Introducing density variation and pressure in thermodynamically self-consistent continuum phase-change models including phase-field

We present a thermodynamically self-consistent method to introduce dilation/density variation in continuum-scale phase-change models. Dilation incurs a pressure response via a hyperelastic contribution to the free energy that generalizes the lattice constraint. The dilation is represented entirely by species concentrations and permits composition, temperature, and phase-dependent specific volumes in a robust form. The impact of this approach is compared with the common assumption of the lattice constraint through demonstrative Stefan and phase-field models applied to the equilibrium of a Ni-Cu nanoparticle in equilibrium with its melt. Furthermore, the effect of phase and composition-dependent specific volume is explored in free dendritic growth behavior.