Formation of new types of inhomogeneous spatial structures in the chemical reaction in imperfect systems

Abstract

ABSTRACT:Taking the system imperfection and the inhomogeneity of the diffusion processes into account derives the extension of a simple chemical reaction model proposed by Schlogl. The Fick equation modification makes the breakdown of the ideality of diffusion. It leads to high-order spatial derivatives of a concentration in an evolution equation. The system imperfection is also taken into account by the excess Gibbs function of a regular solution. It leads to modification of the chemical potential as well as to the dependence of a diffusion coefficient on a reagent concentration. The formation of the spatial inhomogeneous structures being stable during the chemical reaction under definite conditions is due to the breakdown of an ideal system. Certain spatial inhomogeneous structures can exist only in the imperfection system and do not appear in an ideal system. Three new types of spatial inhomogeneous structures appear: periodic, quasi-periodic, and nonperiodic structures. The functions characterizing concentration contain two terms. Note that in the ideal systems, the quasi-periodic and nonperiodic structures cannot exist. This means that such a new spatial structure formation is due to the system imperfection. The parameters characterizing the system imperfection represent the coefficients at nonlinear terms and a high-order spatial derivative in the evolution equation. This permits consideration of a system deviation from the ideal as a significantly nonlinear phenomenon. The conditions of spatial structure stability are determined mainly by parameters that describe the system imperfection.

Conditions and numerical simulation of dissipative structure formation in imperfect double‐component reaction‐diffusion systems

“…[11,12] for the extensional Shlogle model. This means that forming such inhomogeneous spatial structures is due exclusively to the inhomogeneity of diffusion fluxes in the reaction system.…”