Time-dependent electrohydrodynamics of a compressible viscoelastic capsule in the small-deformation limit

A theoretical analysis of the time-dependent electrohydrodynamics of a viscoelastic compressible capsule, characterized by the two-dimensional Young's modulus and surface viscosity, is studied in the small-deformation limit. A systematic ac electrohydrodynamics analysis is conducted, and time-independent and time-periodic deformations are related to the electric capillary number and the membrane properties. Additionally, the relaxation of a capsule stretched by a dc electric field is also presented. This necessitates an accurate estimation of the initial strain field in the stretched capsule. Both an oscillatory analysis and an analysis of the relaxation of a stretched capsule are presented for a capsule containing an aqueous phase, modeled as a perfect conductor, and suspended in a perfect dielectric with an infinitesimally thin viscoelastic membrane separating the two. The membrane is assumed to be a perfect dielectric with no electrical contrast with the suspending fluid.

Figure 1

An elastic capsule under an electric-field spherical coordinate system. ${\mathbf{f}}^{\mathbf{E}}$ is the net electrical traction, ${\mathbf{f}}^{\mathbf{h}}$ is the net hydrodynamic traction, and $T_{\phi }$ and $T_{\theta }$ are the azimuthal and meridional stress.