Microbial transport through heterogeneous porous media: random walk, fractal, and percolation approaches

Interest in microbial communities of the subsurface environment has greatly stimulated research on microbial transport phenomena in heterogeneous porous media. In this paper, we describe several stochastic-geometric modeling techniques that integrate, to varying degrees, random walk, fractal, and percolation approaches as alternatives to traditional mathematical and numerical models for microbial transport in subsurface media across scales. The results presented illustrate how such techniques may shed new light on modeling of microbial transport processes, including microbial cell diffusion on a fractal space, geometric properties of microbial clusters (patches), aggregation processes of microbial clusters, localization of microbial growth sites, and a model for long-term survival of microbial cells in deep strata.