Continuum and random-walk models of magnetic relaxation in porous media

Nuclear magnetic relaxation in porous media can be treated by a continuum model, involving the solution of an initial boundary-value problem, or by a random-walk model, involving a random walk on a lattice with a partially absorbing boundary. Three formulations of the random-walk model have appeared in the literature. These have different step probabilities and different relations between the parameters of the random walk and continuum models. This paper re-examines the formulation presented previously by the author. That formulation is revised to improve the approximation to the continuum model and to simplify comparison with the other formulations. It is shown that the three formulations are largely the same but represent two different orders of approximation to the continuum model and retain some differences that are difficult to understand.