Fractal structure of diffusion and invasion fronts in three-dimensional lattices through the gradient percolation approach

Diffusion of particles in solids may be conveniently described in the framework of the theory of percolation in a gradient of concentration. This approach allows one to study the fractal structure and the scaling properties of the diffusion front in three dimensions. In the region where the concentration is close to the percolation threshold, the fractal dimension of the front is found to be approximately 2.5. In this region, in addition to the usual critical properties of percolation, we prove the existence of a new scaling behavior depending on a unique scaling length. It is suggested that gradient percolation can also account for particular invasion fronts observed in two-phase-flow experiments in porous media.