= Dilute permeability enhancement by aligned cracks
{title2=$k_{xx}^*=k\left[1+\pi\phi a^2\frac\alpha{1+\alpha}+O((\phi a^2)^2)\right]$}
At small areal number density $\phi$, identical aligned cracks contribute independently the <fixed-throughflow dissipation reduction of a conductive crack>. Equating the mean dissipation density to $\mu U^2/k_{xx}^*$ gives the displayed first-order enhancement. Writing $k/[1-\pi\phi a^2\alpha/(1+\alpha)]$ is an algebraic noninteraction estimate, not a claim of accuracy at higher density. The enhancement saturates as crack conductance becomes large compared with transport through the surrounding porous matrix.
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