Self diffusion of nuclear spins in a porous medium with a periodic microstructure

A Fourier approach is developed for evaluating the diffusion eigenstates and the diffusion propagator of a periodic, fluid filled porous medium, and is applied to the calculation of the pulsed-field-gradient-spin-echo amplitude M(k,t). The method is most effective for long times t, but works quite well down to times that are short enough so that asymptotic short time approximations of the diffusion process are still valid. The main advantage of the method is that it is applicable regardless of the value of the porosity or the shape of the periodic pore space. It is used to calculate M(k,t) for a number of examples of periodic porous media with porosities as low as 10%.