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Properties of the Sorptivity for Exponential Diffusivity and Application to the Measurement of the Soil Water Diffusivity¹

ABSTRACT

For certain diffusivities, first integral techniques can be used to decouple the soil-water diffusion equation, in similarity form, into a set of first-order equations. Such a decoupling is possible where the diffusivity depends on the water concentration, as either a power law or as an exponential function. Here we show that the exponential case is related to the power law case, but with some resulting complications.

For this class of diffusivities, the solutions form a special class, and we generate some of their properties. In particular, the sorptivity can be represented by a simple relation to a universal function of the water content. This function is tabulated and compared with results obtained by another method, i.e., optimization. The results are applied to the measurement of soil-water diffusivity.

¹ Contribution from the School of Australian Environmental Studies, Griffith Univ., Brisbane, Queensland, 4111, Aust.

² Senior Lecturer, Professor, and Postgraduate Student, respectively.

Received for publication June 18, 1980. Accepted for publication January 26, 1981.