Generalizing the concept of retardation factors

In multi-phase environments, for example in porous media, and particularly in groundwater and in sediments, the spatial and temporal distribution of a chemical or biological species is usually described by a set of multiple coupled differential equations. Under the conditions that an isotherm exists, the set of equations can be simplified to a single equation. The most well-known application of such a procedure in a fluid-solid system leads to the equation for retarded transport with the retardation factor R. As a generalization of this mathematical concept, factors R-decay, R-adv and R-diff are introduced, which for general situations appear as factors in the single differential equation. The Peclet and Damkoehler numbers depend on these generalized retardation factors. They may also have an effect on the steady state solution - in contrast to the classical retardation factor R. Due to the reduction to a single equation, analytical and numerical tools that are well established for single-phase environments can be utilized. As an example for the application of the presented approach, the case of aquatic sediments is presented, for which the generalized concept allows to study solute transport considering processes like compaction, bioirrigation and bioturbation in addition to the common fluid phase processes.