Non-classical regimes of colloid-facilitated impurity transport in statistically homogeneous double porosity media

•A model of colloid-facilitated impurity transport in dual porosity medium is presented.•Nonequilibrium impurity distribution between fast and slow regions is considered.•Rate limited impurity exchange between solute and colloids is taken into account.•A set of five regimes including ones of anomalous type describes the transport.

In the context of impurity transport study it is shown how complexity of the system leads to emergence of anomalous transport regimes, moreover the power-law behavior of which changes with time. Specifically, a model of nonequillibrium colloid-facilitated transport in statistically homogeneous double porosity media is presented and possible transport regimes are simulated. Depending on the medium and colloids characteristics different sequences of transport regimes can realize. Temporal interval exists where anomalous transport regimes (sub-diffusion and quasi-diffusion) occur. At asymptotically large times the transport is described by the classical advection-diffusion with modified parameters.