Marangoni electroconvection in the presence of an electric field in a fluid heated from above

Summary.

A poorly electrically conducting fluid, bounded below by a rigid boundary embedded with segmented electrodes and above by a perfectly conducting free surface, convects even when it is heated from above when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. Physically the forces driving such convection are due to the interaction of the applied electric field with space charges that develop in the bulk of the fluid and the surface tension at the free surface. The principle of exchange of stability is established using both moment and energy methods. We find the conditions for both marginal and overstable instabilities in terms of the negative Marangoni number M _a , as a function of the dimensionless electric parameter W and the wave number α. The critical values of M _a and α for both marginal and overstable states are computed. We found that the effect of W is to suppress Marangoni electroconvection in the neutral as well as in oscillatory states, and this convection sets in earlier in the case of an oscillatory state than in the neutral state.