Effects of solid layer thickness and nominal composition on double-diffusive instabilities during solidification of a binary alloy cooled from the top

Abstract

When a horizontal layer of fluid is cooled and solidified from the top, a cellular form of natural convection may occur inside the liquid, similar to that observed during classical Rayleigh–Benard convection. As a result of the interaction between the cellular convection and directional solidification, the phase-change interface tends to get wavy. The above situation can be mathematically represented by considering two horizontal parallel plates at z = 0 and z = h. The lower plate at z = h is fixed at temperature $T = T_1$ and the upper plate at z=0 is kept at a temperature $T = T_0$. Due to occurrence of solidification on account of cooling from the top, there is a solid–liquid interface at $z=\eta \leq \eta \leq h)$, which is assumed to be at a quasi-steady state. The physical situation is shown schematically in Fig. 1. As a result of interface perturbation on account of convection occurring below, the interface is likely to assume an irregular shape. It can be noted here that when the solidifying medium is a binary alloy that solidifies nonisothermally, the natural convection in the liquid is double-diffusive in nature (as a consequence of concentration and temperature gradients prevailing in the solidifying domain). Instabilities in thermo-solutal convection in such cases have attracted considerable attention in the literature [1,2]. However, the effects of nominal alloy composition and solid layer thickness on associated double-diffusive instabilities are yet to be addressed in the literature, to the best of our knowledge.