The Maxwell–Stefan equations for diffusion in multiphase systems with intersecting dividing surfaces

In this paper, the Maxwell–Stefan theory for diffusion is extended to multiphase systems with intersecting dividing surfaces. The general Maxwell–Stefan equation is separated into equations for bulk diffusion, surface diffusion and (common) line diffusion. Expressions for the driving forces in these equations are derived using the jump entropy inequality and the entropy inequality at the common line. The resulting equations for surface and line diffusion are more general than previously reported extensions of Fick’s law. They incorporate contributions from forced diffusion, and diffusion resulting from surface tension and line tension gradients into the total diffusive flux.