Freckle criteria for the upward directional solidification of alloys

Macrosegregation defect freckles result from the convective flow due to a density gradient in the mushy zone. Several freckle criteria were proposed in the literature for the evaluation of the freckle tendency of alloys and processes. These criteria were examined using experimental data of the upward directional solidification of Pb-Sn, Pb-Sb, and Pb-Sn-Sb systems. It is found that the freckle criterion given by Flemings and co-workers gives the best description of the freckle tendency. A Rayleigh number is derived from Flemings' criterion. The critical value of the Rayleigh number is found to be Ra-cr approximate to 1.