Composition dependence of the critical Rayleigh number curve for macrosegregation in multicomponent metal alloys
Convective instabilities in the semi-solid mushy zone can trigger channel formation that leads to defects known as freckles, channel segregates and A-type segregates. In the present work, Flemings' model is used to determine conditions for the onset of local remelting when buoyancy-driven flow is suddenly triggered in an initially stagnant mushy zone. An expression in the form of a Rayleigh number $Ra$, and its associated critical value $Ra_{\rm crit}$, above which the local remelting condition is satisfied, are derived. Using thermophysical data from CALPHAD, these expressions are evaluated using results from benchmark experimental and numerical studies for the nickel-based superalloy SX-1 and Pb-Sn alloys. The correlation of this local-remelting criterion with previously reported empirical criteria is also tested for various steel compositions. It is found that $Ra_{\rm crit}$ varies with the local average solid fraction and several thermophysical properties. Since these properties can vary substantially within a relatively narrow composition range, it is suggested that $Ra_{\rm crit}$ is a strongly composition-dependent parameter.