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The Darcy velocity is liquid volume flux relative to the solid skeleton, divided by total cross-sectional area. If porosity is $ϵ$, liquid velocity is ${\mathbf{v}}_l$, and skeleton velocity is ${\mathbf{v}}_s$, then $\mathbf{u}=ϵ({\mathbf{v}}_l-{\mathbf{v}}_s)$. Thus pore-fluid speed relative to the skeleton is $\mathbf{u}/ϵ$, rather than $\mathbf{u}$.

The liquid fraction is the volume fraction occupied by liquid in a solid–liquid mixture. For a saturated rigid mushy layer, it is the porosity available to Darcy flux.

For two fluids with dynamic viscosities ${\mu }_1<{\mu }_2$, uniform permeability of a porous medium $k$, porosity $\varphi$, and imposed Darcy velocity $U$, the Saffman–Taylor instability of a planar interface has growth rate $\sigma =\alpha U({\mu }_2-{\mu }_1)/[\varphi ({\mu }_2+{\mu }_1)]$ without capillarity. With constant interfacial tension $\gamma$ and the stabilizing pressure-jump convention, a perturbation of transverse wavenumber $\alpha >0$ instead hasThe fastest-growing mode satisfies ${\alpha }_m^2=({\mu }_2-{\mu }_1)U/(3k\gamma )$.

With permeability of a porous medium $k(z)=k_0(1+\beta z)$, the Dupuit approximation givesHere $\varphi$ is porosity and $R$ is recharge. The low-height limit has mobility proportional to $h$, whereas large heights have mobility proportional to $h^2$. This changes both the forced filling similarity for power-law diffusion and the separable draining profile for power-law diffusion.