Saturated‐Unsaturated Flow in Radial Directions Generated by an Injection Well

Abstract

AbstractThe paper investigates water movement under saturated‐unsaturated flow conditions. The flows result from a vertically placed line source that injects water at a constant rate into radial directions in space. Soil water diffusivity is assumed to vary as a positive, arbitrary power of water saturation. Singular perturbation methods are applied to derive an analytical form of the solution as a power series in the perturbation parameter. The solution so concentrated is freed from singularities and breakdowns, and is therefore uniformly valid at all points of space and time. Explicit formulae are derived for the location of the wetting front as well as for the transition face between saturated and unsaturated flow regimes. Several cases of the diffusion function and injection rates are illustrated in the form of graphs. Relevance of the analysis to problems of flushing out dissolved salts from soils is briefly commented on.