Electrohydrodynamic Rayleigh-Taylor Bulk Instability

Abstract

A stability criterion is found for an initially static, stratified fluid subject to an electric stress. The equilibrium fluid density, permittivity, viscosity, and space charge distributions are functions of the vertical spatial coordinate, with gradients directed parallel to the imposed electric field intensity and gravitational acceleration. In the limit where the fluid is perfectly insulating, sufficient conditions for stability are found; the principle of exchange of stabilities is shown, and variational principles derived for the eigenfrequencies and, in the case of no space charge, for the critical field strength. An experiment demonstrates instability in the dielectrophoretic limit of no bulk free charge. The property gradients are induced thermally, and incipience of instability, as measured by the Schmidt-Milverton heat-transfer technique, is successfully predicted by the theoretical criterion.