A Derivation of a Phase Field Model with Fluid Properties

We extend the basic phase field model to physical problems in which fluid properties, such as velocity, pressure and density variations, are incorporated along with heat properties within the context of a unified and consistent derivation. One thereby obtains a system of parabolic differential equations with the variables temperature, phase, fluid velocity, density and pressure. The constants in the equations can be related to a rate constant and to equilibrium values in the pure phases.