The effect of macroscopic solute diffusion in the liquid upon surface macrosegregation

An existing one-dimensional mathematical model that predicts the macrosegregation formation due to solidification shrinkage has been modified to also account for the macroscopic diffusion of solute in the liquid. It is shown both numerically and analytically that such solute diffusion has an almost negligible influence on the predicted solute profile, except in a very thin layer near the chill surface, where severe solute depletion develops. This layer is related to a discontinuity in the diffusive solute flux at the surface, and for a moderately cooled Al-4.5 pct Cu alloy, the layer thickness is of the order 100 µm. When the lever rule is imposed, the solute concentration at the surface becomes equal to the partition coefficient multiplied by the nominal alloy concentration, and the boundary layer solidifies completely once the temperature drops below the liquidus temperature of the (initial) melt. This indicates that assuming local thermodynamical equilibrium at a domain boundary when simultaneously accounting for the macroscale solute diffusion should be reconsidered in macrosegregation modeling.