A phase field model with electric current

Abstract

A diffuse interface model is presented for the solidification or melting of a pure single crystal that includes the effect of an applied electric current. A coupled set of differential equations modelling the evolution of the phase, the temperature and the current density are derived by applying principles of non-equilibrium thermodynamics. An asymptotic analysis shows that as the diffuse interfacial region tends to zero thickness, classical results are recovered. For this model classical results mean that Joule heating and the Thomson effect in the bulk phases and the Peltier effect at the interface are included. A one-dimensional numerical solution is presented and compared to an analytical solution verifying the model and asymptotic analysis. This phase field model is relevant for solid–liquid phase changes occurring in pure metallic and semi-conductor materials.