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

Abstract

AbstractIn 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.