Evolution of specific surface area with solid fraction during solidification

The specific surface area varies with solid fraction during phase transformation from liquid to solid. The few measurements available show a non-linear dependence of the specific surface area on the solid fraction, with an initial increase as the amount of solid increases, followed by a decrease as the system moves toward complete transformation. We derive a simple model for this behaviour assuming a combination of growth and coalescence. We obtain a relation exhibiting an increase with the square root of fraction solid at low volume fractions, independent of a growth law, and a decrease at higher volume fractions which depends on the model chosen to describe the coalescence of dendrites. By choosing an appropriate constant, the model accurately describes recent data presented by Limodin and co-workers.