skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Bounds and Estimates for Transport Coefficients of Random and Porous Media with High Contrasts

Journal Article · · Journal of Applied Physics
DOI:https://doi.org/10.1063/1.1854732· OSTI ID:15011586

Bounds on transport coefficients of random polycrystals of laminates are presented, including the well-known Hashin-Shtrikman bounds and some newly formulated bounds involving two formation factors for a two-component porous medium. Some new types of self-consistent estimates are then formulated based on the observed analytical structure both of these bounds and also of earlier self-consistent estimates (of the CPA or coherent potential approximation type). A numerical study is made, assuming first that the internal structure (i.e., the laminated grain structure) is not known, and then that it is known. The purpose of this aspect of the study is to attempt to quantify the differences in the predictions of properties of a system being modeled when such organized internal structure is present in the medium but detailed spatial correlation information may or (more commonly) may not be available. Some methods of estimating formation factors from data are also presented and then applied to a high-contrast fluid-permeability data set. Hashin-Shtrikman bounds are found to be very accurate estimates for low contrast heterogeneous media. But formation factor lower bounds are superior estimates for high contrast situations. The new self-consistent estimators also tend to agree better with data than either the bounds or the CPA estimates, which themselves tend to overestimate values for high contrast conducting composites.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
US Department of Energy (US)
DOE Contract Number:
W-7405-ENG-48
OSTI ID:
15011586
Report Number(s):
UCRL-JRNL-206888; TRN: US0501299
Journal Information:
Journal of Applied Physics, Vol. 96, Issue 6; Other Information: Journal published March 1, 2005; PBD: 24 Sep 2004; ISSN 0021-8979
Country of Publication:
United States
Language:
English

References (47)

On a phase interchange relationship for composite materials journal January 1976
Flow in Heterogeneous Porous Media journal September 1961
Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . journal January 1929
The coherent potential approximation is a realizable effective medium scheme journal December 1985
On the effective viscoelastic moduli of two-phase media. I. Rigorous bounds on the complex bulk modulus
  • Gibiansky, L. V.; Milton, Graeme W.
  • Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, Vol. 440, Issue 1908, p. 163-188 https://doi.org/10.1098/rspa.1993.0010
journal January 1993
Microstructure of two‐phase random media. III. The n ‐point matrix probability functions for fully penetrable spheres journal August 1983
Models of groundwater flow in statistically homogeneous porous formations journal February 1979
On the effective conductivity of polycrystals and a three‐dimensional phase‐interchange inequality journal May 1988
The dielectric constant of a composite material—A problem in classical physics journal July 1978
The Elastic Behaviour of a Crystalline Aggregate journal May 1952
Models for computing geomechanical constants of double-porosity materials from the constituents' properties journal January 2002
A differential scheme for the effective moduli of composites journal March 1985
Elasticity of polycrystals and rocks journal January 1972
Bounds on the complex dielectric constant of a composite material journal August 1980
Note on a variational approach to the theory of composite elastic materials journal April 1961
Effective stress for transport properties of inhomogeneous porous rock journal January 1992
Sphere assemblage model for polycrystals and symmetric materials journal March 1983
On the effective viscoelastic moduli of two–phase media. III. Rigorous bounds on the complex shear modulus in two dimensions
  • Gibiansky, Leonid V.; Milton, Graeme W.; Berryman, James G.
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 455, Issue 1986 https://doi.org/10.1098/rspa.1999.0395
journal June 1999
Analytical model for the dielectric response of brine-saturated rocks journal October 1986
The Electrical Resistance of Binary Metallic Mixtures journal July 1952
Effective conductivity of aggregates of anisotropic grains journal March 1991
Classical Transport in Disordered Media: Scaling and Effective-Medium Theories journal December 1971
Bounds on elastic constants for random polycrystals of laminates journal October 2004
Variational Method of Determining Effective Moduli of Polycrystals: (A) Hexagonal Symmetry, (B) Trigonal Symmetry journal September 1965
Iterated homogenization, differential effective medium theory and applications journal September 1987
Thermal conductivity of porous media journal January 2005
Application of the Bergman–Milton theory of bounds to the permittivity of rocks journal October 1986
Effective electrical conductivity of two‐phase disordered composite media journal November 1985
Measurement of spatial correlation functions using image processing techniques journal April 1985
Rigorous bounds for the complex dielectric constant of a two-component composite journal January 1982
Variational bounds on some bulk properties of a two-phase composite material journal August 1976
Bounds on the complex permittivity of a two‐component composite material journal August 1981
On some variational principles in anisotropic and nonhomogeneous elasticity journal October 1962
Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen journal January 1935
New Pore-Size Parameter Characterizing Transport in Porous Media journal November 1986
LVI. On the influence of obstacles arranged in rectangular order upon the properties of a medium journal December 1892
Exact results for generalized Gassmann’s equations in composite porous media with two constituents journal December 1991
Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material journal May 1980
Methodology for use of isotopic climate forcings in ice sheet models journal October 2000
Confirmation of Biot’s theory journal August 1980
A Theorem on the Conductivity of a Composite Medium journal April 1964
Multiphase interchange inequalities journal August 1991
A critical evaluation for a class of micro-mechanics models journal January 1990
A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials journal October 1962
On the effective viscoelastic moduli of two–phase media. II. Rigorous bounds on the complex shear modulus in three dimensions
  • Milton, G. W.; Berryman, J. G.
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 453, Issue 1964 https://doi.org/10.1098/rspa.1997.0100
journal September 1997
Improved Variational Bounds on Some Bulk Properties of a Two‐Phase Random Medium journal May 1969
Long‐wavelength propagation in composite elastic media I. Spherical inclusions journal December 1980

Similar Records

Related Subjects

54 ENVIRONMENTAL SCIENCES
58 GEOSCIENCES
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
POLYCRYSTALS
TRANSPORT
LAWRENCE LIVERMORE NATIONAL LABORATORY