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Mathematical Study of the First Stage of Drying of a Moist Soil¹

ABSTRACT

In the classical "first stage of drying" of a moist soil, constant external conditions produce a constant evaporation rate. The exponential dependence of moisture diffusivity on water content, suggested by W. R. Gardner, has been used for working out the changing soil moisture profiles in homogeneous soil columns, initially uniformly moistened, with gravity neglected. The characteristic parameter for the process is (ßq₀L/D_I), where q₀ is the evaporation rate [cm.³/(cm.²sec.)], ß is a constant in the diffusivity equation D = · exp (ß ), L is the length of the column, and D_I(cm.²/sec.) is diffusivity at initial moisture content ₁(cm.³/cm.³). If (ß q₀L/D_I) is > 5, then the column behaves as an infinitely long column throughout the first stage of drying, and a newly-computed universal relationship holds: ß(_I – ) = F [(ßq₀ x/D_I), (ß² q₀² t/D_I)], where x is distance from evaporation surface and t is time. If (ßq₀L/D_I) is < 5, then finiteness of length becomes important within the first stage of drying. The variable ß(_I – ) has been computed as a function of (x/L), (ßq₀t/L), and (ßq₀L/D_I) for selected values of the latter. These new mathematical functions facilitate theoretical studies and the determination of desorption parameters from observations.

¹ Contribution from the Soil and Water Conservation Research Division, ARS, USDA, in cooperation with the Department of Agronomy at Cornell University, Ithaca, N. Y. The work was supported in part by the Meteorology Department, U. S. Army Electronic Proving Ground, Fort Huachuca, Ariz. Paper No. 563 in the Agronomy Department Series. Presented before Div. I, Soil Science Society of America, Nov. 27, 1961, in St. Louis, Mo.

² Soil Scientist (Physics), Agricultural Research Service, USDA, and Research Agricultural Climatologist, Cornell University, Ithaca, N. Y.

Received for publication May 29, 1962. Accepted for publication June 11, 1962.