A fast random walk algorithm for computing diffusion-weighted NMR signals in multiscale porous media: a feasibility study for a Menger sponge

A fast random walk (FRW) algorithm is adapted to compute diffusion-weighted NMR signals in a Menger sponge which is formed by multiple channels of broadly distributed sizes and often considered as a model for soils and porous materials. The self-similar structure of a Menger sponge allows for rapid simulations that were not feasible by other numerical techniques. The role of multiple length scales onto diffusion-weighted NMR signals is investigated.