Surface-directed multi-dimensional wave structures in confined binary mixtures

Abstract

In this paper, we consider the process of formation of wave structures in binary mixtures: for example, polymer chains or binary alloys. This process is described by the three-dimensional linear Cahn–Hilliard equation with nonlinear dynamical boundary conditions. The dynamical boundary conditions with “feedback” describe processes of cyclic crystallization and melting, depending on temperature as on a parameter. We describe an initial value boundary problem in cube and in square. It is shown that by action of boundary conditions in cube appears wave structures of relaxation, pre-turbulent and turbulent type. For large time, the wave patterns are in the form of recurrent parallelepiped in volume or parallelogram in plane. Applications to study separation of polymer blends in the square.