Interfaces in Electrophoresis, Two-Phase Models, and Excitable Media

Abstract

Three examples of interfaces will be discussed: all of them somewhat away from the mainstream of the conference. They are modelled by “interior transition layers” in solutions of partial differential equations of reaction-diffusion-advection type. It is there fore no surprise that two of the examples are involved with the transport of chemical species in solution; the interface then is formed by the action of competition between a diffusive process, which acts to smooth out the interface, and a force (chemical reaction or applied electric field) which tends to sharpen it. The third example, though not involving chemicals, does have a diffusive type process, related to a Gibbs free energy, and also an aggregative force (a double-well potential wich attempts to force states into one or another of two preferred ones). Interfaces resulting from the balance of diffusive and aggregative forces like this occur in other contexts as well (especially in biology and geophysics). It is hoped therefore that this exposition will serve to be illustrative and also suggestive of phenomena well beyond the confines the specific examples discussed here.