Concentration-dependent diffusivity and anomalous diffusion: A magnetic resonance imaging study of water ingress in porous zeolite

Magnetic resonance imaging is employed to study water ingress in fine zeolite powders compacted by high pressure. The experimental conditions are chosen such that the applicability of Boltzmann's transformation of the one-dimensional diffusion equation is approximately satisfied. The measured moisture profiles indicate subdiffusive behavior with a spatiotemporal scaling variable eta=x/t(gamma/2) (0<gamma<1). A time-fractional diffusion equation model of anomalous diffusion is adopted to analyze the data, and an expression that yields the moisture dependence of the generalized diffusivity is derived and applied to our measured profiles. In spite of the differences between systems exhibiting different values of gamma a striking similarity in the moisture dependence of the diffusivity is apparent. This suggests that the model addresses the underlying physical processes involved in water transport.