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Electrowetting with contact line pinning: Computational modeling and comparisons with experiments

Phys. Fluids 21, 102103 (2009); doi:10.1063/1.3254022

Published 30 October 2009

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Shawn W. Walker,1 Benjamin Shapiro,2 and Ricardo H. Nochetto3
1Department of Mathematics, Courant Institute, New York University, New York, New York 10012, USA
2Department of Bio-Engineering and the Institute for Systems Research, University of Maryland, College Park, Maryland 20742, USA
3Department of Mathematics and the Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
This work describes the modeling and simulation of planar electrowetting on dielectric devices that move fluid droplets by modulating surface tension effects. The fluid dynamics are modeled by Hele-Shaw type equations with a focus on including the relevant boundary phenomena. Specifically, we include contact angle saturation and a contact line force threshold model that can account for hysteresis and pinning effects. These extra boundary effects are needed to make reasonable predictions of the correct shape and time scale of liquid motion. Without them the simulations can predict droplet motion that is much faster than in experiments (up to 10–20 times faster). We present a variational method for our model, and a corresponding finite element discretization, which is able to handle surface tension, conservation of mass, and the nonlinear contact line pinning in a straightforward and numerically robust way. In particular, the contact line pinning is captured by a variational inequality. We note that all the parameters in our model are derived from first principles or from independent experiments except one (the parameter Dvisc that accounts for the extra resistive effect of contact angle hysteresis and is difficult to measure directly). We quantitatively compare our simulation to available experimental data for four different cases of droplet motion that include splitting and joining of droplets and find good agreement with experiments. ©2009 American Institute of Physics
History: Received 19 March 2009; accepted 20 August 2009; published 30 October 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/102103/1
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KEYWORDS and PACS

Keywords
PACS
  • 85.50.-n
    Dielectric, ferroelectric, and piezoelectric devices
  • 68.08.Bc
    Wetting
  • 68.03.Cd
    Surface tension and related phenomena
  • 47.11.Fg
    Finite element methods in fluid dynamics
  • 47.55.D-
    Drops and bubbles
  • 47.65.-d
    Magnetohydrodynamics and electrohydrodynamics
  • YEAR: 2009

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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AIP is a member of CrossRef AIP

REFERENCES (97)
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  1. B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3, 159 (2000).
  2. S. K. Cho, H. Moon, and C. -J. Kim, “Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits,” J. Microelectromech. Syst. 12, 70 (2003).
  3. R. A. Hayes and B. J. Feenstra, “Video-speed electronic paper based on electrowetting,” Nature (London) 425, 383 (2003).
  4. J. Lee, H. Moon, J. Fowler, T. Schoellhammer, and C. -J. Kim, “Electrowetting and electrowetting-on-dielectric for microscale liquid handling,” Sens. Actuators, A 95, 259 (2002).
  5. F. Mugele and J. -C. Baret, “Electrowetting: From basics to applications,” J. Phys.: Condens. Matter 17, R705 (2005).
  6. M. G. Pollack, R. B. Fair, and A. D. Shenderov, “Electrowetting-based actuation of liquid droplets for microfluidic applications,” Appl. Phys. Lett. 77, 1725 (2000).
  7. C. Quilliet and B. Berge, “Electrowetting: a recent outbreak,” Curr. Opin. Colloid Interface Sci. 6, 34 (2001).
  8. H. Ren, R. B. Fair, M. G. Pollack, and E. J. Shaughnessy, “Dynamics of electro-wetting droplet transport,” Sens. Actuators, B 87, 201 (2002).
  9. T. Roques-Carmes, R. A. Hayes, B. J. Feenstra, and L. J. M. Schlangen. “Liquid behavior inside a reflective display pixel based on electrowetting,” J. Appl. Phys. 95, 4389 (2004).
  10. T. Roques-Carmes, R. A. Hayes, and L. J. M. Schlangen, “A physical model describing the electro-optic behavior of switchable optical elements based on electrowetting,” J. Appl. Phys. 96, 6267 (2004).
  11. F. Saeki, J. Baum, H. Moon, J. -Y. Yoon, C. -J. Kim, and R. L. Garrell, “Electrowetting on dielectrics (ewod): Reducing voltage requirements for microfluidics,” Polym. Mater. Sci. Eng. 85, 12 (2001).
  12. E. Seyrat and R. A. Hayes, “Amorphous fluoropolymers as insulators for reversible low-voltage electrowetting,” J. Appl. Phys. 90, 1383 (2001).
  13. H. J. J. Verheijen and W. J. Prins, “Reversible electrowetting and trapping of charge: Model and experiments,” Langmuir 15, 6616 (1999).
  14. C. G. Cooney, C. -Y. Chen, M. R. Emerling, A. Nadim, and J. D. Sterling, “Electrowetting droplet microfluidics on a single planar surface,” Microfluid. Nanofluid. 2, 435 (2006).
  15. N. Kumari, V. Bahadur, and S. V. Garimella, “Electrical actuation of electrically conducting and insulating droplets using ac and dc voltages,” J. Micromech. Microeng. 18, 105015 (2008).
  16. B. Berge, “Électrocapillarité et mouillage de films isolants par l'eau (including an English translation),” C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Sci. Terre Univers 317, 157 (1993).
  17. B. Shapiro, H. Moon, R. Garrell, and C. -J. Kim, “Equilibrium behavior of sessile drops under surface tension, applied external fields, and material variations,” J. Appl. Phys. 93, 5794 (2003).
  18. S. K. Cho, H. Moon, J. Fowler, S. -K. Fan, and C. -J. Kim, “Splitting a liquid droplet for electrowetting-based microfluidics,” in International Mechanical Engineering Congress and Exposition, New York, NY, November 2001 (ASME, New York, 2001).
  19. J. Gong, S. K. Fan, and C. J. Kim, “Portable digital microfluidics platform with active but disposable lab-on-chip,” in 17th IEEE International Conference on Micro Electro Mechanical Systems (MEMS), Maastricht, The Netherlands, January 2004 (IEEE, Piscataway, 2004), pp. 355–358.
  20. S. W. Walker and B. Shapiro, “A control method for steering individual particles inside liquid droplets actuated by electrowetting,” Lab Chip 5, 1404 (2005).
  21. S. W. Walker and B. Shapiro, “Modeling the fluid dynamics of electrowetting on dielectric (ewod),” J. Microelectromech. Syst. 15, 986 (2006).
  22. K. J. Aström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers (Princeton University Press, Princeton, NJ, 2008).
  23. A. Isidori, Nonlinear Control Systems (Communications and Control Engineering) (Springer, New York, 1995).
  24. B. Shapiro, H. Moon, R. Garrell, and C. -J. Kim, Proceedings of the 16th Annual International Conference on Micro Electro Mechanical Systems (MEMS), Kyoto, Japan, January 2003, pp. 201–205.
  25. S. W. Walker. “Modeling, simulating, and controlling the fluid dynamics of electro-wetting on dielectric,” Ph.D. thesis, University of Maryland, College Park, 2007.
  26. S. W. Walker, “A hybrid variational-level set approach to handle topological changes,” M.S. thesis, University of Maryland at College Park, 2007.
  27. G. Lippmann, “Relations entre les phénomènes électriques et capillaires,” Ann. Chim. Phys. 5, 494 (1875).
  28. J. -L. Lin, G. -B. Lee, Y. -H. Chang, and K. -Y. Lien, “Model description of contact angles in electrowetting on dielectric layers,” Langmuir 22, 484 (2006).
  29. M. Vallet, M. Vallade, and B. Berge, “Limiting phenomena for the spreading of water on polymer films by electrowetting,” Eur. Phys. J. B 11, 583 (1999).
  30. V. Peykov, A. Quinn, and J. Ralston, “Electrowetting: A model for contact-angle saturation,” Colloid Polym. Sci. 278, 789 (2000).
  31. T. B. Jones, “On the relationship of dielectrophoresis and electrowetting,” Langmuir 18, 4437 (2002).
  32. T. D. Blake, A. Clarke, and E. H. Stattersfield, “An investigation of electrostatic assist in dynamic wetting,” Langmuir 16, 2928 (2000).
  33. C. Decamps and J. De Coninck, “Dynamics of spontaneous spreading under electrowetting conditions,” Langmuir 16, 10150 (2000).
  34. H. -W. Lu, K. Glasner, A. L. Bertozzi, and C. -J. Kim, “A diffuse-interface model for electrowetting drops in a Hele-Shaw cell,” J. Fluid Mech. 590, 411 (2007).
  35. A. Quinn, R. Sedev, and J. Ralston, “Contact angle saturation in electrowetting,” J. Phys. Chem. B 109, 6268 (2005).
  36. A. G. Papathanasiou, A. T. Papaioannou, and A. G. Boudouvis, “Illuminating the connection between contact angle saturation and dielectric breakdown in electrowetting through leakage current measurements,” J. Appl. Phys. 103, 034901 (2008).
  37. J. -C. Baret, B. Cross, A. Kumar, F. Mugele, and M. Pluntke, “Finite conductivity effects and apparent contact angle saturation in ac electrowetting,” Mater. Res. Soc. Symp. Proc. 899E, 69 (2005).
  38. R. S. Burdon, Surface Tension and the Spreading of Liquids (Cambridge University Press, Cambridge, 1949).
  39. Apparent and Microscopic Contact Angles, edited by J. Drelich, J. S. Laskowski, and K. L. Mittal (VSP BV, Zeist, The Netherlands, 2000).
  40. P. -G. de Gennes, F. Brochard-Wyart, and D. Quéré, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer-Verlag, New York, 2004).
  41. E. Wolfram and R. Faust, Wetting, Spreading and Adhesion (Academic, Leicestershire, England, 1978).
  42. E. Schaffer and P. Z. Wong, “Dynamics of contact line pinning in capillary rise and fall,” Phys. Rev. Lett. 80, 3069 (1998).
  43. E. B. Dussan, “On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. Part 2. Small drops or bubbles having contact angles of arbitrary size,” J. Fluid Mech. 151, 1 (1985).
  44. A. Hennig, K. -J. Eichhom, U. Staudinger, K. Sahre, M. Rogalli, M. Stamm, A. W. Neumann, and K. Grundke, “Contact angle hysteresis: Study by dynamic cycling contact angle measurements and variable angle spectroscopic ellipsometry on polyimide,” Langmuir 20, 6685 (2004).
  45. J. Berthier, P. Dubois, P. Clementz, P. Claustre, C. Peponnet, and Y. Fouillet, “Actuation potentials and capillary forces in electrowetting based microsystems,” Sens. Actuators, A 134, 471 (2007).
  46. F. Li and F. Mugele, “How to make sticky surfaces slippery: Contact angle hysteresis in electrowetting with alternating voltage,” Appl. Phys. Lett. 92, 244108 (2008).
  47. J. S. Kuo, P. Spicar-Mihalic, I. Rodriguez, and D. T. Chiu, “Electrowetting-induced droplet movement in an immiscible medium,” Langmuir 19, 250 (2003).
  48. P. -G. de Gennes, “Wetting: Statics and dynamics,” Rev. Mod. Phys. 57, 827 (1985).
  49. J. Lienemann, A. Greiner, and J. G. Korvink, “Modeling, simulation, and optimization of electrowetting,” IEEE Trans. Comput.-Aided Des. 25, 234 (2006).
  50. K. Brakke, “The surface evolver,” Exp. Math. 1, 141 (1992).
  51. K. Mohseni and A. Dolatabadi, “An electrowetting microvalve: Numerical simulation,” Ann. N. Y. Acad. Sci. 1077, 415 (2006).
  52. C. Eck, M. Fontelos, G. Grün, F. Klingbeil, and O. Vantzos, “On a phase-field model for electrowetting,” Interfaces Free Boundaries 11, 259 (2009).
  53. V. Berejnov and R. E. Thorne, “Effect of transient pinning on stability of drops sitting on an inclined plane,” Phys. Rev. E 75, 066308 (2007).
  54. M. O. Robbins and J. F. Joanny, “Contact angle hysteresis on random surfaces,” Europhys. Lett. 3, 729 (1987).
  55. J. P. Stokes, M. J. Higgins, A. P. Kushnick, S. Bhattacharya, and M. O. Robbins, “Harmonic generation as a probe of dissipation at a moving contact line,” Phys. Rev. Lett. 65, 1885 (1990).
  56. J. F. Joanny and M. O. Robbins, “Motion of a contact line on a heterogeneous surface,” J. Chem. Phys. 92, 3206 (1990).
  57. S. Kumar, D. H. Reich, and M. O. Robbins, “Critical dynamics of contact-line motion,” Phys. Rev. E 52, R5776 (1995).
  58. H. S. Hele-Shaw, “The flow of water,” Nature (London) 58, 34 (1898).
  59. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, New York, 1967).
  60. M. P. do Carmo, Differential Geometry of Curves and Surfaces (Prentice Hall, Upper Saddle River, NJ, 1976).
  61. R. F. Probstein, Physicochemical Hydrodynamics: An Introduction, 2nd ed. (Wiley, New York, 1994).
  62. Y. D. Shikhmurzaev, Capillary Flows with Forming Interfaces, 1st ed. (Chapman & Hall/CRC, Boca Raton, 2007).
  63. Lecture Notes in Physics: Capillarity Today, edited by G. Pétré and A. Sanfeld (Springer-Verlag, New York, 1990).
  64. J. A. Marsh, S. Garoff, and E. B. Dussan, “Dynamic contact angles and hydrodynamics near a moving contact line,” Phys. Rev. Lett. 70, 2778 (1993).
  65. P. A. Thompson and M. O. Robbins, “Simulations of contact-line motion: Slip and the dynamic contact angle,” Phys. Rev. Lett. 63, 766 (1989).
  66. M. Haataja, J. A. Nieminen, and T. Ala-Nissila, “Molecular ordering of precursor films during spreading of tiny liquid droplets,” Phys. Rev. E 52, R2165 (1995).
  67. G. He and N. G. Hadjiconstantinou, “A molecular view of Tanner's law: molecular dynamics simulations of droplet spreading,” J. Fluid Mech. 497, 123 (2003).
  68. V. M. Samsonov and A. S. Ratnikov, “Comparative molecular dynamics study of simple and polymer nanodroplet spreading,” Colloids Surf., A 298, 52 (2007).
  69. D. Bonn, J. Eggers, J. Indekeu, J. Meunier, and E. Rolley, “Wetting and spreading,” Rev. Mod. Phys. 81, 739 (2009).
  70. T. D. Blake, “The physics of moving wetting lines,” J. Colloid Interface Sci. 299, 1 (2006).
  71. T. Qian, X. P. Wang, and P. Sheng, “A variational approach to moving contact line hydrodynamics,” J. Fluid Mech. 564, 333 (2006).
  72. L. C. Evans, Partial Differential Equations (American Mathematical Society, Providence, RI, 1998).
  73. F. Ben Belgacem, Y. Renard, and L. Slimane, “A mixed formulation for the Signorini problem in nearly incompressible elasticity,” Appl. Numer. Math. 54, 1 (2005).
  74. R. Glowinski, Numerical Methods for Nonlinear Variational Problems (Springer-Verlag, New York, 1984).
  75. E. B. Dussan, “The moving contact line: The slip boundary condition,” J. Fluid Mech. 77, 665 (1976).
  76. P. A. Durbin, “Considerations on the moving contact-line singularity, with applications to frictional drag on a slender drop,” J. Fluid Mech. 197, 157 (1988).
  77. Y. D. Shikhmurzaev, “Singularities at the moving contact line: Mathematical, physical and computational aspects,” Physica D 217, 121 (2006).
  78. V. Girault and P. A. Raviart, Finite Element Methods for Navier–Stokes Equations: Theory and Algorithms (Springer-Verlag, Berlin, 1986).
  79. S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, 2nd ed. (Springer, New York, 2002).
  80. T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, 1st ed. (Dover, Mineola, NY, 2000).
  81. G. Evans, J. Blackledge, and P. Yardley, Numerical Methods for Partial Differential Equations (Springer-Verlag, London, 2000).
  82. S. Larsson and V. Thomée, Partial Differential Equations with Numerical Methods, Texts in Applied Mathematics, 1st ed. (Springer, New York, 2008).
  83. E. Bänsch, “Finite element discretization of the Navier–Stokes equations with a free capillary surface,” Numerische Mathematik 88, 203 (2001).
  84. E. Bänsch, P. Morin, and R. H. Nochetto, “A finite element method for surface diffusion: The parametric case,” J. Comput. Phys. 203, 321 (2005).
  85. G. Dziuk, “An algorithm for evolutionary surfaces,” Numerische Mathematik 58, 603 (1990).
  86. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer, New York, 2001).
  87. T. Aubin, Nonlinear Analysis on Manifolds: Monge–Ampere Equations (Springer, New York, 1982).
  88. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications (SIAM, Philadelphia, 1987).
  89. G. Duvaut and J. L. Lions, Inequalities in Mechanics and Physics (Springer, New York, 1976).
  90. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer-Verlag, New York, 1991).
  91. P. G. Ciarlet, The Finite Element Method for Elliptic Problems: Classics in Applied Mathematics, 2nd ed. (SIAM, Philadelphia, 2002).
  92. J. M. Escobar, G. Montero, R. Montenegro, and E. Rodríguez, “An algebraic method for smoothing surface triangulations on a local parametric space,” Int. J. Numer. Methods Eng. 66, 740 (2006).
  93. J. R. Shewchuk, “Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator,” Lect. Notes Comput. Sci. 1148, 203 (1996).
  94. S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer-Verlag, New York, 2003).
  95. Handbook of Chemistry and Physics, 82th ed., edited by D. R. Lide (CRC, Boca Raton, FL, 2002).
  96. K. -L. Wang and T. B. Jones, “Electrowetting dynamics of microfluidic actuation,” Langmuir 21, 4211 (2005).
  97. See EPAPS supplementary material at http://dx.doi.org/10.1063/1.3254022 for a short writeup on deriving the Young–Lippman equation via shape differentiation. [EPAPS]

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