A SCALING ANALYSIS OF THE UNIDIRECTIONAL SOLIDIFICATION OF A BINARY ALLOY

A scaling analysis of the conservation equations for momentum, heat an d species transport inside the solidifying mushy zone of a binary allo y is performed to examine systematically common assumptions and predic t general behavior of the mixture during freezing. Several terms in th e momentum equation are found to be negligible throughout the solidify ing domain, and the use of D'Arcy's law to approximate the momentum eq uations in the mushy zone is found to be valid except in the region ne ar the liquidus isotherm. A criterion is developed to define this regi on, and the dependence of the streamfunction and buoyancy driven veloc ity on material properties and fraction solid is determined. The energ y equation is examined to provide scaling laws for the mushy zone and solid region thicknesses, as well as the transient chill wall temperat ure. Advection is shown to dominate solute transport throughout the mu sh, although, in the denser regions of the solid-liquid region, liquid velocities are so small as to have a negligible effect on macrosegreg ation. Numerical calculations performed for Pb-Sn and Al-Mg alloys at different cooling rates confirm trends suggested by the scaling analys is. Copyright (C) 1996 Elsevier Science Ltd.