Analysis of longitudinal dispersion in unsaturated flow: 1. The analytical method

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Abstract
An analytical technique is developed for the analysis of solute displacement in unsaturated soils involving one‐, two‐, or three‐dimensional flow with fixed streamlines. The transport processes are separated into two parts: convection with the mean flow and dispersive mixing. The convective process is solved exactly using the method of characteristics; the effects of dispersion are incorporated in the analysis by using singular perturbation techniques. The analytical technique is illustrated by application to solute transport during steady and transient infiltration. It is observed that nonuniform moisture content in space results in stretching or contracting of a solute pulse as it travels through the soil, with or without the presence of dispersive mixing. For transient infiltration into initially moist unsaturated systems the rate of solute displacement is usually much smaller than the rate of movement of moisture change.