Transient solution for droplet deformation under electric fields

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 formulas on their contributions. The theoretical framework can be extended to study similar problems, e.g., vesicle electrodeformation and relaxation.