Dynamic Scaling Properties of Invasion Percolation SOS Interfaces in Porous Media

We introduce an invasion percolation (Yp) model to study the scaling properties d rough interfaces with a s&d-on-s&d (SOS) restrkticm for a driven interface in a two dhensiozal disordered medium. A remarkabie characteristic of our model is the absence of an external parameter, such as the occupation pobability pc in pinning interface models used previously to simulate the rough inte6ce displacement in random media. In ow model the interface &ways advances and there is no pinning. The exponents corresponding to temporal and spa&l scaling of the interface obtained with our IP model are in good agreement with previous theoretical and experimental results.