Suitability of the first-order mass transfer concept for describing cyclic diffusive mass transfer in stagnant zones

The concept of first-order mass transfer between mobile and immobile regions, which mathematically simplifies the concept of Fickian diffusion in stagnant areas, has often been used to describe physical nonequilibrium transport of solutes into natural porous media. This study compares the two concepts, using analytical expressions describing cyclic mass transfer into and out of stagnant layers. The results show that the first-order mass transfer concept cannot describe continuous diffusion into the immobile zone during period of net outward diffusion if the immobile zone has not filled completely during the period of net inward diffusion. This sets phenomenological limitations to the first-order mass transfer concept when short periods of relative time are involved; these limitations have to be compared with the practical limitations to the Fickian diffusion concept.