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We consider the homogenisation of a coupled reaction-diffusion process in aporous medium with evolving microstructure. A concentration-dependent reactionrate at the interface of the pores with the solid matrix induces aconcentration-dependent evolution of the domain. Hence, the evolution is fullycoupled with the reaction-diffusion process. In order to pass to thehomogenisation limit, we employ the two-scale-transformation method. Thus, wehomogenise a highly non-linear problem in a periodic and in time cylindricaldomain instead. The homogenisation result is a reaction-diffusion equation,which is coupled with an internal variable, representing the local evolution ofthe pore structure.

Homogenisation of local colloid evolution induced by reaction and diffusion