The Spatial-Temporal Lamellar Structures in the Confined Ideal Polymer Blends

Abstract

We consider the formation of self-organized spatial-temporal oscillating structures in symmetric binary polymer blends confined by two flat walls. An influence of these walls on the formation of the oscillating volume structures is studied. This phenomenon is simulated by an initial boundary-value problem for the conserved order parameter (or the concentration of one of the components in a binary mixture). Under a special choice the dynamical Puri-Binder’s boundary conditions these structures look like the lamellar structures. The behavior of the order parameter is described by the modified Cahn-Hilliard equation which models so-called the non-Fickian diffusion in the symmetric binary polymer blends. The nonlinear dynamical boundary conditions correspond to the process of adsorption-desorption on the walls. As a result, these nonlinear surface processes induce into the volume the spatial-temporal asymptotically periodic structures of relaxation, pre-turbulent or turbulent type with finite, countable or non-countable points of discontinuities on the period correspondingly. The frequency of oscillations on the period follows a power-law for the relaxation type and increases exponentially in the other cases.