Transient diffusion in a system partitioned by permeable barriers. Application to NMR measurements with a pulsed field gradient

A general treatment of time-dependent (transient) diffusion coefficients in a system of parallel planar barriers of arbitrary permeability has been performed, with emphasis on the results expected for NMR pulsed-field-gradient, spin-echo measurements. This is the first such derivation for permeable barriers of any geometry. The calculated distribution functions and diffusion coefficients are in agreement with expectations in most of the limiting cases tried, except that an unexplained dependence of the diffusion coefficients on the magnitude of the field gradient, even at long diffusion times, was found. The application of the results to the interpretation of experimental results is discussed.