An analytical solution of macrodispersivity for adsorbing solute transport in unsaturated soils

An analytical solution of macrodispersivity was derived for the adsorbing solute transport in physically and chemically heterogeneous unsaturated soils under the condition of gravity-dominated flow. The unsaturated hydraulic conductivity and water content were treated as spatial random functions. The chemical adsorption was described by a linear equilibrium isotherm, and the adsorption coefficient was represented as a spatial random function with specified correlation structures. The closed-form expression for macrodispersivity was expressed as a function of the hydraulic and adsorbing statistical properties of the unsaturated soil. For a short solute travel distance the macrodispersivity linearly increased with the increase of the solute plume travel distance. The macrodispersivity approached an asymptotic value when the center of the solute plume moved a long distance, The general solution quantified the effects of various factors, such as variabilities of the water content and unsaturated hydraulic conductivity, mean water content, and the retardation factor, on the macrodispersivity.