Abstract The theoretical basis of the pulsed-held-gradient spin-echo experiment and its applicability to the study of diffusive transport through a spherical interface into an external medium containing a relaxation agent are examined in the long-time diffusion limit. The theory is compared with previous experimental findings involving bicarbonate diffusion in and across human red blood cell membranes. To a first approximation, the addition of a relaxation agent to the external medium results in the interface becoming a "partially absorbing wall." However, the results of this study show that it is experimentally difficult to achieve the partially absorbing wall conditions, and, in any case, this one-site model is not very sensitive to permeability differences. The treatment is then extended to include the case where the transported spins do not relax instantly but instead have a small but finite lifetime. This model is shown to be more sensitive to permeability differences as well as being experimentally realizable.