Effect of Dielectrophoretic Forces on the Bénard Instability

When a fluid is heated from below, there is a critical temperature gradient above which the fluid becomes unstable and convection results. The effect of dielectrophoretic forces on this critical temperature gradient is studied. Dielectrophoretic forces are caused by an electric field and a gradient in dielectric constant. The principle of exchange of stabilities is shown to hold for a certain set of boundary conditions. Variational principles are derived for various boundary conditions. These variational principles and the Galerkin method are then used to find approximate solutions for the critical temperature gradient as a function of the wavelength and the electric field.