  The axisymmetric electrohydrodynamic deformation of an elastic capsule with
capacitive membrane obeying Skalak law under uniform AC electric field is
investigated using analytical and boundary integral theory. The low capillary
number (the ratio of destabilizing shear or electric force to the stabilizing
elastic force) regime shows time-averaged prolate and oblate spheroid
deformations, and the time-periodic prolate-sphere, oblate-sphere breathing
modes are commensurate with the time averaged-deformation. A novel
prolate-oblate breathing mode is observed due to an interplay of finite
membrane charging time and the field reversal of the AC field. The study, when
extended to high capillary number, shows new breathing modes of
cylinder-prolate, cylinder-oblate, and biconcave-prolate deformation. These are
the results of highly compressive normal Maxwell stress at the poles and are
aided by weak compressive equatorial stress, characteristic of a capacitive
membrane. The findings of this work should form the basis for the understanding
of more complex biological cells and synthetic capsules for industrial
applications.
