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Solutions and Tests of the Diffusion Equation for the Movement of Water in Soil
Author(s) -
Gardner W. R.,
Mayhugh M. S.
Publication year - 1958
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1958.03615995002200030003x
Subject(s) - thermal diffusivity , diffusion equation , soil water , exponential function , water content , richards equation , infiltration (hvac) , moisture , diffusion , thermodynamics , mechanics , chemistry , mathematics , soil science , mathematical analysis , physics , geotechnical engineering , environmental science , geology , economy , organic chemistry , economics , service (business)
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.