GALERKIN ANALYSIS OF ELECTROTHERMAL INSTABILITIES IN PLANE LIQUID LAYERS

The stability of a horizontal layer of poorly conducting dielectric li quid subjected to a unipolar injection if 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 analy sis has been carried out by means of a Galerkin method with one and tw o trial functions. A single trial function provides useful analytical relations between parameters for the neutral stability surface. A seco nd trial function is necessary to account for the existence of oversta bility in the absence of thermal gradient and to achieve better accura cy in the solution.