Surface Tension Driven Instability Due to Internal Heat Sources in a Horizontal Layer of Binary Liquid Mixture

Abstract

Linear stability theory is applied to the problem of the onset of surface-tension-driven instability in a horizontal layer of binary liquid mixture confined at the bottom by a rigid, thermally insulating wall and at the top by a non-deformable free surface at which Newton’s cooling law is assumed to hold. It is also assumed that the liquid layer is heated by uniformly distributed internal heat sources which produce a nonlinear temperature profile and, in addition, a nonlinear concentration profile through the Soret effect. By neglecting small terms including the Soret coefficient S_T, an eigenvalue system of eighth order is derived and is then solved exactly. For wide ranges of various parameters, the conditions under which instability sets in are determined numerically. As compared with the corresponding linear temperature case (M. Takashima: J. Phys. Soc. Jpn. 47 (1979) 1321; 49 (1980) 802), it is found that the nonlinear temperature profile produced by internal heat sources makes the liquid layer less stable for both stationary and oscillatory modes.