Seepage Theory for Two-scale Porous Media

We consider the micro-Zmacro-problem for a saturated two-scale porous medium as shown in Fig. 8.1 with the macro-domain and the micro-domain and is the fluid phase in the micro-domain, is the solid phase in the micro-domain, T is the fluid/solid interface, and 9f2i/ is the periodic boundary of the fluid phase in the micro-domain. 

Let us introduce a macroscale coordinate system and a microscale coordinate system x as 

Macroscale Problem with periodic micro-structure 

Note 8.1 (On the size of a unit cell). We can determine the size of the micro-domain based on (8.5). If the dimensions of the unit cell are given by Xl, X, Xl in each direction as shown Fig. 8.1, we have the following relations in the macro-domain  

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