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The continuous-time random walk (CTRW) model is useful for alleviating thecomputational burden of simulating diffusion in actual media. In principle,isotropic CTRW only requires knowledge of the step-size, $P_l$, andwaiting-time, $P_t$, distributions of the random walk in the medium and it thengenerates presumably equivalent walks in free space, which are much faster.Here we test the usefulness of CTRW to modelling diffusion of finite-sizeparticles in porous medium generated by loose granular packs. This is done byfirst simulating the diffusion process in a model porous medium of meancoordination number, which corresponds to marginal rigidity (the loosestpossible structure), computing the resulting distributions $P_l$ and $P_t$ asfunctions of the particle size, and then using these as input for a free spaceCTRW. The CTRW walks are then compared to the ones simulated in the actualmedia.  In particular, we study the normal-to-anomalous transition of the diffusionas a function of increasing particle size. We find that, given the same $P_l$and $P_t$ for the simulation and the CTRW, the latter predicts incorrectly thesize at which the transition occurs. We show that the discrepancy is related tothe dependence of the effective connectivity of the porous media on thediffusing particle size, which is not captured simply by these distributions.  We propose a correcting modification to the CTRW model -- adding anisotropy-- and show that it yields good agreement with the simulated diffusion process.We also present a method to obtain $P_l$ and $P_t$ directly from the poroussample, without having to simulate an actual diffusion process. This extendsthe use of CTRW, with all its advantages, to modelling diffusion processes offinite-size particles in such confined geometries.

Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media