Electroconductivity of a medium with thin low-resistivity inclusions

Journal of Electrostatics

Volumn 61, Issue 2, 2004, Pages 129-145

  Levin, V M ^a   Markov, M G ^a  

^a INSTITUTO MEXICANO DEL PETRÓLEO   (Mexico)

Author keywords

Effective conductivity; Effective field method; Heterogeneous systems

Indexed keywords

COMPUTER SIMULATION; ELECTRIC CONDUCTIVITY; INCLUSIONS; MATHEMATICAL MODELS; PARTICLE SIZE ANALYSIS; TENSORS;

ELLIPSOIDAL CORRELATION HOLE; ELLIPSOIDAL PARTICLES; HETEROGENEOUS MEDIA; SPATIAL DISTRIBUTION;

ELECTROSTATICS;

ELECTROSTATICS;

EID: 16544362127     PISSN: 03043886     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.elstat.2004.02.003     Document Type: Article

References (29)

1. Maxwell J.C. A Treatise on Electricity and Magnetism 1891 Clarendon Press Oxford
2. Markov K.Z. Elementary micromechanics of heterogeneous solids Markov K.Z. Preziosi L. Heterogeneous Media: Micromechanics Modeling Methods and Simulation 2000 1-162 Birkhauser Boston
3. Van Beek L.K.H. Dielectric behavior of heterogeneous systems Prog. Dielectr. 7 1976 71-114
4. Fricke H. A mathematical treatment of the electric conductivity and capacity of disperse systems Phys. Rev. 24 1924 575-587
5. Shafiro B. Kachanov M. Anisotropic effective conductivity of materials with nonrandomly oriented inclusions of diverse ellipsoidal shapes J. Appl. Phys. 87 12 2000 8561-8569
6. Bruggeman D.A. Berechnung verschidener physikalischer Konstanten von heterogenen Substanzen Ann. Phys. (Leipzig) 24 1935 636-664
7. Sen P. Kenyon W. Takezaki H. Petricola M. Formation factor of carbonate rocks with microporosity: Model calculations J. Pet. Sci. Eng. 17 1997 345-352
8. Yonesawa F. Cohen M. Granular effective medium approximation J. Appl. Phys. 54 1983 2895-2899
9. Hori M. Yonesawa F. Statistical theory of effective electrical, thermal and magnetic properties of random heterogeneous materials J. Math. Phys. 16 1975 352-364
10. Moctesuma-Berthier A. Visice A. Adler P.M. Macroscopic conductivity of vugular porous media Transp. Porous Media 49 2002 313-332
11. Sen P. Scala C. Cohen M. A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beard Geophysics 46 1981 781-796
12. Mendelson K.S. Cohen M.N. The effect of grain anisotropy on the electrical properties of isotropic sedimentary rocks Geophysics 47 1982 257-263
13. Norris A.N. Sheng P. Callegari A.J. Effective-medium theories for two-phase dielectric media J. Appl. Phys. 57 1985 1990-1996
14. Giordano S. Effective medium theory for dispersion of dielectric ellipsoids J. Electrostat. 58 2003 59-76
15. J. Berryman, Mixture theories for rock properties, in: A Handbook of Physical Constants, American Geophysical Union, Washington, 1995, pp. 205-228.
16. M. Markov, A. Mousatov, E. Kazatchenko, Joint inversion of acoustic and resistivity data for carbonate microstructure evaluation, 44th Annual Symposium SPWLA, Galveston, 2003.
17. Hashin Z. Strikman S. Variational approach to the theory of the effective magnetic permeability of multiphase materials J. Appl. Phys. 33 1962 3125-3131
18. Kanaun S.K. The effective field method in the linear problems of the statics of composite media PMM Appl. Math. Mech. 46 1982 655-665
19. Kanaun S.K. Elastic medium with random fields of inhomogeneities Kunin I.A. Elastic Media with Microstructure II, Three-dimensional Models 1983 165-228 Springer Berlin (Chapter 7)
20. S.K. Kanaun, V.M. Levin, The effective field method in mechanics of composite materials, Petrozavodsk University, 1993, 600pp.
21. Kanaun S.K. Levin V.M. Effective field method in mechanics of matrix composite materials Markov K.Z. Recent Advances in Mathematical Modelling of Composite Materials 1994 1-58 World Scientific Singapore
22. Markov K.Z. Justification of an effective field method in elasto-statics of heterogeneous solids J. Mech. Phys. Solids 49 2001 2621-2634
23. Mori T. Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions Acta Metall. 21 1973 571-579
24. Levin V. To the determination of elastic and thermoelastic constants of composite materials Mech. Solids 6 1976 137-145
25. Benveniste Y. On the effective thermal conductivity of multiphase composites Z. Angew. Math. Phys. 37 1986 696-713
26. Kanaun S.K. On the singular models of the thin inclusions in the homogeneous elastic medium Appl. Math. Mech. 48 1 1984 81-91
27. Kanaun S.K. The thin defect in a homogeneous elastic medium Mech. Solids 3 1984 74-83
28. Kanaun S.K. Effective elastic properties of the medium with an array of thin inclusions Rev. Mex. Fis. 39 6 1993 850-869
29. Wilchevskaya E.N. Kanaun S.K. Integral equations of the problem on the thin inclusion in a homogeneous elastic medium Appl. Math. Mech. 56 2 1992 275-285