F. Pontiga et A. Castellanos, GALERKIN ANALYSIS OF ELECTROTHERMAL INSTABILITIES IN PLANE LIQUID LAYERS, IEEE transactions on industry applications, 30(4), 1994, pp. 862-876
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.