Theory of Infiltration

Philip, J. R.

doi:10.1016/b978-1-4831-9936-8.50010-6

Cited by 1,157 publications

(383 citation statements)

References 95 publications

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“…Although solutions of the equation satisfying any well-posed set of conditions may always be found, in principle, by the direct use of finite-difference methods on high speed computers, for both intellectual and economic reasons it is desirable to take the study of various problems in nonlinear diffusion as far as possible by the methods of mathematical analysis. Treatments which have proved fruitful include similarity techniques (Boltzmann 1894;Philip 1955), perturbation of similarity solutions (Philip 1966(Philip , 1969, and integral methods (Macey 1959;Parlange 1971;Philip and Knight 1973); a short general review of the subject has been given by Philip (1973). The methods developed to date, however, are ill-fitted to consideration of periodic nonlinear diffusion, and there seems to have been no progress with analytical approaches to this class of problem.…”

Section: Introductionmentioning

confidence: 99%

Periodic Nonlinear Diffusion: An Integral Relation and its Physical Consequences

Philip¹

1973

Aust. J. Phys.

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A general integral relation in steady periodic nonlinear diffusion is established through a Kirchhoff transformation. The time average e of the transformed concentration e satisfies Laplace's equation and may therefore be evaluated readily. Results for e not only serve as simple and exact checks on detailed numerical solutions of the nonlinear diffusion equation but also provide, immediately and exactly, the principal information often sought about these solutions. The results are especially simple in many steady periodic nonlinear diffusion problems where the time average of the flux density is everywhere zero and i!j is constant. The method is applied to examples in fluid mechanics and geophysics: spatially periodic laminar boundary layers, tidal influence and seasonal stream effects on groundwater levels, and soil temperature waves.

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Section: Introductionmentioning

confidence: 99%

Periodic Nonlinear Diffusion: An Integral Relation and its Physical Consequences

Philip¹

1973

Aust. J. Phys.

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“…Sorptivity is the measure of the capacity of a medium to absorb or desorb liquid through capillary forces [31]. Culligan et al [39] states that the sorptivity depends on the properties of both the fluid and the porous material.…”

Section: Model Discussionmentioning

confidence: 99%

“…However, Richards' equation is unable to simulate fingering phenomenon [25][26][27], thus extensions are normally added to account for certain aspects of multiphase flow [28]. Previous studies [2,6,12,24,29,30] have proposed models to explain experiments based on parameters that condition wetting front instability, such as water repellency [3,7,14] and water redistribution [31]. However, to our knowledge, most studies on infiltration have focused on morphology of the water channels that form during infiltration.…”

Section: Introductionmentioning

confidence: 99%

Kinetics of gravity-driven water channels under steady rainfall

et al. 2014

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We investigate the formation of fingered flow in dry granular media under simulated rainfall using a quasi-twodimensional experimental setup composed of a random close packing of monodisperse glass beads.Using controlled experiments, we analyze the finger instabilities that develop from the wetting front as a function of fundamental granular (particle size) and fluid properties (rainfall, viscosity). These finger instabilities act as precursors for water channels, which serve as outlets for water drainage. We look into the characteristics of the homogeneous wetting front and channel size as well as estimate relevant time scales involved in the instability formation and the velocity of the channel fingertip. We compare our experimental results with that of the wellknown prediction developed by Parlange and Hill [D. E. Hill and J. Y. Parlange, Soil Sci. Soc. Am. Proc. 36, 697 (1972)]. This model is based on linear stability analysis of the growth of perturbations arising at the interface between two immiscible fluids. Results show that, in terms of morphology, experiments agree with the proposed model. However, in terms of kinetics we nevertheless account for another term that describes the homogenization of the wetting front. This result shows that the manner we introduce the fluid to a porous medium can also influence the formation of finger instabilities. The results also help us to calculate the ideal flow rate needed for homogeneous distribution of water in the soil and minimization of runoff, given the grain size, fluid density, and fluid viscosity. This could have applications in optimizing use of irrigation water. We investigate the formation of fingered flow in dry granular media under simulated rainfall using a quasitwo-dimensional experimental setup composed of a random close packing of monodisperse glass beads. Disciplines Physical Sciences and Mathematics | PhysicsUsing controlled experiments, we analyze the finger instabilities that develop from the wetting front as a function of fundamental granular (particle size) and fluid properties (rainfall, viscosity). These finger instabilities act as precursors for water channels, which serve as outlets for water drainage. We look into the characteristics of the homogeneous wetting front and channel size as well as estimate relevant time scales involved in the instability formation and the velocity of the channel fingertip. We compare our experimental results with that of the well-known prediction developed by Parlange and Hill [D. E. Hill and J. Y. Parlange, Soil Sci. Soc. Am. Proc. 36, 697 (1972)]. This model is based on linear stability analysis of the growth of perturbations arising at the interface between two immiscible fluids. Results show that, in terms of morphology, experiments agree with the proposed model. However, in terms of kinetics we nevertheless account for another term that describes the homogenization of the wetting front. This result shows that the manner we introduce the fluid to a porous medium can also influence the formation...

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“…A more recent review by Hall [20] gives the theoretical background and practical aspects of assessing the sorptivity of building materials in the laboratory. Since the interpretation of experimental data requires some understanding of the theoretical basis of unsaturated flow, a brief explanation of the theory of sorptivity is given in section 2 [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, the concept of sorptivity, developed originally from unsaturated flow theory for water transport in soil physics [6][7][8], has been applied successfully to describe capillary water absorption processes in many porous building materials [9][10][11][12][13][14][15]. The total volume of liquid absorbed by a porous building material during one-dimensional capillary absorption is given by (1) where i(t) is the cumulative volume of liquid absorbed at time t per unit area of surface.…”

Section: Introductionmentioning

confidence: 99%

Magnetic resonance imaging studies of spontaneous capillary water imbibition in aerated gypsum

Song¹,

Mitchell²,

Jaffel³

et al. 2011

J. Phys. D: Appl. Phys.

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In this paper we investigate both capillary water imbibition and the sorptivity of aerated gypsum plaster, and how these sorption characteristics are related to the pore structure of the material. These characteristics are examined by monitoring mass change using the conventional gravimetric method and by obtaining water content profiles using non-destructive magnetic resonance imaging (MRI) techniques during capillary imbibition of water. Here, three different gypsum samples are investigated: one non-aerated reference gypsum sample and two aerated gypsum samples produced with different volumetric air fractions. The capillary water absorption into the reference sample follows t 1/2 kinetics (Fickian diffusion), where t is the time of ingress. However, in the aerated gypsum samples there are deviations from t 1/2 kinetics. The MRI results show unambiguously that two wetting fronts advance through the aerated structure; an observation that cannot be made from the gravimetric data alone. The water content profiles of the aerated gypsum samples are therefore analysed by treating them as the sum of two separate absorption processes using sharp front analysis. The capillary water absorption properties of this material are well described as a parallel combination of fast absorption into fine matrix pores and slow absorption into a modified structure of matrix pores inter-connected to air voids introduced into the slurry by aeration.

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Theory of Infiltration

Cited by 1,157 publications

References 95 publications

Periodic Nonlinear Diffusion: An Integral Relation and its Physical Consequences

Periodic Nonlinear Diffusion: An Integral Relation and its Physical Consequences

Kinetics of gravity-driven water channels under steady rainfall

Magnetic resonance imaging studies of spontaneous capillary water imbibition in aerated gypsum

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