Thermocapillary instability of a spherical shell is investigated in terms of the usual Marangoni number in conventional notation with the exception of L, which stands for the thickness of fluid layer. The main objective of this study is the analytical investigation of the curvature effect on the instability of surface tension driven flow between two horizontal plates (Pearson 1958). The critical Marangoni number Mac, including the curvature effect, is related to the critical value of the usual Mac where , R and B respectively denote the effect of a surfactant and spherical curvature on the cartesian Laplacian, and B is the Biot number (a measure for the heat loss from outer free surface). Results on the fluid motion in a spherical shell with a solid core and a free surface stressed by thermo capillary force shows that the effect of curvature and that of surfactant are to increase the stability of the motion.
Arpaci, V.S., Selamet, E., Chai, A.T., Thermocapillary Instability of Spherical Shells, Fund. of Forced & Mixed Convection and Transport Phenomena, ASME, New York, NY, HTD Vol. 180, pp. 65-71, December 1, 1991.