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.
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