Multiscale HA for Diffusion Problems in Porous Media

Let us introduce a perturbation of c x,t) for the macro-Zmeso/micro-coordinate systems at°, a x as 

Therefore, for each power series of e we obtain the following equations For terms 0 e )  

The terms dc /dxj and dc /dxj are null, and c is a function of only x and x. This suggests that for c we can intfoduce the following )iryf order characteristic function fVf (x )  

For terms 0(s ) Second order characteristic function and microscale equation Since c is a function of only at and c is a function of only a and a and we have the following equation in the micro-domain  

Substituting (9.51) into (9.49), we obtain the following microscale equation in the 

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