Extension of the Fujita Solution to air and water movement in soils

Abstract

For specific soil properties the fundamental solution of Fujita (1952b) is extended to include the effect of air movement on horizontal absorption. This exact solution is then used to determine the accuracy and range of applicability of two approximations to the sorptivity with air effects previously presented by Parlange et al. (1982) and Sander and Parlange (1984). The optimal sorptivity of Parlange et al. has very good accuracy while the surface water content θs is near saturation but decreases in accuracy as θs decreases. The approximate sorptivity of Sander and Parlange, however, proves to be extremely accurate for all θs with a maximum error of only 0.5%. Sander and Parlange additionally give an approximation to the water profile which is also shown by comparison with the exact solution to have a maximum error of only 0.5%. The aim of this paper is primarily of a theoretical nature in that we use the exact solution to check the accuracy of the approximate solutions as stated above. Alternatively, the solution may be used for checking the accuracy of numerical models.

Lie group symmetry analysis of transport in porous media with variable transmissivity

“…The main use of symmetries is to obtain a reduction of variables as described by Sander et al [13]. A reduction of variables of the coupled equations (6) will result in a coupled system of ordinary differential equations, which may or may not be solvable.…”

Two-phase flow of water and air during aerated subsurface drip irrigation

“…The revigoration following six decades of neglect of the quantitative studies of water movement and associated soil air effects was mainly due to Morel-Seytoux and his co-workers. The representative work include Brustkern andMorelSeytoux (1970), McWhorter (1971), Morel-Seytoux (1973, 1983, Vachaud et al (1973Vachaud et al ( , 1974, Parlange and Hill (1979), Parlange et al (1982), , Sander et al ( , 1988a, and Philip and van Duijn (1999). Those studies were either theoretical or undertaken in the laboratory.…”

n-Dimensional first integral and similarity solutions for two-phase flow

“…Rogers et al [ 16] then extended this to include the effect of gravity through a linear hydraulic conductivity function. Solutions were also obtained for two-phase absorption under Dirichlet boundary conditions by Sander et al [18] using the same D a n d / as Fokas and Yortsos [7], and Sander et al [17] with the same D but with / (61) = (/, + f 2 9 + / 3 <? 2 )/(l -vd), where / , , f 2 and / 3 are constants.…”