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ORIGINAL RESEARCH

New Analytic Solution of Boltzmann Transform for Horizontal Water Infiltration into Sand

^a Soils and Agricultural Engineering Dep., Paraná State Univ., Rua dos Funcionários 1540, CEP 80030-035, Curitiba, PR, Brazil
^b Civil Construction Dep., Parana State Univ., CEP 81531-990, Curitiba, PR, Brazil
^c Soil Physics Lab., CENA/Univ. of São Paulo, Av. Centenário 303, CEP 13418-900, Piracicaba, SP, Brazil
^d Dep. of Land, Air and Water Resources, Univ. of California, Davis, CA 95616
^* Corresponding author (klaus{at}cena.usp.br).

Received 7 December 2007.

The use of the Boltzmann transform function, (), to solve the Richards equation when the diffusivity, D, is a function of only soil water content, , is now commonplace in the literature. Nevertheless, a new analytic solution of the Boltzmann transform (h) as a function of matric potential for horizontal water infiltration into a sand was derived without invoking the concept or use of D(). The derivation assumes that a similarity exists between the soil water retention function and the Boltzmann transform (). The solution successfully described soil water content profiles experimentally measured for different infiltration times into a homogeneous sand and agrees with those presented by Philip in 1955 and 1957. The applicability of this solution for all soils remains open, but it is anticipated to hold for soils whose air-filled pore-size distribution before wetting is sufficiently narrow to yield a sharp increase of water content at the wetting front during infiltration. It also improves and provides a versatile alternative to the well-known analysis pioneered by Green and Ampt in 1911.

Abbreviations: TZ, transmission zone • WF, wetting front • WZ, wetting zone

This article has been cited by other articles:

				C. L. Prevedello, J. M. T. Loyola, K. Reichardt, and D. R. Nielsen New Analytic Solution Related to the Richards, Philip, and Green-Ampt Equations for Infiltration Vadose Zone J., February 10, 2009; 8(1): 127 - 135. [Abstract] [Full Text] [PDF]