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Steady Infiltration from Spherical Cavities¹

ABSTRACT

The problem of quasilinearized steady infiltration from spherical cavities, with the moisture potential fixed at the cavity surface, is solved exactly. Solutions are presented numerically and graphically for values of the dimensionless cavity radius R₀ in the range 0 to 10. The dependence on R₀ of total cavity flow, of the variation of infiltration rate around the cavity surface, and of the distributions of moisture content and potential, are examined. As R₀ increases, gravity increasingly distorts the moisture distribution from the symmetry produced by capillarity alone. This distortion, although marked, is less than one-hundredth that for infiltration from circular cylindrical cavities: a vivid illustration of the stronger dominance of gravity over capillarity in two-dimensional systems than in three-dimensional ones. An earlier approximate solution of this problem proves accurate only for R₀ 0.27. The cavity flow, evaluated by the present analysis, may be combined with the point source solution to give approximate results useful for the region deeper than 20 radii below the cavity.

¹ Contribution from CSIRO, Australia.

² Chief, CSIRO Division of Environmental Mechanics, GPO Box 821, Canberra, A.C.T. 2601, Australia.

Received for publication June 10, 1983. Accepted for publication January 20, 1984.