Convection-dispersion-sorption equation

The above equations, based on the conservation of mass for chemical transport, yield the convection-dispersion-sorption equation CDSE (Eq. 3.41 and its variations), which is widely used in industrial applications, including dyeing. Many researchers call the term (D d ddx ) in Eq. 3.41b either dispersion or diffusion, and D is usually treated as a constant. In the context of this analysis, dispersion is used to describe this phenomenon, and the diffusion is considered a special case of dispersion when the velocity of the fluid is zero. 

One can use the above equation to discretise a partial difference equation (PDE) and implement a numerical method to solve the PDE. For example, if it is required to calculate numerical solutions of the convection-dispersion-sorption equation (CDSE, see Eq. 3.41b, also shown below) ... 

If Rt. does not change (i.e., the distribution coefficient K. does not depend on the concentration), total equation of the convective-dispersive mass transport may be rewritten in consideration of sorption of the component ... 

Equation (35) shows the applied type of convection-dispersion-equation about the transport of a pollutant in the model soil column. The term on the lefthand side describes the change of adsorbate concentration with time at a certain location z. The first term on the righthand side calculates the dispersion, the second term calculates the convection, and the third term the sorption of the transported pollutant at the respective location. 

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