Thermal instability in spherical liquid shells induced by surface tension

Abstract

A linear perturbation method is employed to determine the condition for neutral stability in spherical liquid shells induced by surface tension mechanism. Three possible boundary conditions are considered: at least one boundary free or both. The critical Marangoni numbers for the onset of cellular convections are found for two types of steady radial temperature distributions in the spherical shells. Results are compared with those induced by buoyancy mechnism. It is concluded that surface tension forces are much more effective than buoyancy forces in producing thermal instability and a parabolic steady temperature distribution is more susceptible than a linear one to thermal disturbances due to surface tension forces. Heat transfer between a free surface and the ambient promotes thermal stability in liquid shells.