Surface Conservation Laws at Microscopically Diffuse Interfaces

In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities coupled via surface conservation laws of excess surface quantities. While this approach is for microscopically sharp interfaces, its applicability in the context of microscopically diffuse is less theoretically well-established. Furthermore, surface conservation laws (and interfacial in general) are often derived phenomenologically rather than systematically. In this article, provide a mathematically rigorous justification for surface conservation laws at diffuse interfaces on an asymptotic analysis of transport processes in the boundary layer and derive general the surface and normal fluxes that appear in surface conservation laws. Next, we use non-thermodynamics to formulate surface conservation laws in terms of chemical potentials a method for systematically deriving the structure of the interfacial layer. Finally, we conservation laws for a few examples from diffusive and electrochemical transport.