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Published in Soil Sci Soc Am J 22:197-201 (1958)
© 1958 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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Solutions and Tests of the Diffusion Equation for the Movement of Water in Soil1

W. R. Gardner and M. S. Mayhugh2

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.

NOTES

1 Contribution from the U. S. Salinity Laboratory, Soil and Water Conservation Research Division, A.R.S., U.S.D.A., Riverside, Calif., in cooperation with the 17 Western States and the Territory of Hawaii.

2 Physicist and Physical Science Aid, respectively.

Received for publication September 30, 1958. Accepted for publication January 25, 1958.






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