The field of hydrogeology is primarily concerned with the flow of water below the ground surface and with transport, normally of solutes and heat, within that water. Many disciplines have contributed to this endeavor which requires skills from across the spectrum of science, engineering and beyond. The diffusion equation describes not only solute transport but also the flow of water, via Darcy’s law. Of particular interest is transport in fractured rock where most of the flow is through the fractures while most of the storage is in the rock pores: a ‘double-porosity’ system. Hydrogeology remains a field that welcomes those who bring techniques from other areas of science to address problems as varied as water supply, radioactive waste disposal and geothermal energy.

The formal solution to the diffusion equation for transient adsorption in a semiinfinite medium with a strongly concentration dependent diffusivity, originally derived by Fujita ( 3 ), has been extended to desorption. Profiles for adsorption and desorption are compared and simplified asymptotic expressions which are useful when the diffusivity ratio is large are derived. The effect of a strongly concentration dependent diffusivity on adsorption and desorption kinetics is briefly considered.

The quasi-elastic neutron scattering (QENS) technique was first used to derive self-diffusivities of hydrocarbons in zeolites, but transport diffusivities of deuterated molecules and of molecules which do not contain hydrogen atoms can now be measured. The technique allows to probe diffusion over length scales ranging from an Å to hundreds of Å. The mechanism of diffusion can thus be followed from the elementary jumps between adsorption sites to Fickian diffusion. Since the space and time scales of the neutron techniques match closely the ones covered by molecular simulations, one expects, and usually finds, good agreement between neutrons and simulations. The neutron data give therefore reference values, so that lower values obtained by other techniques measuring diffusion over longer length scales have to be explained by additional transport barriers.

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