Mathematical modelling of surface segregation in aluminum DC casting caused by exudation

A mathematical model for the development of a segregated layer of exudated droplets during DC casting of aluminum ingots is established. The model accounts for the metallostatic pressure driven interdendritic melt flow through the mushy zone by a Darcy type equation, the surface segregation due to this melt flow, and the decrease of the total solute concentration in different positions of the mush as a result of the exudation. The solution domain for the governing differential equations is constituted by the mushy zone of the cast. The main physical phenomena included in the model have been studied in a simple one dimensional case study.