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Large-deformation electrohydrodynamics of an elastic capsule in a DC electric field

Published online by Cambridge University Press:  23 February 2018

Sudip Das  and
Rochish M. Thaokar Open the ORCID record for Rochish M. Thaokar [Opens in a new window]
Sudip Das
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India
Rochish M. Thaokar*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India
*
†Email address for correspondence: rochish@che.iitb.ac.in
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Abstract

The dynamics of a spherical elastic capsule, containing a Newtonian fluid bounded by an elastic membrane and immersed in another Newtonian fluid, in a uniform DC electric field is investigated. Discontinuity of electrical properties, such as the conductivities of the internal and external fluid media as well as the capacitance and conductance of the membrane, leads to a net interfacial Maxwell stress which can cause the deformation of such an elastic capsule. We investigate this problem considering well-established membrane laws for a thin elastic membrane, with fully resolved hydrodynamics in the Stokes flow limit, and describe the electrostatics using the capacitor model. In the limit of small deformation, the analytical theory predicts the dynamics fairly satisfactorily. Large deformations at high capillary number, though, necessitate a numerical approach (axisymmetric boundary element method in the present case) to solve this highly nonlinear problem. Akin to vesicles, at intermediate times, highly nonlinear biconcave shapes along with squaring and hexagon-like shapes are observed when the outer medium is more conducting. The study identifies the essentiality of parameters such as high membrane capacitance, low membrane conductance, low hydrodynamic time scales and high capillary number (the ratio of the destabilizing electric force to the stabilizing elastic force) for observation of these shape transitions. The transition is due to large compressive Maxwell stress at the poles at intermediate times. Thus such shape transition can be seen in spherical globules admitting electrical capacitance, possibly irrespective of the nature of the interfacial restoring force.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Biological Fluid Dynamics: Capsule/cell dynamics Drops and Bubbles: Electrohydrodynamic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 841 , 25 April 2018 , pp. 489 - 520
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Copyright
© 2018 Cambridge University Press 

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