Dynamic Capillary Pressure in Porous Media: Origin of the Viscous-Fingering Length Scale

We measure the velocity dependence of the capillary pressure, $\Delta P_c\mathrm{}\left(v\right)\mathrm{}$, between two fluids in a porous medium. At zero velocity, the interface is pinned, and a critical $\Delta P_c$ must be achieved before the interface moves. For nonzero velocities, there is an additional dynamic component to $\Delta P_c$, which scales as $v^{\frac{1}{2}}$ when a wetting fluid displaces a nonwetting fluid. We suggest that this dynamic component of $\Delta P_c$ can stabilize viscous fingers, and obtain excellent agreement with experiment.