Homogenisation of local colloid evolution induced by reaction and diffusion. (February 2023)

• Record Type: Journal Article
• Authors: Wiedemann, David; Peter, Malte A.
• Is Part Of: Nonlinear analysis. Volume 227(2023)
• Publication Date: 2023-02
• Subjects: 35B27 -- 35K57 -- 35R35; Homogenisation -- Evolving microstructure -- Free boundary problem -- Two-scale convergence -- Porous medium -- Reaction–diffusion process; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113168
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the homogenisation of a coupled reaction–diffusion process in a porous medium with evolving microstructure. A concentration-dependent reaction rate at the interface of the pores with the solid matrix induces a concentration-dependent evolution of the domain. Hence, the evolution is fully coupled with the reaction–diffusion process. In order to pass to the homogenisation limit, we employ the two-scale-transformation method. Thus, we homogenise a highly non-linear problem in a periodic and in time cylindrical domain instead. The homogenisation result is a reaction–diffusion equation, which is coupled with an internal variable, representing the local evolution of the pore structure. Highlights: Two-scale transformation for a priori not given microscopic domain evolution. Homogenisation of a highly non-linear system by means of two-scale convergence. Evolution of the pore space induced by the solution of the reaction–diffusion equation.