Transient electrohydrodynamics of a liquid drop

The transient behavior of a leaky dielectric liquid drop under a uniform electric field of small strength is investigated. It is shown that for small distortion from a spherical shape, the drop deforms to an ellipsoid, and the deformation time history is represented by D=D_∞[1-exp(-t/τ)], where D_∞ is the steady-state deformation and ${τ}=(a{{μ}}ₒ/{γ})(19{ ̃ \~{}{}}{{μ}}+16)(2{ ̃ \~{}{}}{{μ}}+3)/(40{ ̃ \~{}{}}{{μ}}+40)$is the characteristic time, $a$, ${γ}$, ${{μ}}ₒ$ and ${ ̃ \~{}{}}{{μ}}$ being the drop radius, the surface tension, the viscosity of ambient fluid, and ratio of the drop viscosity to that of the ambient fluid, respectively. The contributions of the net normal and tangential electrical stresses in the degree of deformation and fluid flow strength are also determined.