Self-diffusion in a periodic porous medium: A comparison of different approaches

We compare two different approaches for computing the propagator for a particle diffusing in a fluid filled porous medium, where the pore space has a periodic structure and some absorption of the particle can occur at the pore-matrix interface. One of these approaches is based on computer simulations of a random walker in this structure, while the other is based on an explicit calculation of the diffusion eigenstates using a Fourier series expansion of the diffusion equation. Both methods are applied to the same nondilute model systems in order to calculate the wave-vector and time-dependent nuclear magnetization measured in pulsed-field-gradient-spin-echo experiments. When the physical parameters are confined to the range of values found in most systems of interest, good quantitative agreement is found between the two methods. However, as the interfacial relaxation strength, the time, or the wave vector becomes large, calculations based on eigenstate expansion are more stable and less subject to the sampling problems inherent in random walk simulations. In the absence of surface relaxation, our calculations are also used to test the results predicted by a recently proposed ansatz for the behavior of the diffusion propagator. Finally, a problem is identified and discussed regarding the relation between random walk and continuum diffusion treatments of interface absorption.