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Patchy-Saturation Transport

We next must address the internal fluid-pressure equilibration between the two phases with the goal of obtaining the internal transfer coefficient $\gamma$ of equation (9). The mathematical definition of the rate of internal fluid transfer is  
\dot{\zeta}_{\rm int} = \frac{1}{V} \int_{\partial \Omega_{12}} 
{\bf n} \cdot {\bf Q}_1 \, dS\end{displaymath} (53)
where V is the volume occupied by the composite. A possible concern in the patchy-saturation analysis is whether capillary effects at the local interface $\partial \Omega_{12}$ separating the two phases need to be allowed for.