Dynamical Transition in Quasistatic Fluid Invasion in Porous Media

Numerical simulations of capillary displacement in 2D porous media indicate a dynamical critical transition as the contact angle $\theta$ of the invading fluid varies. In the nonwetting limit ($\theta =180\mathrm{}°$), growth patterns are fractal as in the invasion percolation model. As $\theta$ decreases, cooperative smoothing mechanisms involving neighboring throats become important. The typical width of invading fingers appears to diverge at a critical angle which depends on porosity. Below this angle the fluid floods the system uniformly.