Solute trapping in Cahn–Hilliard diffusion equation

We solve analytically the one-dimensional Cahn–Hilliard diffusion equation for a dilute alloy, and calculate steady-state concentration profiles across the solid/liquid interface as a function of equilibrium partition coefficient ke and interface velocity. The calculated partition coefficient k reproduces correctly limiting behavior in both low and high interface velocity limits: at low interface velocity k→ke, and at high interface velocity k→1. This calculation also predicts that partitionless solidification occurs at higher interface velocity in alloys with smaller equilibrium partition coefficient, which is in agreement with the previously reported experimental results by Smith and Aziz.