  A transient analysis to quantify droplet deformation under DC electric fields
is presented. The full Taylor-Melcher leaky dielectric model is employed where
the charge relaxation time is considered to be finite. The droplet is assumed
to be spheroidal in shape for all times. The main result is an ODE governing
the evolution of the droplet aspect ratio. The model is validated by
extensively comparing predicted deformation with both previous theoretical and
numerical studies, and with experimental data. Furthermore, the effects of
parameters and stresses on deformation characteristics are systematically
analyzed taking advantage of the explicit formulae on their contributions. The
theoretical framework can be extended to study similar problems, e.g., vesicle
electrodeformation and relaxation.
