Longitudinal Dispersion with Dead Zones

The dispersion process for an instantaneous line source of solute in a two-dimensional turbulent shear flow with dead zones is formulated to two differential equations, one for the solute in the flow zones and the other for the solute trapped in the dead zones on the bed. Exchange of material occurs between dead zones and flow. Using the Aris moment transformation these equations are converted to a more tractable system of equations which are solved by numerical methods with the aid of a digital computer for zeroth, first, second, and third moments of the longitudinal concentration distribution. Various forms of dead zone volume are imposed, and its effects on the dispersion process are demonstrated. It is shown for the numerical model employed that dead zones not only increase the rate of dispersion but delay the occurrence of Fickian type dispersion.