Morphological instability on Bénard-Marangoni convection during solidification: single-component system

Abstract

The critical conditions for the Bénard-Marangoni convective and morphological instabilities of a horizontal liquid layer of a single component, subject to a solidification process from below, are studied. The morphological effects, including the thickness and thermal conductivity of the solid layer and the capillary effect of the solid-liquid interface, have significant influences on the onset of instabilities at the marginal state. The analysis is based on the linear stability theory and the resulting eigenvalue equations are solved, using the shooting technique of Runge-Kutta-Gill's method of order four. The eigenvalue Rayleigh number, R, or Marangoni number, M, is evaluated. The numerical results indicate that the critical conditions decrease sensitively with the thickness ratio A for 0 < A < 1 and approach fixed values for A becoming large. The effects of the capillary at the solid-liquid interface and thermal conductivity in the solid layer tend to stabilize the system. The conducting ways of the latent heat act as dominant roles on determining the possible instability of the system.