,

where is the effective dispersion coefficient, is the fluid phase concentration, is distance, is time, is the interstitial fluid velocity, is a retardation factor defined as , is a general decay constant defined as , and is the zeroth-order fluid phase source term. Here is the porous medium bulk density, is the ratio of adsorbed to fluid phase concentration, is the volumetric moisture content, is a first-order liquid phase decay constant, and is the first-order solid phase decay constant.

The transport equation is solved subject to the following initial and boundary conditions:

,

,

and

, where and are the constant initial fluid and surface boundary concentrations, taken here as .