Analysis of oscillations of concentration in bounded binary mixtures taking into account surface effects

Abstract

We consider a binary mixture bordering a substrate and vacuum and forming a film. The distribution of one of the mixture components is described by the Cahn-Hillard equation with asymmetric boundary conditions taking into account (wetting) processes occurring at the boundary and in surface layers of the film and, probably, the effect of a constant external magnetic field. The parameters of the problem characterize the bulk correlation length, pair interaction intensity in the nearest neighbor approximation at the film boundary, and the renormalized magnetic field acting on the spins in the surface layers of the system. The range of parameters generating oscillations of the concentration over the film thickness is determined. Subranges of parameters generating the preset number of oscillations over the film cross section are indicated. The analytic results are qualitatively confirmed in numerical experiments.