Modification of mathematical analyses and related physical descriptions used to describe channel segregation

The aim in this paper is to develop further and extend the application of the mathematical descriptions based on the previously developed local solute redistribution equation’ for the alloy-solidification process. To this end, a modified local solute redistribution equation for unidirectional solidification is presented and, using channel perturbation analysis based on this equation, a condition is developed for unstable flow and possible channel segregation which relates the interdendritic fluid velocity to the isotherm velocity. On assuming this condition to hold, a physical description related to the modified local solute redistribution equation is proposed, and a possible mechanism is presented for local remelting and the formation of channel segregation.