An analysis is conducted on the coupling between thermosolutal convection due to the Soret effect and a solid-liquid interface. This phase boundary forms when a thin layer of a dilute binary mixture is partially solidified from above. A nonlinear evolution equation for the amplitude of the concentration perturbation has been derived [L. Hadji, Phys. Rev. E 47, 1078 (1993)]. The derivation takes into account the coupled effects of steady convection in the Soret regime and the deformations in the solid-liquid interface. In this paper, the solution of the equation is reexamined using a fully implicit finite difference scheme combined with Newton linearization with coupling. We have obtained results which were previously unobtainable when a fully explicit scheme was used. It is found that, for a range of values of the various parameters, the solid-liquid interface exhibits a cellular morphology consisting of thin fingers that extend deep into the liquid.

• Received 2 May 1994

DOI:https://doi.org/10.1103/PhysRevE.50.2361