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Exact Desorptivities for Power Law and Exponential Diffusivities¹

ABSTRACT

The desorption of water from a soil is analyzed for a soil-water diffusivity function obeying a power or an exponential law, and precise numerical values for desorptivity are found. An effective reduction in the number of parameters allows the cumulative desorption for various boundary conditions to be calculated from a short table of results. For the power law case, desorptivity for arbitrary initial water content can be obtained from tabulated values by a simple scaling transformation. A similar scaling transformation yields the exponential desorptivity for arbitrary initial and surface water content. An approximate desorptivity formula of Parlange is discussed, and found to give an accuracy within 2.5% over the whole parameter range. In general, the present results should be useful to assess numerical and analytical procedures.

¹ Contribution from the School of Australian Environmental Studies, Griffith Univ., Brisbane, 4111, Australia, and the Dep. of Agric. Eng., Cornell Univ., Ithaca, NY 14853.

² Research Assistant, School of Australian Environmental Studies, Griffith Univ., Brisbane, 4111, Australia.

³ Professor, Agric. Eng., Cornell Univ., Ithaca, NY 14853.

⁴ Senior Research Scientist, Institut de Mecanique, Grenoble, France.

Received for publication May 5, 1986.

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