  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.
