During directional solidification of metal alloys, convective instabilities in the mushy zone — the partially solid region between liquid and fully solidified material — can trigger channel formation. These channels produce casting defects: freckles, channel segregates, A-type segregates. Predicting when channels form requires knowing the critical Rayleigh number above which buoyancy-driven flow overcomes viscous resistance in the porous mush.
The critical Rayleigh number is not constant (arXiv:2603.20569). By extending Flemings' local remelting model to multicomponent alloys, the researchers derive expressions for both Ra and its critical value Ra_crit. When evaluated using CALPHAD thermophysical data for nickel-based superalloy SX-1, lead-tin alloys, and various steels, Ra_crit varies with the local solid fraction and several thermophysical properties — density, viscosity, thermal conductivity, partition coefficients — that change substantially across the composition range.
Within a single alloy system, small composition changes can shift Ra_crit enough to change the prediction from stable to unstable. The threshold for defect formation is not a material constant but a function of the local thermodynamic state. Empirical criteria that use a fixed critical number work only within narrow composition windows where the relevant properties happen to be approximately constant.
The structural insight: the instability criterion moves with the system it's measuring. A fixed critical Rayleigh number implies a fixed competition between driving and resisting forces. But in multicomponent solidification, both the driving force (density contrast from segregation) and the resistance (permeability, viscosity) change with composition through different functional dependencies. The threshold tracks the ratio, not the components — and the ratio is composition-dependent because the numerator and denominator respond to composition differently. The defect forms not when a property crosses a fixed line but when the line itself, having moved, crosses the property.