ON THE PROBLEM OF RADIAL SEGREGATION IN AN IDEALIZED HORIZONTAL BRIDGMAN CONFIGURATION - SCALING AND NUMERICAL APPROACHES

An order-of-magnitude analysis is carried out in order to estimate the maximum concentration difference DELTA-c at the interface in an idealized horizontal Bridgman configuration. In the convective regime limit, both DELTA-c and the region delta-y where solute buildup is important are seen to decrease when the intensity of convection in the melt (measured by the product of the Grashof and Schmidt numbers Gr x Sc) becomes stronger. Our theoretical approach predicts that DELTA-c and delta-y should follow a GrSc-2/9 power law in the high GrSc range and this result is confirmed by means of a two-dimensional numerical simulation of the problem. A detailed discussion of the domain of validity of both the convective regime approximation and the quasi-stationary assumption is also presented.