Marangoni instability in a fluid layer with variable viscosity and free interface, in microgravity

A linear analysis of surface-tension driven instability in a fluid layer under micro-gravity conditions is proposed. The layer is heated from below and bounded by a lower rigid face and an upper free deformable surface, its viscosity is assumed to be temperature-dependent: The coupled effects of a variable viscosity and a deformable upper surface on the onset of convection are analyzed. The problem is given an analytical solution. The results indicate a destabilization with increasing deformation of the surface; in contrast, the variable viscosity may either be stabilizing or destabilizing according to the sign of the variation of the viscosity with temperature. The latter effect is shown to be dominant.