Relationships between flow and NMR relaxation of fluids in porous solids

Measurements are presented which correlate the displacements, X(Delta), determined by PGSE NMR, with the multi-mode transverse 1H NMR relaxation of water flowing through a glass bead pack, for which the dominant relaxation mechanism is diffusion through inhomogeneous internal magnetic fields. Analytical solution for the joint amplitude A[X(Delta), T(2k)] for the case of laminar flow in a circular pipe, with a diffusion-to-surface mechanism, shows that, for other than the lowest mode (k = 0), the contributions to the observed relaxation for a given X(Delta) may involve negative as well as positive amplitudes. The experimental measurements are shown to agree with this general conclusion, showing clear evidence of the presence of relaxation modes with negative amplitude at larger values of X(Delta). It is shown that in these, or similar measurements, which provide a spatially-resolved view of surface-mediated relaxation, allowance must be made for fitting with both positive and negative amplitudes.