Large deformation electrohydrodynamics of an elastic capsule in DC electric field

TL;DR

This study investigates how a spherical elastic capsule deforms under a uniform DC electric field, revealing complex shape transitions driven by electrical and hydrodynamic parameters, using analytical and numerical methods.

Contribution

It combines analytical theory and boundary element simulations to analyze large deformations of elastic capsules in DC electric fields, highlighting shape transitions and parameter effects.

Findings

Large deformations occur at high capillary numbers.

Intermediate times show biconcave, squaring, and hexagon shapes.

Shape transitions depend on membrane capacitance and conductance.

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 conductivities of the internal and external fluid media as well as capacitance and conductance of the membrane lead 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 (Boundary element method in the present case) to solve this highly non-linear 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 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.