wettability (ed. Berg, J. C.), pp. 311–429. Marcel Dekker.Google Scholar
Ko, S. H., Lee, H. & Kang, K. H. 2008 Hydrodynamic flows in electrowetting. Langmuir 24, 1094–1101.Google Scholar
Ledesma-Aguilar, R., Hernández-Machado, A. & Pagonabarraga, I. 2013 Theory of wetting-induced fluid entrainment by advancing contact lines on dry surfaces. Phys. Rev. Lett. 110, 264502.Google Scholar
Li, X.-L., He, G.-W. & Zhang, X. 2013 Numerical simulation of drop oscillation in AC electrowetting. Sci. China Phys. Mech. Astron. 56, 383–394.Google Scholar
Lienemann, J., Greiner, A. & Korvink, J. G. 2006 Modeling, simulation, and optimization of electrowetting. IEEE Trans. CAD Integr. Circ. Syst. 25, 234–247.Google Scholar
Lu, H.-W., Glasner, K., Bertozzi, A. L. & Kim, C.-J. 2007 A diffuse-interface model for electrowetting drops in a Hele-Shaw cell. J. Fluid Mech. 590, 411–435.Google Scholar
McHale, G., Brown, C. V. & Sampara, N. 2013 Voltage-induced spreading and superspreading of liquids. Nature Commun. 4, 1605.CrossRefGoogle ScholarPubMed
Mondal, P. K., Ghosh, U., Bandopadhyay, A., DasGupta, D. & Chakraborty, S. 2013 Electric-field-driven contact-line dynamics of two immiscible fluids over chemically patterned surfaces in narrow confinements. Phys. Rev. E 88, 023022.Google Scholar
Mugele, F. 2009 Fundamental challenges in electrowetting: from equilibrium shapes to contact angle saturation and drop dynamics. Soft Matt. 5, 3377–3384.Google Scholar
Mugele, F. & Baret, J.-C. 2005 Electrowetting: from basics to applications. J. Phys.: Condens. Matter 17, R705–R774.Google Scholar
Mugele, F. & Buehrle, J. 2007 Equilibrium drop surface profiles in electric fields. J. Phys.: Condens. Matter 19, 375112-1–20.Google Scholar
Mugele, F., Duits, M. & van den Ende, D. 2010 Electrowetting: A versatile tool for drop manipulation, generation, and characterization. Adv. Colloid Interface Sci. 161, 115–123.Google Scholar
Mugele, F., Klingner, A., Buehrle, J., Steinhauser, D. & Herminghaus, S. 2005 Electrowetting: a convenient way to switchable wettability patterns. J. Phys.: Condens. Matter 17, S559–S576.Google Scholar
Oh, J. M., Ko, S. H. & Kang, K. H. 2008 Shape oscillation of a drop in ac electrowetting. Langmuir 24, 8379–8386.Google Scholar
Oh, J. M., Ko, S. H. & Kang, K. H. 2010 Analysis of electrowetting-driven spreading of a drop in air. Phys. Fluids 22, 032002.CrossRefGoogle Scholar
Qian, T., Wang, X. P. & Sheng, P. 2003 Molecular scale contact line hydrodynamics of immiscible flows. Phys. Rev. E 68, 016306.Google Scholar
Quilliet, C. & Berge, B. 2001 Electrowetting: a recent outbreak. Curr. Opin. Colloid Interface Sci. 6, 34–39.CrossRefGoogle Scholar
Ren, H., Fair, R. B., Pollack, M. G. & Shaughnessy, E. J. 2002 Dynamics of electro-wetting droplet transport. Sensors Actuators B 87, 201–206.Google Scholar
Schlichting, H. 1975 Boundary-Layer Theory, 7th edn. McGraw-Hill.Google Scholar
Shin, S. & Juric, D. 2002 Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J. Comput. Phys. 180, 427–470.Google Scholar
Song, J. H., Evans, R., Lin, Y.-Y., Hsu, B.-N. & Fair, R. B. 2009 A scaling model for electrowetting-on-dielectric microfluidic actuators. Microfluid. Nanofluid. 7, 75–89.Google Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381–411.Google Scholar
Sui, Y., Ding, H. & Spelt, P. D. M. 2014 Numerical simulations of flows with moving contact lines. Annu. Rev. Fluid Mech. 46, 97–119.Google Scholar
Sui, Y. & Spelt, P. D. M. 2013 An efficient computational model for macroscale simulations of moving contact lines. J. Comput. Phys. 242, 37–52.Google Scholar
Suzuki, K., Homma, H., Murayama, T., Fukuda, S., Takanobu, H. & Miura, H. 2010 Electrowetting-based acutuation of liquid droplets for micro transportation systems. J. Adv. Mech. Des. Syst. Manuf. 4, 365–372.Google Scholar
Takada, N., Matsumoto, J., Matsumoto, S. & Ichikawa, N. 2008 Application of a phase-field method to the numerical analysis of motions of a two-phase fluid with high density ratio on a solid surface. J. Comput. Sci. Technol. 2, 318–329.Google Scholar
Unverdi, S. O. & Tryggvason, G. 1992 A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 25–37.Google Scholar
Vallet, M., Berge, B. & Vovelle, L. 1996 Electrowetting of water and aqueous solutions on poly(ethylene terephthalate) insulating films. Polymer 37, 2465–2470.Google Scholar
Walker, S. W. & Shapiro, B. 2006 Modeling the fluid dynamics of electrowetting on dielectric (EWOD). J. Microelectromech. Syst. 15, 986–1000.Google Scholar
Walker, S. W., Shapiro, B. & Nochetto, R. H. 2009 Electrowetting with contact line pinning: computational modeling and comparisons with experiments. Phys. Fluids 21, 102103.Google Scholar
Yamamoto, Y., Higashida, S., Tanaka, H., Wakimoto, T., Ito, T. & Katoh, K. 2016 Numerical analysis of contact line dynamics passing over a single wettable defect on a wall. Phys. Fluids 28, 082109.Google Scholar
Yamamoto, Y., Ito, T., Wakimoto, T. & Katoh, K. 2013 Numerical simulations of spontaneous capillary rises with very low capillary numbers using a front-tracking method combined with generalized Navier boundary condition. Intl J. Multiphase Flow 51, 22–32.Google Scholar
Yamamoto, Y., Tokieda, K., Wakimoto, T., Ito, T. & Katoh, K. 2014 Modeling of the dynamic wetting behavior in a capillary tube considering the macroscopic–microscopic contact angle relation and generalized Navier boundary condition. Intl J. Multiphase Flow 59, 106–112.Google Scholar
Zeng, J. 2006 Modeling and simulation of electrified droplets and its application to computer-aided design of digital microfluidics. IEEE Trans. CAD Integr. Circ. Syst. 25, 224–233.Google Scholar