Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T15:25:45.344Z Has data issue: false hasContentIssue false
  • English
  • Français

A Contact Line Dynamic Model for a Conducting Water Drop on an Electrowetting Device

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Two-phase and multiphase flows Magnetohydrodynamics and electrohydrodynamics

Published online by Cambridge University Press:  31 August 2016

Dongdong He  and
Huaxiong Huang
Dongdong He*
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China
Huaxiong Huang*
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada Fields Institute, Toronto, Ontario, M5T 3J1, Canada
*
*Corresponding author. Email addresses:dongdonghe@tongji.edu.cn (D. He), hhuang@yorku.ca (H. Huang)
*Corresponding author. Email addresses:dongdonghe@tongji.edu.cn (D. He), hhuang@yorku.ca (H. Huang)
Get access

Abstract

The static shape of drop under electrowetting actuation is well studied and recent electrowetting theory and experiments confirm that the local contact angle (microscopic angle) is unaffected while the apparent contact angle (macroscopic angle) is characterized by the Lippmann-Young equation. On the other hand, the evolution of the drop motion under electrowetting actuation has received less attention. In this paper, we investigate the motion of a conducting water drop on an electrowetting device (EWD) using the level set method. We derive a contact line two-phase flow model under electrowetting actuation using energy dissipation by generalizing an existing contact line model without the electric field. Our model is consistent with the static electrowetting theory as the dynamic contact angle satisfies the static Young's equation under equilibrium conditions. Our steady state results show that the apparent contact angle predicted by our model satisfies the Lippmann-Young's relation. Our numerical results based on the drop maximum deformation agree with experimental observations and static electrowetting theory. Finally, we show that for drop motion our results are not as good due to the difficulty of computing singular electric field accurately. Nonetheless, they provide useful insights and ameaningful first step towards the understanding of the drop dynamics under electrowetting actuation.

Keywords

Moving contact linecontact anglelevel set methodelectrowettingslip conditions

MSC classification

Secondary: 76T99: None of the above, but in this section 76W05: Magnetohydrodynamics and electrohydrodynamics 65M06: Finite difference methods
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 3 , September 2016 , pp. 811 - 834
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Cho, S.K., Moon, H. and Kim, C.-J., Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfludic circuits, J. Microelectromechan. Syst, 12 (2003) 70–80.Google Scholar
[2] Shapiro, B., Moon, H., Garrell, R., and Kim, C.-J., “Equilibrium behavior of sessile drops under surface tension, applied external fields, and material variations.” J. Appl. Phys., vol.93, 2003.CrossRefGoogle Scholar
[3] Mugele, F., and Baret, J.-C., Electrowetting: from basics to applications, J. Phys.: Condensed Matter, 17 (2005) 705–774.Google Scholar
[4] Bahadur, V. and Garimella, S. V., Energy Minimization-Based Analysis of Electrowetting for Microelectronics Cooling Applications, J. Microelectron. 39 (2008) 957–965.CrossRefGoogle Scholar
[5] Hayes, R. A, Feenstra, B. J, Video-speed electronic paper based on electrowetting, Nature, 425, 383–385, doi:10.1038/nature01988 (2003).CrossRefGoogle ScholarPubMed
[6] Srinivasan, V, Pamula, V. K., Fair, R. B., An integrated digital microfluidic lab-on-a-chip for clinical diagnostics on human physiological fluids, Lab Chip 2004, 4, 310-315.CrossRefGoogle Scholar
[7] Ren, W. and E, W., Boundary conditions for the moving contact line problem, Phys Fluids, 19 (2007) 022101.CrossRefGoogle Scholar
[8] Li, J. and Renardy, M., Numerical simulation of moving contact line problems using a volume-of-fluid method, J. Comput. Phys. 171 (2001) 243–263.Google Scholar
[9] Afkhami, S., Zaleski, S. and Sussmann, M., A mesh-dependent model for applying dynamic contact angles to VOF simulations, J. Comput. Phys. 228 (2009) 5370–5389.CrossRefGoogle Scholar
[10] J.-B., , Dupont, , Legendre, D., Numerical simulation of static and sliding drop with contact angle hysteresis. J. Comput. Phys. 229 (2010) 2453–2478.Google Scholar
[11] Huang, H., Liang, D. and Wetton, B., Computation of a moving drop/bubble on a solid surface using a front-tracking method, Comm. Math. Sci. 2 (2004) 535–552.CrossRefGoogle Scholar
[12] Spelt, P.D.M., A level-set approach for simulations of flows with multiple moving contact lines with hysteresis, J. Comput. Phys. 207 (2005) 389–404.CrossRefGoogle Scholar
[13] Sui, Y., Spelt, Peter D.M., An efficient computational model for macroscale simulations of moving contact lines. J. Comput. Phys. 242 (2013) 37–52.CrossRefGoogle Scholar
[14] Sui, Y., Spelt, Peter D.M., Validation and modification of asymptotic analysis of slow and rapid droplet spreading by numerical simulation. J. Fluid Mech. 715 (2013) 283–313.CrossRefGoogle Scholar
[15] Sui, Y., Ding, H., and Spelt, Peter D.M., Numerical Simulations of Flows with Moving Contact Lines, Annu. Rev. Fluid Mech. 46 (2014) 97–119.CrossRefGoogle Scholar
[16] Mugele, F., Fundamental challenges in electrowetting: from equilibrium shapes to contact angle saturation and drop dynamics, Soft Matter 5 (2009) 3377–3384.CrossRefGoogle Scholar
[17] Ren, W., Hu, D. and E, W., Continuum Models for the Moving Contact Line Problem, Phys. Fluids 22 (2010) 102103.CrossRefGoogle Scholar
[18] Lippmann, M.G., Relations entre les phénomènes electriques et capillaires, Ann. Chim. Phys. 5 (1875) 494–549.Google Scholar
[19] Mugele, F., and Buehrle, J., Equilibrium drop surface profiles in electric fields, J. Phys.: Condensed Matter, 19 (2007) 375112.Google Scholar
[20] Scheid, C., Witomski, P., A proof of the invariance of the contact angle in the electrowetting, Math. Comput. Model. 49 (2009) 647–665.CrossRefGoogle Scholar
[21] Harlow, F. and Welch, J., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fluids, 8, 2182–2189, 1965.CrossRefGoogle Scholar
[22] Li, Z., Lai, M.-C., Wei, G., Zhao, H., An augmented method for the free boundary problems with moving contact lines. Comput. Fluids, 39 (2010) 1033–1040.CrossRefGoogle Scholar
[23] Peskin, C. S., The immersed boundary method, Acta Numerica., 11 (2002) 479–517.CrossRefGoogle Scholar
[24] Chang, Y. C., Hou, T. Y., Merriman, B. and Osher, S., A level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows, J. Comput. Phys., 124 (1996) 449–464.CrossRefGoogle Scholar
[25] Cottet, G.-H. and Maitre, E., A level set method for fluid-structure interactions with immersed surfaces, MATH. MOD. METH. APPL. S., 16 (2006) 415–438.CrossRefGoogle Scholar
[26] Cottet, G.-H., Maitre, E. and Milcent, T., Eulerian formulation and level set models for incompressible fluid-structure interaction. ESAIM:M2AN, 42 (2008) 471–492.CrossRefGoogle Scholar
[27] Jiang, G. and Peng, D., Weighted ENO schemes for Halmiton-Jacobi equations. SIAM J. SCI. Comput. 21 (2000) 2126–2143.CrossRefGoogle Scholar
[28] He, D., Huang, H. and Tan, Y., Numerical simulation for a droplet fission process of electrowetting on dielectric device. Commun. Comput. Phys. 7 (2010) 1076–1094.CrossRefGoogle Scholar
[29] Xu, J. J., Ren, W., A level-set method for two-phase flows with moving contact line and insoluble surfactant, J. Comp. Phys. 263 (2014) 71–90.CrossRefGoogle Scholar
[30] He, D., Huang, H., A Constrained Level Set Method for Simulating the Formation of Liquid Bridges. Commun. Comput. Phys., 12 (2012) 577–594.CrossRefGoogle Scholar
[31] Li, Z. and Ito, K., The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains. SIAM Frontiers in Applied Mathematics, 33, ISBN-10: 0-89871-609-8 / ISBN-13: 978-0-898716-09- 2, 2006.Google Scholar
[32] Castellanos, A., Electrohydrodynamics, Springer-Verlag, 1998.CrossRefGoogle Scholar
[33] Eck, C., Fontelos, M., Grn, G., Klingbeil, F., and Vantzos, O., On a phase field model for electrowetting, Interfaces Free Boundaries, 11 (2009) 259–290.Google Scholar