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Soil Water Dynamics$
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Arthur W. Warrick

Print publication date: 2003

Print ISBN-13: 9780195126051

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195126051.001.0001

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One-Dimensional Absorption

One-Dimensional Absorption

(p.135) 4 One-Dimensional Absorption
Soil Water Dynamics

Arthur W. Warrick

Oxford University Press

In this chapter we address one-dimensional absorption. Absorption denotes movement of water (or other liquid) into a soil under the influence of capillarity without the effects of gravity. Although important for horizontal flow conditions, there is more interest in the results and principles relevant to the early stage of infiltration and in general relationships descriptive of the physical principles for all unsaturated systems. At the outset, two simplified systems will be considered. Included is the classical problem of linear diffusion into a semi-infinite domain. Then the Boltzmann similarity transform will be applied, confirming results from the simplified solutions and leading to methods for finding soil-water diffusivity and Philip’s quasi-analytical solution. Finally, simultaneous water flow will be considered as a two-phase process. Figure 4-1 shows water introduced into a horizontal column of soil at a matric potential hwet. The value of hwet is maintained as zero or negative by the “mariotte” device to the left. The initial condition is that the matric potential is hdry with hdry < hwet ≤ 0. A porous plate at x = 0 allows water to come into the system but prevents air from flowing from the soil back into the water supply. The right-hand end allows air to freely escape the system as the water displaces the air. Vertical movement in the soil column is ignored. We make key simplifying assumptions that the conductivity is a constant K = Kwet in the wet part of the column and K = 0 for the dry part. Furthermore, we assume a sharp division between the wet and dry part at xf. On the supply side of the column (0 < x < xf), the water content is a constant (θ = θwet) and, to the dry side, the initial value is maintained (θ = θdry). These are equivalent to the “Green–Ampt” assumptions used in chapter 5, when gravity will be included as a driving force.

Keywords:   absorption, capillarity, diffusion equation, error function, horizontal flow, sorptivity, unidirectional flow, wetting front

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