The statistical mechanical theory of groundwater flow

Sposito, Garrison; Chu, Shu‐Yuan

doi:10.1029/wr017i004p00885

Cited by 19 publications

(15 citation statements)

References 17 publications

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“…The macroscopic balance equations, (21) and (26), and the differential equation for the isothermal transport of water, (44), are the principal mathematical results of the present study. These equations formally are identical with expressions for the balance of mass and linear momentum and for the transport of water in porous media that have been derived on the basis of the REV concept I' Klute, 1968a, b, 1969;Sposito, 1979a, b;Gray, 1979a, b, 1980;Sposito and Chu, 1981]. As pointed out in the third section of this paper the principal reason for this formal similarity is the assumption that all macroscopic field variables (e.g., those in (17)) are associated with the same weighting function in (6) or (13).…”

Section: Discussionmentioning

confidence: 97%

“…The seminal work of Raats [1965] provides a convenient method of deriving the macroscopic water transport equation in unsaturated, deformable porous media and will be adopted here. The choice of this method is motivated by its conceptual simplicity as compared with other fundamental approaches [Sposito, 1978a, b;Hassanizadeh and Gray, 1980;Sposito, 1980;Sposito and Chu, 1981]. In this approach, for example, constitutive relations between the field variables appearing in the macroscopic mass and linear momentum balance equations are postulated on the basis of experim,ental data, physical intuition, and the implications of simplified molecular models [Raats and Klute, 1968b].…”

Section: T• I•t•rmal Wa•r Transport Equationmentioning

confidence: 99%

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The Operational Significance of the Continuum Hypothesis in the Theory of Water Movement Through Soils and Aquifers

Baveye¹,

Sposito²

1984

Water Resources Research

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201

103

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The operational meaning of the representative elementary volume (REV) concept, on which current foundational theories of water movement through porous media are based, is analyzed critically. It is concluded that the REV concept as applied to real porous media is both unnecessarily restrictive and experimentally unverifiable. In its place a relativist concept is proposed in which macroscopic physical variables are defined as convolution products of microscopic properties of a porous medium with weighting functions that represent the appropriate measuring instruments. The effects of resolution and precision differences among experimental measuring devices, now recognized as critical in the assessment of spatial variability in the properties of soils and aquifers, can be incorporated naturally within the relativist concept but are excluded a priori in the REV concept. The relativist point of view, unlike the REV concept, has a clear operational meaning and, in principle, extends theoretical validity to all local measurements made on porous media. It is sufficient mathematically to derive conventional macroscopic balance equations for mass and linear momentum as well as a differential equation for the isothermal transport of water through an unsaturated, anisotropic, deformable soil or aquifer.

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Section: Discussionmentioning

confidence: 97%

Section: T• I•t•rmal Wa•r Transport Equationmentioning

confidence: 99%

The Operational Significance of the Continuum Hypothesis in the Theory of Water Movement Through Soils and Aquifers

Baveye¹,

Sposito²

1984

Water Resources Research

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201

103

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“…Thermodynamics is used to define state variables controlling the multiphase transfer in porous media (e.g., Hassanizadeh and Gray, 1979; 1980; Sposito and Chu, 1981; 1982) and to identify and define forms of energy changes in the process of interest. Matric potential in soil can be defined as “the amount of work that must be done per unit quantity of pure water to transport reversibly and isothermally to the soil water at a considered point, an infinitesimal quantity of water from a reference pool” (Nitao and Bear, 1996):

{{normalψ}_{normala} = \partial G / \partial V_{normalw} |}_{T, P}

where V w is volume of soil water and G is defined as the Gibbs free energy for water retention (e.g., Nye and Tinker, 1977).…”

Section: Theoretical and Experimental Methodsmentioning

confidence: 99%

“…Under the transferable or reversible energy concept defined by Gibbs free energy, several types of transferable work acting on water molecules during water sorption on a soil have been identified and formulated in the existing thermodynamic theories for unsaturated soil systems (e.g., Sposito and Chu, 1981; Iwata and Tabuchi, 1988). Below are synopses of the energy forms relevant to the three soil water retention regimes shown in Fig.…”

Section: Theoretical and Experimental Methodsmentioning

confidence: 99%

Intrinsic Relationship between Matric Potential and Cation Hydration

Khorshidi

2016

Vadose Zone Journal

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Core Ideas Exchangeable cations are important in water sorption, hydraulic conductivity, swelling, flocculation–deflocculation, and fertility. Intrinsic relationship exists between matric potential and cation hydration at very low water contents. Proposed model predicts soil water content at low matric potentials for different exchangeable cations in soil. Model is applicable for soil water retention models and quantification of different types of exchangeable cations. The origin of matric potential in the tightly adsorbed soil water retention (SWR) regime, where matric potentials are generally less than −150 MPa, remains unsettled. Surface tension in soil pores and van der Waals attraction (VDW) near particle surfaces are known, respectively, as the sources of matric potential for capillary and adsorbed film water. However, theories based on VDW fail to predict the SWR for matric potentials less than −150 MPa. Recent studies show that cation hydration occurs at matric potentials much lower than those predicted by considering a particle surface hydration originating from the VDW forces. With this basis, a theoretical soil water retention curve (SWRC) model for drying path is proposed to quantify matric potential and its retained water by accounting for all water sorption mechanisms on or within soil particles, particularly the cation–water molecule or charge–dipole interaction. It is found that clays at very low soil water content, typically less than a few percentage gravimetric, charge–dipole interaction energy, dominate matric potential. Experimental SWR data for various cation‐exchanged soils confirms the validity of the theoretical SWRC model and its accuracy, indicating that cation hydration is mainly responsible for SWR for matric potentials less than −150 MPa. Furthermore, the predicted lowest matric potentials at zero water content for various soils agree well with experimental data. The lowest matric potential of a soil depends mainly on the type of exchangeable cations and thus is not a universal constant for all soils. These results have potential applications in using SWRC for the determination of cation exchange capacity and types of exchangeable cations in soils.

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“…Cosserat and Cosserat, 1909;Grad, 1952;Glinther, 1958;Aero and Kuvshinskii, 1960;Truesdell and Toupin, 1960;Toupin, 1962;Eringen, 1962;Mindlin, 1964;Green and Rivlin, 1964;Eringen and Suhubi, 1964;Eringen, 1967;Marie, 1967;Anderson and Jackson, 1967;Slattery, 1967;Whitaker, 1967;Raats and Klute, 19680q b;Bear, 1972;Bowen, 1976;Gray, 1979a, b, 1980;Ene, 1981;Marie, 1982, Cushman, 1983, 1984aGray, 1983]. Sposito [1978a, b], Sposito and Chu [1981], and Bhattacharya and Gupta [1983] have considered threescale transport problems. One of the salient features of this article will be the consideration of N-scale transport in a multiphase media.…”

Section: Introductionmentioning

confidence: 99%

On unifying the concepts of scale, instrumentation, and stochastics in the development of multiphase transport theory

Cushman¹

1984

Water Resources Research

160

108

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A generalized theory of multiphase transport is presented which combines the concepts of scale, instrumentation, stochastics, and time series with the development of transport equations. By defining the filtering process as a convolution of a measure P with a field property ψ, we are able to exploit the Fourier transform to place plausible restrictions on an instrument in frequency space so as to make its measurement relevant to its physical environment. An ideal instrument is defined which filters out high‐frequency noise (corresponding to short distances) and yet does not alter the structure of low frequencies. Using ideal instruments we successively filter out lower frequency noise in a multiscale, multiphase environment. Formulas are developed to relate the autocorrelation of a field property on one scale of motion to that on any other scale while taking into account the types of instruments used in the measuring process. An equation relating the integral scale on one scale of motion to the integral scale on any other scale of motion is developed. Power spectra are developed which relate spectra on different scales to the measuring instrument used. By successively applying filtering theorems, a hierarchy of multiscale transport equations is developed. Filtered properties in the transport equations are mass averages. Different properties are allowed to be measured by different instruments and different instruments are allowed on different scales of motion and for different phases. The concept of a wide sense stationary, ergodic process is introduced to develop mass average autocorrelations and spectra over scales of motion as a function of measuring devices.

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The statistical mechanical theory of groundwater flow

Cited by 19 publications

References 17 publications

The Operational Significance of the Continuum Hypothesis in the Theory of Water Movement Through Soils and Aquifers

The Operational Significance of the Continuum Hypothesis in the Theory of Water Movement Through Soils and Aquifers

Intrinsic Relationship between Matric Potential and Cation Hydration

On unifying the concepts of scale, instrumentation, and stochastics in the development of multiphase transport theory

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