Diffusion through confined media at variable concentrations in reservoirs

The problem of transient linear 1D diffusion with mass-transfer limitations (boundary layers) at the medium boundaries and variable diffusant concentrations in both perfectly stirred reservoirs is solved in terms of Fourier transforms. This novel solution is especially relevant to the interpretation of measurements of diffusion of adsorbing radio-nuclides in compacted clays where porous filters are routinely used to confine the swelling clay. An analytical expression is obtained for the break-through time with a due account for the mass-transfer limitations at the medium boundaries. An analysis is carried out of the influence of finite inlet volume on the time evolution of diffusant flux into the outlet reservoir. A simple “renormalization” procedure is put forward to make corrections for the decrease in the inlet concentration, which makes applicable the classical procedure of interpretation in terms of stationary flux and break-through time. It is shown that this “renormalization” procedure is fairly accurate in the case of relatively small absolute sorption capacities of medium (as compared to the inlet reservoir), but its accuracy deteriorates with an increase in this parameter. Several examples are considered for the application of these approaches to the interpretation of experimental data on the diffusion of traces of radioactive 22Na through compacted sodium montmorillonite.