Material Transport in a Pore Network

Now consider the total material flux in a porous solid. We postulate a thoroughly cross-linked main pore network with singly attached dead-end pore branches. 

Because of the cross-linking, the fluid states in neighboring pores of the main network are similar. The gradients along each of these pores can then be approximated as 

Here 5(, is a unit vector along the given pore segment, and p and c are smoothed profiles for the main pore network. 

Let f r, 17) denote the void fraction of main-network pores per unit intervals of pore radius r and orientation (solid angle) 17. Then the smoothed molar flux of species i in the medium is 

This result can be expressed in terms of measurable quantities, under the assumption that p and [c] are independent of i and r in the main network  

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