Diffusion of solutes into porous rocks is a very important process for understanding transport of contaminants in the subsurface environment. Steady state diffusive transport (e.g. through rock slabs; Fick's first Law) is very well understood and the effective diffusion coefficients can be predicted analogous to Archie's law, i.e. empirical relationships, which relate the diffusivity to the rock porosity (e.g.: DŽ=porosity^^m; m is an empirical exponent close to 2). Under transient conditions (Fick's second Law) the interaction (=reaction) of the solute between pore water and solids has to be considered. In the case of persistent hydrophobic organic pollutants, sorption to organic matter included e.g. in sedimentary rocks (often micro-porous coal and charcoal particles) causes retardation of the diffusive transport into the rock matrix. Since the sorption isotherms are often non-linear, concentration-dependent apparent diffusion coefficients are observed.

The same process, retarded matrix diffusion, but at a smaller scale (grain scale) is important for reactive contaminant transport with groundwater. Aquifers often consist of highly heterogeneous quaternary sediments containing various-sized fragments of different sedimentary and igneous rocks (depending on the source rock formations). Transient diffusion into these rock fragments ("intra-particle pore diffusion") causes the slow sorption/desorption kinetics of organic contaminants as confirmed in long-term experiments (up to 1000 days) on sorption of phenanthrene with petrographically homogeneous and heterogeneous sand and gravel samples (see references).

Rügner, H., Kleineidam, S., Grathwohl, P. (1999): Long-term sorption kinetics of phenanthrene in aquifer materials. Environ. Sci. Tech., 33, 1645 - 1651

Kleineidam, S., Rügner, H., Grathwohl, P. (2000): Influence of petrographic composition/organic matter distribution of fluvial aquifer sediments on the sorption of hydrophobic contaminants. Sedimentary Geology, 129, 311 - 325