Diffusive and phase change instabilities in a ternary mushy layer

Abstract

AbstractWe analyse the stability of a mushy layer during the directional solidification of a ternary alloy. Our model includes diffusive and convective transport of heat and solutes, coupled by an equilibrium thermodynamic constraint of the ternary phase diagram. The model contains phase change effects due to latent-heat release, solute rejection and background solidification. We identify novel convective instabilities, both direct and oscillatory, which are present under statically stable conditions. We examine these instabilities asymptotically by simplifying to a thin mushy layer with small growth rates. We also discuss numerical results for the full problem, confirming the asymptotic predictions and providing the stability characteristics outside the small-growth-rate approximation. A physical explanation for these instabilities in terms of parcel arguments is proposed, indicating that the instability mechanisms generally involve different rates of solute diffusion, different rates of solute rejection and different background solute distributions induced by the initial alloy composition.