Non-Equilibrium Phase Boundaries

When a dynamic equilibrium prevails at the a/p phase boundary, the exchange fluxes Pi b and Jfb occur across the interface and cancel each other individually. 

Let us consider ionic systems. In non-equilibrium state, the potential drop across the interface differs from the equilibrium value A tpb (eq). If the adjacent phases a and P chemically buffer the interface on their respective sides, as is normally true considering the large number of particles in the bulk relative to the small number of interface particles, the overall potential drop, Atjb, is only due to the electric potential change 8 pb. Let us then expand jf (A/ f) in a series and linearize 

Equation (4.119) reflects the dynamic situation at the interface. For higher order approximations we have to introduce kinetic interface models. This will be done for different phase boundaries in Chapter 10. At this point we introduce the most simple assumption the interface is a kinetic barrier which must be overcome by the individual ions through thermal activation. In such a model, the externally applied electric field increases the activation barrier in one direction and decreases it in the reverse direction. Letting a denote the asymmetry factor of the barrier, we can then formulate 

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Truskinovskii, L.M. Dynamics of non-equilibrium phase boundaries in a heat conducting non-linearly elastic medium. PMM USSR 51 (1987) 777-784 (English transl. of Prikl. Matem. Mekhan. 51 (1987), 1009-1019. 

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