Darcy velocity ($\mathbf{u}=ϵ({\mathbf{v}}_l-{\mathbf{v}}_s)$)

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 $\mathbf{u}$.