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This article in SSSAJ

  1. Vol. 22 No. 3, p. 197-201
     
    Received: Sept 30, 1958


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doi:10.2136/sssaj1958.03615995002200030003x

Solutions and Tests of the Diffusion Equation for the Movement of Water in Soil1

  1. W. R. Gardner and
  2. M. S. Mayhugh2

Abstract

Abstract

A diffusion equation with concentration-dependent diffusivity has been proposed to describe the movement of water in unsaturated soils. For certain initial and boundary conditions the Boltzmann transformation converts the flow equation into an ordinary differential equation. The time dependence of the infiltration rate and distance to the wetting front for flow into a semi-infinite sample can be inferred from this equation without the necessity of solving it.

Numerical solutions of the equation are presented for one-dimensional flow, assuming the diffusivity to be an exponential function of the moisture content. Water-entry rates and moisture content distributions measured experimentally are in good agreement with those predicted by the solutions of the equation. The assumption of an exponential diffusivity is satisfactory for the soils investigated. Agreement between diffusivities determined from this study are in agreement with those calculated from pressure plate outflow data.

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