Mathematical Study of the First Stage of Drying of a Moist Soil
1963
Covey, Winton
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 (βq₀L/DI), where q₀ is the evaporation rate [cm.³/(cm.²sec.)], β is a constant in the diffusivity equation D = γ · exp (β θ), L is the length of the column, and DI(cm.²/sec.) is diffusivity at initial moisture content θ₁(cm.³/cm.³). If (β q₀L/DI) is > 5, then the column behaves as an infinitely long column throughout the first stage of drying, and a newly-computed universal relationship holds: β(θI − θ) = F [(βq₀ x/DI), (β² q₀² t/DI)], where x is distance from evaporation surface and t is time. If (βq₀L/DI) is < 5, then finiteness of length becomes important within the first stage of drying. The variable β(θI − θ) has been computed as a function of (x/L), (βq₀t/L), and (βq₀L/DI) for selected values of the latter. These new mathematical functions facilitate theoretical studies and the determination of desorption parameters from observations.
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