Localization in a single pore

We explore, by direct numerical simulations of the Bloch-Torrey equation in a single model pore, NMR decay by “diffusion in a gradient”. Illustrative results from the finite-element package COMSOL are shown for a single “pore” taken from a numerical model (unrelated) of a human vertebra reduced 3 orders of magnitude in size, with the internal field modelled by numerical solution of the local magnetostatic problem. Results are shown for a single Hahn echo in the known limits of “Short Time” (ST), “Motionally Averaged” (MAV) and “Localization” (LOC) behaviour. Computing time on a laptop is less than 1 min; the approach is entirely practical for obvious immediate extensions. The LOC regime is shown explicitly to be qualitatively different from both the ST and MAV limits, where the dominant diffusion eigenmode is uniform. In LOC, the intra-pore magnetization is rapidly distorted, and “Localized” to small pockets, either where restricted by the pore walls, or around internal field extrema. Surviving magnetization may comprise only a small and possibly unrepresentative fraction of the fluid-filled pore volume. These features are in agreement with the limited analytical results.