The Stability of a Horizontal Layer of Dielectric Fluid Under the Simultaneous Action of a Vertical Dc Electric Field and a Vertical Temperature Gradient

Linear stability theory is applied to the problem of the onset of convective instability in an infinite layer of poorly conducting dielectric fluid confined between two horizontal rigid planes under the simultaneous action of a vertical dc electric field and a vertical temperature gradient. Both the dielectric constant and the electrical conductivity of the fluid are assumed to be functions of temperature. Applying approximations analogous to the usual Boussinesq approximation an equation of sixth order, with space-varying coefficients, and the relevant boundary conditions are derived. Under the assumption that the neutral state is a stationary one, the method of power series expansion is used to obtain the eigenvalue relationship which is then computed numerically. It is shown that (1) the temperature dependence of the dielectric constant has no significant effect on the fluid layer; (2) when the electrical conductivity is assumed to be a linear function of temperature the electric field exhibits a stabilizing effect on the fluid layer; (3) when the electrical conductivity is assumed to be a quadratic function of temperature the electric field can exhibit a strongly destabilizing effect on the fluid layer, and the numerical results in this case coincide with the existing experimental results in order of magnitude.