Galerkin analysis of electrothermal instabilities in plane liquid layers

The stability of a horizontal layer of poorly conducting dielectric liquid subjected to a unipolar injection of ions and a thermal gradient is studied. Ions arising from injections and dissociation are supposed to have the same nature. Ionic mobility and electric permittivity are allowed to vary linearly with temperature. The linear stability analysis has been carried out by means of a Galerkin method with one and two trial functions. A single trial function provides useful analytical relations between parameters for the neutral stability surface. A second trial function is necessary to account for the existence of overstability in the absence of a thermal gradient and to achieve better accuracy in the solution