A SOLUTION FOR VERTICAL INFILTRATION INTO A DRY POROUS MEDIUM

An exact solution is derived for the second term of J. R. Philip's [1957] series expansion originally developed for his numerical method of solution of the diffusion equation with diffusivity concentration dependent. The exact solution is made possible by the adoption of simple algebraic functions to describe the water content‐capillary suction and the water content‐capillary conductivity relationships of the porous medium and of a solution for horizontal infiltration presented in an earlier paper [Brutsaert, 1968]. Because of the fast convergence of the series, all terms of order higher than the second are negligible. Thus the present solution for the second term used in combination with the first term, representing the solution for horizontal infiltration, provides an adequate solution for vertical infiltration. Good agreement is obtained with published experimental data. © 1968 by the Chinese Geophysical Society