Abstract
A microsegregation model, based on a boundary layer concept, is proposed for solidification of alloys. The model is derived by considering finite-rate solute diffusion both in the liquid and in the solid. A solutal Fourier number is used to characterize the extent of finite-rate solute diffusion in the liquid phase ahead of the moving solid/liquid interface. This new parameter is the liquid counterpart of the solutal Fourier number in the solid phase used before to characterize finite-rate back-diffusion in the solid. It can be obtained through the knowledge of either the local solidification time or the operating point of the cell/dendrite tip (among other parameters). The present microsegregation model covers the entire spectrum of solidification rates, up to the limit of a microsegregation free solid. The model predictions show good agreement with a previous rapid solidification experiment involving an Ag–Cu alloy. Also, a new relation is derived for the primary dendrite arm spacing.
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