Multiscale Permeability Theory

As mentioned previously, the flow field of water in a porous medium can be represented by Stokes equation (8.3). 

We introduce permrbations of the velocity v and the pressure such that (8.9) and (8.10) now become 

3) Kozeny-Donat s equation Q=2.3 Angular quartz sand 

The reason why the perturbation of v (x) starts with a -term is to ensure reduction to the corresponding Stokes equation in the micro-domain as a microscale equation (to be discussed later). We assume that the first-order term of pressure is a function of only the macroscale coordinate system x.  

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