The drainage of liquids from porous materials

Youngs, E. G.

doi:10.1029/jz065i012p04025

Cited by 61 publications

(36 citation statements)

References 6 publications

(1 reference statement)

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“…During such drainage scenario, the interface at height

z_{p}

between the wet (unmodified uniform profile region) and the drier (partially drained) region travels downward. Very simple analytical solutions for the dynamic of such drainage processes were developed by Kraynik [] for wet foam drainage and by Youngs [] for draining porous media. The two solutions share a representation of the volumetric drainage rate

Q

(volume per time) at the lower boundary given by:

Q = C \cdot \frac{Δ H true(z_{p} true)}{z_{p}}

with a (volumetric) hydraulic conductivity

C

, and the driving pressure head difference

Δ H

between interface position

z_{p}

and lower boundary.…”

Section: Solutions For the Soil Foam Drainage Equation (Sfde)mentioning

confidence: 99%

“…While Kraynik [] assumed constant drainage rate defined by unit gradient (

Q = C

) as long as the drainage interface position

z_{p}

is above the lower boundary of the channel (

z_{p} > z_{b o t}

), Youngs [], considering draining cylindrical capillaries and a gradually decreasing driving pressure gradient (defined by distance

δ

of the interface at height

z_{p}

to its hydrostatic equilibrium height

z_{e q}

δ = z_{p} - z_{e q}

), obtained a simple representation of the volumetric drainage rate

Q

and drained volume

V

as exponential functions of time

t

V true(t true) = V_{\infty} true[1 - \exp true(- \frac{Q_{0} \cdot t}{V_{\infty}} true) true]

Q true(t true) = Q_{0} \cdot \exp true(- \frac{Q_{0} \cdot t}{V_{\infty}} true)

with the volume of water

V_{\infty}

that can be drained to attain hydrostatic equilibrium, and the initial water flow

Q_{0}

(equal to flow conductivity

Q_{0} = C

for unit gradient conditions). Youngs [] derived the equations for cylindrical capillaries with no liquid left behind the receding main meniscus. As we will show in Appendix , better results can be obtained with angular capillaries considering the contribution of liquid above the interface position

…”

Section: Solutions For the Soil Foam Drainage Equation (Sfde)mentioning

confidence: 99%

See 1 more Smart Citation

The foam drainage equation for drainage dynamics in unsaturated porous media

Lehmann

Hoogland

Assouline

et al. 2017

Water Resources Research

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Similarity in liquid‐phase configuration and drainage dynamics of wet foam and gravity drainage from unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation—SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. The study provides new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions. Two novel analytical solutions for saturation profile evolution were derived and tested in good agreement with a numerical solution of the SFDE. The study and the proposed solutions rectify the original formulation of foam drainage dynamics of Or and Assouline (2013). The new framework broadens the scope of methods available for quantifying unsaturated flow in porous media, where the intrinsic conductivity and geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.

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“…During such drainage scenario, the interface at height

z_{p}

Q

(volume per time) at the lower boundary given by:

Q = C \cdot \frac{Δ H true(z_{p} true)}{z_{p}}

with a (volumetric) hydraulic conductivity

C

, and the driving pressure head difference

Δ H

between interface position

z_{p}

and lower boundary.…”

Section: Solutions For the Soil Foam Drainage Equation (Sfde)mentioning

confidence: 99%

“…While Kraynik [] assumed constant drainage rate defined by unit gradient (

Q = C

) as long as the drainage interface position

z_{p}

is above the lower boundary of the channel (

z_{p} > z_{b o t}

), Youngs [], considering draining cylindrical capillaries and a gradually decreasing driving pressure gradient (defined by distance

δ

of the interface at height

z_{p}

to its hydrostatic equilibrium height

z_{e q}

δ = z_{p} - z_{e q}

), obtained a simple representation of the volumetric drainage rate

Q

and drained volume

V

as exponential functions of time

t

V true(t true) = V_{\infty} true[1 - \exp true(- \frac{Q_{0} \cdot t}{V_{\infty}} true) true]

Q true(t true) = Q_{0} \cdot \exp true(- \frac{Q_{0} \cdot t}{V_{\infty}} true)

with the volume of water

V_{\infty}

that can be drained to attain hydrostatic equilibrium, and the initial water flow

Q_{0}

(equal to flow conductivity

Q_{0} = C

…”

Section: Solutions For the Soil Foam Drainage Equation (Sfde)mentioning

confidence: 99%

The foam drainage equation for drainage dynamics in unsaturated porous media

Lehmann

Hoogland

Assouline

et al. 2017

Water Resources Research

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show abstract

“…Interesting derivations of equation (7) were made by Youngs (1960) and later by Youngs and Aggel ides (1976). In his 1960 paper, Youngs treated drainage of liquids from porous media by equating the media to bundles of capillary tubes.…”

Section: Developmentmentioning

confidence: 99%

Evaluation of major dike-impounded ground-water reservoirs, Island of Oahu

Takasaki¹

1985

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“…Obviously, in this case gravity and capillary forces are co-oriented and with time the front acquires a constant velocity, unless an impeding lowconductivity horizon stops this propagation. If an initially saturated column drains to a water table of zero-pressure (Youngs 1960) a piston-type drainage front descends but the tension-saturated zone shrinks (provided the water table remains stationary). Clearly, in this regime capillarity counteracts gravity and the front velocity decreases to zero with time (Youngs and Aggelides 1976, YA hereafter).…”

Section: Introductionmentioning

confidence: 99%

“…(This list is, of course, not complete and, for the sake of brevity, we do not review the referenced papers in detail; we can relate each of the referenced papers to our own problem in the manuscript.) The pioneering paper by Youngs (1960) linked the GA model with the kinetics of the HamelPoiseuille water slugs in bundles of capillary tubes, where the so-called Washburn-Lukas models are utilized (Dullien 1992). A Newtonian viscosity of the liquid and individual tube-meniscus characteristics (surface tension and contact angle) in the WashburnLukas models serve as analogues of saturated ("resaturated") hydraulic conductivity and suction pressure on the front in the GA model.…”

Section: Introductionmentioning

confidence: 99%

Pseudo-hysteretic double-front hiatus-stage soil water parcels supplying a plant–root continuum: the Green-Ampt-Youngs model revisited

Kacimov

2013

Hydrological Sciences Journal

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Editor D. KoutsoyiannisCitation Kacimov, A. and Obnosov, U., 2013. Pseudo-hysteretic double-front hiatus-stage soil water parcels supplying a plant-root continuum: the Green-Ampt-Youngs model revisited. Hydrological Sciences Journal, 58 (1), 237-248.Abstract A tension-saturated water slug descends through a homogenous soil after a rainfall (irrigation) event and shrinks due to transpiration by a distributed root-sink and evaporation. The upper (drainage) and lower (imbibition) sharp fronts of the slug separate it from the superjacent and subjacent vadose zones, where water is immobile. In the slug, the hydraulic conductivity is constant according to the Green-Ampt model. The capillary pressures as well as effective porosities on the fronts are given (generally, different) constants that can be viewed as a kind of hysteresis. A volumetric sink models mild (no desaturation of the slug) soil water withdrawal by the plant roots. The sink intensity varies with the depth from the soil surface and with time. Mathematically, the hydraulic head is immediately expressed by double integration of a governing 1-D flow equation. The pressure and kinematic conditions on the fronts result in a Cauchy problem for a system of two ODEs, which is solved by computer algebra routines.Key words infiltration; two-front Green-Ampt approximation; evapotranspiration; drainage-imbibition; root water uptake; ecohydrology Masses d'eau du sol à double front et pseudo-hystérésis alimentant le continuum plante-racines: retour sur le modèle de Green-Ampt-YoungsRésumé Une bulle saturée en eau descend à travers un sol homogène après un épisode de pluie ou d'irrigation et s'amincit en raison de la transpiration du prélèvement racinaire et de l'évaporation. Les fronts abrupts supérieur (drainage) et inférieur (imbibition) de la bulle la séparent des zones non-saturées sus-jacentes et sous-jacentes, où l'eau est immobile. Dans la bulle, la conductivité hydraulique est constante selon le modèle de Green-Ampt. Les pressions capillaires ainsi que des porosités efficaces sur les fronts sont des constantes données (en général différentes) ce qui peut être vu comme une sorte d'hystérésis. Un prélèvement volumétrique modélise le faible prélèvement d'eau du sol (pas de désaturation de la bulle) par les racines des plantes. L'intensité du prélèvement varie avec la profondeur depuis la surface du sol et au cours du temps. Mathématiquement, la charge hydraulique s'exprime immédiatement par la double intégration de l'équation régissant l'écoulement à une dimension. La pression et les conditions cinématiques sur les fronts permettent de poser un problème de Cauchy pour un système de deux équations différentielles ordinaires, qui peut être résolu par des routines de calcul formel.

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The drainage of liquids from porous materials

Abstract: An equation is derived to describe the yield of liquid at a given time from a freely draining column of initially saturated porous material in a gravitational field by using a capillary tube model. The equation is supported by experimental evidence.

Cited by 61 publications

References 6 publications

The foam drainage equation for drainage dynamics in unsaturated porous media

The foam drainage equation for drainage dynamics in unsaturated porous media

Evaluation of major dike-impounded ground-water reservoirs, Island of Oahu

Pseudo-hysteretic double-front hiatus-stage soil water parcels supplying a plant–root continuum: the Green-Ampt-Youngs model revisited

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