Solidification in Closed Systems: Cluster Size Distribution and Its Driving Force

A multiphase model for liquid-solid and solid-liquid phase transitions is developed using the framework of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC). The morphology is described by the cluster size distribution function, including both unstable embryos as well as stable crystallites, for which a diffusion equation is proposed. The driving forces therein are identified in terms of the thermodynamic states of the two competing phases and of the surface tension. The connection to a previously developed model, which considered only the zeroth to third moments of the distribution function, is established. Whereas the growth rates of the crystallites are similar, the striking difference is the expression for the nucleation rate. The latter is furnished by the diffusion of clusters over a potential barrier in the model developed here, whereas such effects are absent in the previous model.