Density change effects on crystal growth from the melt

When a crystal grows from its undercooled melt the local density changes, driving a convective flow in the liquid phase. Then. the purely diffusional description of the process ceases to be satisfactory. Moreover, the dynamic pressure associated with the How field may affect the melting temperature (and the effective undercooling) of the system. Both these effects have been addressed in recent experimental work. In the present study we derive a thermodynamically consistent phase-field model that accounts, for the density change effects in the solidification of a pure substance. Starting from a thermodynamic potential that includes squared gradient terms for both the order parameter and the density. the field equations are derived assuming positive local entropy production, The model is numerically solved in one dimension to show deviations from the classic phase-field description of the same phenomenon.