Onset of double-diffusive convection of unidirectionally solidifying binary solution with variable viscosity

Abstract

As a metallic melt solidifies, the viscosity variation may dramatically influence the convection induced by solidification as well as the microstructure of the resultant casting. In the present paper, we study the effect due to viscosity variation on the onset of double-diffusive convection occurring during the directional solidification of a binary solution cooling from below. Results show that as the viscosity contrast, denoted by γ in Eq. (14), increases the stability of convection is enhanced and the mode of convection can change from the mushy-layer mode into the boundary-layer mode. The critical Rayleigh number R^c_m, for both the mushy-layer and boundary-layer modes, increases exponentially with γ for all the parameter ranges considered, in contrast to the thermal convection case in which the critical Rayleigh number increases linearly with γ. This difference emerges mainly from the length scale of the convection layer, which is of solutal boundary-layer thickness in the present study and is of thermal boundary-layer thickness in the thermal convection case.