Critical phenomena in fluid invasion of porous media

We present a phase diagram for fluid invasion of porous media as a function of pressure P and the contact angle θ of the invading fluid. Increasing P leads to perculation above a critical ${\mathrm{\theta }}_{\mathit{c}}$, and depinning below ${\mathrm{\theta }}_{\mathit{c}}$. Depinning is characterized by a diverging coherence length and the power-law distribution of events typical of self-organized critical phenomena. At the transition from percolation to depinning another correlation length diverges and an order parameter, an effective macroscopic surface tension, becomes nonzero. The fluid interface changes from self-similar to self-affine. Results are compared to experiments.