Coupled reaction-diffusion processes inducing an evolution of the microstructure: Analysis and homogenization. (English) Zbl 1151.35308

Summary: Chemical processes in porous media often cause a change of the microstructure of the porous material due to interaction with the solid matrix, by reaction or adsorption, e.g. We consider a reaction-diffusion problem where a solid matrix constituent is converted into another one of different density. Thus, the solid matrix locally grows or shrinks in volume, which in turn changes the pore-air volume. This affects the transport of reactants in the pore air. The homogenization of this problem with evolving microstructure is performed using the method of transformation to a periodic reference domain, which has recently been put forward by the author. The final system to be homogenized consists of three coupled partial differential equations for the concentrations coupled to one ordinary differential equation for a quantity describing the evolution of the pore-air volume.


35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K57 Reaction-diffusion equations
74F25 Chemical and reactive effects in solid mechanics
92E20 Classical flows, reactions, etc. in chemistry
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