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Numerical simulations of capillary displacement in 2D porous media indicate a dynamical critical transition as the contact angle of the invading fluid varies. In the nonwetting limit (=180^), growth patterns are fractal as in the invasion percolation model. As 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.
Cieplak et al. (Mon,) studied this question.