Thermodynamically consistent incorporation of the Schneider rate equationsinto two-phase models - art. no. 011209

We formulate a solid-liquid two-phase model including viscous stresses, hea t conduction in the two phases, as well as heat exchange through the interf ace, and a phase change in the structure of nonequilibrium thermodynamics d escribed by a general equation for the nonequilibrium reversible-irreversib le coupling (GENERIC). The evolution of the microstructure is studied in te rms of the Schneider rate equations introducing the nucleation rate and the radial growth rate of the solid phase. The application of the GENERIC stru cture shows that this radial growth factor is not an additional, independen t material function but is to be expressed in terms of the difference in th e chemical potentials, in the temperatures, and in the pressures between th e two phases. The contribution due to the pressure difference appears in co njunction with the surface tension in such a way, that a driving force resu lts only if deviations from a generalized version of the Laplace equation o ccur. Furthermore, it is found that for conditions under which the radial g rowth rate is zero, the nucleation rate must vanish.