On solving the unsaturated flow equation: 1. the flux-concentration relation
1973
PHILIP, J. R.
The flux-concentration relation [F(θ)] expresses in reduced form the dependence of flux density on moisture content during various unsteady flow phenomena in unsaturated soils. In this first paper of a series, the general properties of F(θ) are established for various phenomena: one-dimensional sorption and infiltration with constant concentration conditions and one-dimensional sorption (for the ‘linear’ soil only) with constant and variable flux and variable concentration conditions. These studies provide a guide to the properties of F(θ) in more complicated phenomena in one-, two-, and three-dimensional systems.F(θ) is independent of time for some phenomena and it varies only mildly with time for some others; and, for some phenomena, the dependence of F(θ) on the ‘shape’ of the moisture diffusivity function lies within fairly narrow bounds, which are fixed by reference to the extreme cases of the ‘delta-function’ and the ‘linear’ soil. This relative stability of F(θ) makes it a useful aid to the study of methods of solving the unsaturated flow equation. It is employed in later papers in a critique of Parlangeʼs method and in the development of a new quasi-analytical technique.An appendix demonstrates that the approximation of step-function moisture profiles implies a delta-function moisture diffusivity function.
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