A Standard Mathematical Treatment of Retardation in Mobile/Immobile Zone Models Violates the Principle of Conservation of Mass

A widely used treatment of coupling between mobile and immobile zones in mathematical transport models assumes continuity of aqueous concentration across the zone interface and estimates cross-interface flux using a standard expression, based on Fick's Law. This particular formulation has been used in numerous existing papers, including key analytical solutions for discretely fractured porous media. In cases where matrix sorption retards diffusion in the immobile zone, this is often handled by employing a retardation coefficient other than unity in the model. In this circumstance, it can be shown that the standard formulation ceases to enforce mass balance across the interface between the mobile and immobile zones. The standard treatment generates incorrect results--even if the environment has been characterized perfectly. A novel analysis proves the existence of this mathematical error and shows how to correct it, without introducing any additional physical information. A summary of the analysis, as well as its implications (including the invalidation of parts of a number of published analytic solutions) will be discussed.