A theory is developed to describe the one-dimensional movement of electrolyte in clay-electrolyte systems that are free to swell in the direction of electrolyte movement. This theory develops from the observation that Darcy's law describes flow of fluid relative to the comparatively immobile particles of clay, and is based on a scale of length defined with reference to the distribution of mass of the clay rather than the more conventional fixed scale of length. It is shown, theoretically and experimentally, that in this scale of length the appropriate equation is the diffusion equation, for the use of which there exists a large body of information in soil physics and other literature.
The paper reports an experimental study of hydrodynamic dispersion of low concentration solutions during absorption into horizontal columns of soil with initially uniform moisture and solute contents. The initial soil solutions were of relatively high salt concentration. It was found that both the water and salt concentration profiles preserved similarity in terms of distance divided by the square root of time. This observation implies that the longitudinal dispersion coefficient is insensitive to pore water velocity and may be taken as a function of the volumetric water content only, at least for a given initial (low) moisture content.The formulation which follows is frankly phenomenological. It provides a simple means of predicting dispersion during flow in unsaturated soils which promises to be sufficiently accurate for most purposes.
It is suggested that, as a matter of course, data from infiltration experiments should be graphed with (it-1/2) as a function of t1/2 Early-time linearity of this curve confirms the appropriateness during this/ time of the two-parameter equation of Philip. The two parameters emerge as the intercept and slope of the line. If subsequently infiltration is described by the equation di/dt = K0, then this part also will emerge as the asymptote of i = K0t.
Absorption of water into soil as the result of a constant flux condition at the soil surface is examined.Experiments for a fine sand show that the surface water content, movement of the wetting front, and the water content profiles may be predicted from the soil water diffusivity function using the notion of the flux‐concentration relation of Philip (1973).Reduced space and time variables X = Vox and T = Vost are introduced. Use of these variables greatly simplifies treatment of the system and reveals that the surface water content and the reduced position of the wetting front are uniquely defined by T while the water content profiles at any value of T are unique in terms of X.
An analysis of hydrodynamic dispersion accompanying constant flux absorption of KCl solution by an initially relatively dry soil, is developed for the case when the hydrodynamic dispersion coefficient is pore water velocity‐independent. It is shown that in this process both the water content and the soil water salt concentration are uniquely defined by θ(X,T) and C(X,T), where X = vox and T = vo2t are space and time‐like coordinates, and vo is the constant surface flux of water.Quasi‐analytical methods based on the flux‐concentration relation predict θ(X,T) while an error‐function solution, based on a material coordinate Q labeling parcels of water, predicts the salt profile.The analysis is demonstrated using a chemically inert sandy soil. The results show that during transient, unsaturated flow a simple piston‐flow model described the process over a range of water contents. The method may be extended to explore dispersion in structured and chemically reactive soils.
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