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Long-wave dynamics of an inextensible planar membrane in an electric field

Published online by Cambridge University Press:  20 June 2014

Y.-N. Young ,
Shravan Veerapaneni  and
Michael J. Miksis
Y.-N. Young*
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
Shravan Veerapaneni
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MN 48109, USA
Michael J. Miksis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
*
†Email address for correspondence: yyoung@oak.njit.edu
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Abstract

In this paper the dynamics of an inextensible capacitive elastic membrane under an electric field is investigated in the long-wave (lubrication) leaky dielectric framework, where a sixth-order nonlinear differential equation with an integral constraint is derived. Steady equilibrium profiles for a non-conducting membrane in a direct current (DC) field are found to depend only on the membrane excess area and the volume under the membrane. Linear stability analysis on a tensionless flat membrane in a DC field gives the growth rate in terms of membrane conductance and electric properties in the bulk. Numerical simulations of a capacitive conducting membrane under an alternating current (AC) field elucidate how variation of the membrane tension correlates with the nonlinear membrane dynamics. Different membrane dynamics, such as undulation and flip-flop, are found at different electric field strength and membrane area. In particular a travelling wave on the membrane is found as a response to a periodic AC field in the perpendicular direction.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Membranes Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , pp. 406 - 431
Copyright
© 2014 Cambridge University Press 

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