Electroconvective instability with a stabilizing temperature gradient. I. Theory

Abstract

A uniform vertical electric field produces an instability in a poorly conducting liquid subject to a vertical temperature gradient. A gradient in conductivity resulting from the temperature gradient causes free charge to accumulate in the fluid when an electric field is applied. For the cases considered, the gradient in dielectric constant can be neglected with the significant electric force being that due to the free charge. The threshold conditions for the instability are predicted using linear perturbation theory. Approximations are made which allow the equations with space-varying coefficients to be solved. The analysis shows that, for liquids with short or moderate electrical relaxation times, the electric field causes the internal gravity wave propagating downward to become unstable.