Dielectrophoretic,thermal instability in a spherical shell of fluid

Abstract

This paper is concerned with the dielectrophoretic instability of a spherical shell of fluid. A dielectric fluid, contained in a spherical shell, with rigid boundaries is subjected to a simultaneous radial temperature gradient and radial a.c. electric field. Through the dependence of the dielectric constant on temperature, the fluid experiences a body force somewhat analogous to that of gravity acting on a fluid with density variations. Linear perturbation theory and the assumption of exchange of stabilities lead to an eighth order differential equation in radial dependence of the perturbation temperature. The solution to this equation, satisfying appropriate boundary conditions, yields a critical value of the electrical Rayleigh number and corresponding critical wave number at which convective motion begins. The dependence of each critical number is presented as a function of the gap size and temperature gradient. In the limit of zero shell thickness both the critical Rayleigh number and critical wave number agree with results for the case in the infinite plane problem.