Continuum Thermodynamics of the Phase Transformation of Thermoelastic Fluids

Abstract

This study uses continuum thermodynamics of pure thermoelastic fluids to examine their phase transformation. To examine phase transformation kinetics, a special emphasis is placed on the jump condition for the axiom of entropy inequality, thereby recovering the conventional result that stable phase equilibrium coincides with continuity of temperature, pressure, and free enthalpy across the phase boundary. Moreover, this jump condition leads to the formulation of a constitutive relation for the phase transformation mass flux, $-\left[\left[\frac{1}{T}\mathbf{q}\right]\right]\cdot\mathbf{n}^{\Gamma}/\left[\left[s\right]\right]$, where $\left[\left[\frac{1}{T}\mathbf{q}\right]\right]\cdot\mathbf{n}^{\Gamma}$ is the jump in entropy flux normal to, and across the phase interface $\Gamma$, and $\left[\left[s\right]\right]$ is the corresponding jump in entropy. This relation implies that phase transformations must be accompanied by a jump in temperature across the phase boundary. Encouraging agreement is found between this formula and limited available experimental data. Further evidence is needed to conclusively validate this proposed constitutive model. This continuum framework is well suited for implementation in a computational framework, such as the finite element method.