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Numerical-asymptotic models for the manipulation of viscous films via dielectrophoresis

Published online by Cambridge University Press:  02 September 2020

David J. Chappell Open the ORCID record for David J. Chappell [Opens in a new window]  and
Reuben D. O'Dea Open the ORCID record for Reuben D. O'Dea [Opens in a new window]
David J. Chappell
Affiliation:
School of Science and Technology, Nottingham Trent University, Clifton Campus, NottinghamNG11 8NS, UK
Reuben D. O'Dea*
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, NottinghamNG7 2RD, UK
*
†Email address for correspondence: reuben.odea@nottingham.ac.uk
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Abstract

The effect of an externally applied electric field on the motion of an interface between two viscous dielectric fluids is investigated. We first develop a powerful, efficient and widely applicable boundary integral method to compute the interface dynamics in a general multiphysics model comprising coupled Laplace and Stokes flow problems in a periodic half-space. In particular, we exploit the relevant Stokes and Laplace Green's functions to reduce the problem to one defined on the interfacial part of the domain alone. Secondly, motivated by recent experimental work that seeks to underpin the development of switchable liquid optical devices, we concentrate on a fluid–air interface and derive asymptotic approximations suitable to describe the behaviour of a thin film of fluid above an array of electrodes. In this case, the problem is reduced to a single nonlinear partial differential equation describing the film height, coupled to the electrostatic problem via suitable numerical solution or via an asymptotic formula for electrostatic forcing. Comparison against numerical simulations of the full problem shows that the reduced models successfully capture key features of the film dynamics in appropriate regimes; all three approaches are shown to reproduce experimental results.

JFM classification

Interfacial Flows (free surface): Thin films Mathematical Foundations: Computational methods Complex Fluids: Dielectrics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A35
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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