Electrohydrodynamics of a liquid drop: the time-dependent problem

This theoretical paper is an extension of Sir Geoffrey Taylor's work on the flow field induced by an electric field in and about a liquid drop immersed in an incompressible conducting fluid. In the present work it is assumed that the inducing electric field varies with time $t$ as cos $\omega $$t$, where $\omega $ is a constant. The solution presented is based on the assumption that the flow field set up is weak and the convection terms in the momentum equation can be ignored. It is shown that for fluids of low viscosity or when the applied electric field is oscillating very rapidly the term $\rho \partial u/\partial t$, where $\rho $ and $u$ are the fluid density and velocity, respectively, cannot be neglected. In these cases the results of the authors who have completely ignored this term are not correct.