Multi-pulsed free-induction NMR signal from spins diffusing in a spatially restricted flow

Abstract

A multi-pulsed free-induction NMR experiment is described theoretically for spins diffusing within a cylindrical capillary. The characteristic time for the particles to move on a distance of the capillary diameter is smaller or comparable to the time interval between the applied 90° rf pulses and the relaxation times entering the Bloch equations. In this case the spin diffusion is restricted and the classical solutions of these equations for unbounded media are not applicable. We have calculated the mean magnetization in the cross-section of the capillary after any of the rf pulses and found the induced NMR signal within the Bloch-Torrey-Stejskal theory for spins reflected at boundaries. The problem is extended by considering a possible macroscopic (plug and Poiseuille) flow of the fluid inside a capillary. It is found that with the increase of the rf pulse number, the maxima of the observed signals do not decay to zero but converge to a nonzero value. The proposed theory thus seems to be suitable for the description of experiments on systems rapidly relaxing due to diffusion and flow.