Diffusion Theory for Two-scale Porous Media

Referring to Fig. 8.1, we consider a diffusion problem for a two-scale porous medium in which is the fluid-phase domain, Q.s is the solid-phase domain, V is the solid/fluid interface, and Tf is the periodic boundary of the fluid-phase in the micro-domain. 

Following the HA theory we introduce the coordinate systems and for the macro-domain and the micro-domain, respectively, and we have 

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