Effect of surface tension on the onset of convection in a double-diffusive layer

Abstract

The effect of surface tension on the stability of a double-diffusive layer is considered using linear stability analysis. The surface tension is assumed to vary linearly with temperature and solute concentration. The eigenvalue problem is solved by the Galerkin method. Results show that the predicted stability boundary based on Marangoni effects alone is completely altered in the presence of buoyancy effects induced by low gravity levels (∼10−5 g). At reduced gravity levels, salt-finger instability may onset in the overstable mode due to the stabilizing effect of surface tension. Fluid properties in terms of the Prandtl and the Lewis numbers have a profound effect on the stability conditions; opposite stability characteristics are found in salt solutions and in molten metals. In the diffusive case, the competition between the surface-tension and the double-diffusive effects can generate bimodal marginal stability curves, thus resulting in the simultaneous occurrence of two instability modes with different wave numbers and oscillation frequencies.