Skip to main content
SpringerLink
Log in

Numerical simulation of drop oscillation in AC electrowetting

  • Article
  • Special Topic: Fluid Mechanics
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

In this paper, a “macroscopic-scale” numerical method for drop oscillation in AC electrowetting is presented. The method is based on a high-fidelity moving mesh interface tracking (MMIT) approach and a “microscopic model” for the moving contact line. The contact line model developed by Ren et al. [Phys Fluids, 2010, 22: 102103] is used in the simulation. To determine the slip length in this model, we propose a calibration procedure using the experimental data of drop spreading in DC electrowetting. In the simulation, the frequency of input AC voltage varies in a certain range while the root-mean-square value remains fixed. The numerical simulation is validated against the experiment and it shows that the predicted resonance frequencies for different oscillation modes agree reasonably well with the experiment. The origins of discrepancy between simulation and experiment are analyzed in the paper. Further investigation is also conducted by including the contact angle hysteresis into the contact line model to account for the “stick-slip” behavior. A noticeable improvement on the prediction of resonance frequencies is achieved by using the hysteresis model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kang K H. How electrostatic fields change contact angle in electrowetting. Langmuir, 2002, 18: 10318–10322

    Article  Google Scholar 

  2. Mugele F, Baret J C. Electrowetting: From basics to applications. J Phys-Condens Matter, 2005, 17: 705–774

    Article  ADS  Google Scholar 

  3. Pollack MG, Fair R B, Shenderov A D. Electrowetting-based actuation of liquid droplets for microfluidic applications. Appl Phys Lett, 2000, 77: 1725–1726

    Article  ADS  Google Scholar 

  4. Pollack MG, Shenderov A D, Fair R B. Electrowetting-based actuation of droplets for integrated microfluidics. Lab Chip, 2002, 2: 96–101

    Article  Google Scholar 

  5. Hayes R A, Feenstra B J. Video-speed electronic paper based on electrowetting. Nature, 2003, 425: 383–385

    Article  ADS  Google Scholar 

  6. Krupenkin T, Yang S, Mach P. Tunable liquid microlens. Appl Phys Lett, 2003, 82: 316–318

    Article  ADS  Google Scholar 

  7. Huh D, Tkaczyk A H, Bahng J H. Reversible switching of high-speed air-liquid two-phase flows using electrowetting-assisted flow pattern change. J Am Chem Soc, 2003, 125: 14678–14679

    Article  Google Scholar 

  8. Sen P, Kim C J. A fast liquid-metal droplet microswitch using EWODdriven contact-line sliding. J Microelectromech S, 2009, 18: 174–185

    Article  Google Scholar 

  9. Oh J M, Ko S H, Kang K H. Shape oscillation of a drop in ac electrowetting. Langmuir, 2008, 24: 8379–8386

    Article  Google Scholar 

  10. Oh J M, Ko S H, Kang K H. Analysis of electrowetting-driven spreading of a drop in air. Phys Fluids, 2010, 22: 032002

    Article  ADS  Google Scholar 

  11. Sen P, Kim C J. Capillary spreading dynamics of electrowetted sessile droplets in air. Langmuir, 2009, 25: 4302–4305

    Article  Google Scholar 

  12. Decamps C, Coninck J D. Dynamcis of spontaneous spreading under electrowetting conditions. Langmuir, 2000, 16: 10150–10153

    Article  Google Scholar 

  13. Ko S H, Lee H, Kang K H. Hydrodynamic flows in electrowetting. Langmuir, 2008, 24: 1094–1101

    Article  Google Scholar 

  14. Garcia-Sanchez P, Ramos A, Mugele F. Electrothermally driven flows in ac electrowetting. Phys Rev E, 2010, 81: 0153039 (R)

    Article  Google Scholar 

  15. Lee H, Yun S, Ko S H. An electrohydrodynamic flow in ac electrowetting. Biomicrofluidics, 2009, 3: 044113

    Article  Google Scholar 

  16. Baret J C, Decre M M J, Mugele F. Transport dynamics in open microfluidic grooves. Langmuir, 2007, 23: 5200–5204

    Article  Google Scholar 

  17. Cooney C G, Chen C Y, Emerling M R, et al. Electrowetting droplet microfluidics on a single planar surface. Microfluid Nanofluid, 2006, 2: 435–446

    Article  Google Scholar 

  18. Chung S K, Zhao Y, Yi U C, Separation and collection of microparticles using oscillating bubbles. In: the 20th International Conference on Micro Electro Mechanical Systems. Hyogo: IEEE, 2007. 21–25

    Google Scholar 

  19. Gunji M, Washizu M J. Self-propulsion of a water droplet in an electric field. J Phys D-Appl Phys, 2005, 38: 2417–2423

    Article  ADS  Google Scholar 

  20. Mugele F, Baret J C, Steinhauser D. Microfluidic mixing through electrowetting-induced droplet oscillations. Appl Phys Lett, 2006, 88: 204106

    Article  ADS  Google Scholar 

  21. Blake T D, Clarke A, Stattersfield E H. An investigation of electrostatic assist in dynamic wetting. Langmuir, 2000, 16: 2928–2935

    Article  Google Scholar 

  22. Gabay C, Berge B, Dovillaire G, et al. Dynamic study of a varioptic variable focal lens. Proc SPIE, 2002, 4767: 159–165

    Article  Google Scholar 

  23. Rayleigh L. On the capillary phenomena of jets. Proc R Soc London, 1879, 29: 71–79

    Article  Google Scholar 

  24. Lamb H. Hydrodynamics. 6th ed. Cambridge: Cambridge University Press, 1932

    MATH  Google Scholar 

  25. Strani M, Sabetta F. Free vibrations of a drop in partial contact with a solid support. J Fluid Mech, 1984, 141: 233–247

    Article  ADS  MATH  Google Scholar 

  26. Noblin X, Buguin A, Brochard-Wyart F. Self-propulsion of a water droplet in an electric field. Eur Phys J E, 2004, 14: 395–404

    Article  Google Scholar 

  27. Noblin X, Buguin A, Brochard-Wyart F. Triplon modes of puddles. Phys Rev Lett, 2005, 94: 166102

    Article  ADS  Google Scholar 

  28. Dong L, Chaudhury A, Chaudhury M K. Lateral vibration of a water drop and its motion on a vibrating surface. Eur Phys J E, 2006, 21: 231–242

    Article  Google Scholar 

  29. Fayzrakhmanova I S, Straube A V. Stick-slip dynamics of an oscillated sessile drop. Phys Fluids, 2009, 21: 072104

    Article  ADS  Google Scholar 

  30. Dupont J B, Legendre D. Numerical simulation of static and sliding drop with contact angle hysteresis. J Comput Phys, 2010, 229: 2453–2478

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Li Z L, Lai M C, He GW, et al. An augmented method for free boundary problems with moving contact lines. Comput Fluids, 2010, 39: 1033–1040

    Article  MathSciNet  MATH  Google Scholar 

  32. Hong F J, Cheng P, Sun Z, et al. Simulation of spreading dynamics of a EWOD droplet with dynamic contact angle and contact angle hysteresis. In: Proceedings of the ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer, 2009. MNHMT 2009-18558: 635–641

  33. Perot B, Nallapati R. A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows. J Comput Phys, 2003, 184: 192–214

    Article  ADS  MATH  Google Scholar 

  34. Chang W, Giraldo F, Perot B. Analysis of an exact fractional step method. J Comput Phys, 2002, 180: 183–199

    Article  ADS  MATH  Google Scholar 

  35. Dai M Z, Wang H, Perot B, et al. Direct interface tracking of droplet deformation. Atomiz Spr, 2002, 12: 721–736

    Article  Google Scholar 

  36. Dai M Z, Schmidt D P. Adaptive tetrahedral meshing in free-surface flow. J Comput Phys, 2005, 208: 228–252

    Article  ADS  MATH  Google Scholar 

  37. Quan S P, Schmidt D P. A moving mesh interface tracking method for 3D incompressible two-phase flows. J Comput Phys, 2007, 221: 761–780

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. Anderson D M, McFadden G B, Wheeler A A. Diffusive-interface method in fluid mechanics. Annu Rev Fluid Mech, 1998, 30: 139–165

    Article  MathSciNet  ADS  Google Scholar 

  39. Dussan E B. On the shredding of liquids on solid surfaces: Static and dynamic contact lines. Annu Rev Fluid Mech, 1979, 11: 371–400

    Article  ADS  Google Scholar 

  40. Ren W, EW. Boundary conditions for the moving contact line problem. Phys Fluids, 2007, 19: 022101

    Article  ADS  Google Scholar 

  41. Ren W, Hu D, E W. Continuum models for the contact line problem. Phys Fluids, 2010, 22: 102103

    Article  ADS  Google Scholar 

  42. Lavi B, Marmur A. The exponential power law: Partial wetting kinetics and dynamic contact angles. Colloid Surf A, 2004, 250: 409–414

    Article  Google Scholar 

  43. Walker SW, Shapiro B, Nochetto R H. Electrowetting with contact line pinning: Computational modeling and comparisons with experiments. Phys Fluids, 2009, 21: 102103

    Article  ADS  Google Scholar 

  44. Tanner L H. The spreading of silicone oil drops on horizontal surfaces. J Phys D-Appl Phys, 1979, 12: 1473–1484

    Article  ADS  Google Scholar 

  45. De Gennes P G, Hua X, Levinson P. Dynamics of wetting: Local contact angles. J Fluid Mech, 1990, 212: 55–63

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. Cox R G. Inertial and viscous effects on dynamic contact angles. J Fluid Mech, 1998, 357: 249–278

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. Eggers J. Toward a description of contact line motion at higher capillary numbers. Phys Fluids, 2004, 16: 3491–3494

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    XiaoLiang Li, GuoWei He & Xing Zhang

Authors
  1. XiaoLiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. GuoWei He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xing Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, X., He, G. & Zhang, X. Numerical simulation of drop oscillation in AC electrowetting. Sci. China Phys. Mech. Astron. 56, 383–394 (2013). https://doi.org/10.1007/s11433-012-4986-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-012-4986-0

Keywords

Search

Navigation