Dynamic scaling properties of invasion percolation SOS interfaces in porous media

We introduce an invasion percolation (IP) model to study the scaling properties of rough interfaces with a solid-on-solid (SOS) restriction for a driven interface in a two dimensional disordered medium. A remarkable characteristic of our model is the absence of an external parameter, such as the occupation probability pc in pinning interface models used previously to simulate the rough interface displacement in random media. In oar model the interface always advances and there is no pinning. The exponents corresponding to temporal and spacial scaling of the interface obtained with our IP model are in good agreement with previous theoretical and experimental results.