A two-scale model for coupled electro-chemo-mechanical phenomena and Onsager's reciprocity relations in expansive clays: I homogenization analysis

Transport in Porous Media

Volumn 62, Issue 3, 2006, Pages 333-380

  Moyne, Christian ^a   Murad, Márcio A ^b  

^a NANCY UNIVERSITÉ   (France)

^b LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

Author keywords

Chemico osmosis; Closure problems; Disjoining (swelling) pressure; Distortion of the double layer; Electro migration; Electro osmosis; Hartman number; Homogenization; Modified Terzaghi's principle; Onsager's relations; Poisson Boltzmann; Streaming current; Swelling clay

Indexed keywords

ELECTROCHEMISTRY; ELECTROHYDRODYNAMICS; ELECTROLYTES; ELECTROMIGRATION; ELECTROOSMOSIS; FLOW INTERACTIONS; MATHEMATICAL MODELS; PRESSURE EFFECTS; SOLUTIONS; SWELLING;

CHEMICO-OSMOSIS; CLOSURE PROBLEMS; DISJOINING (SWELLING) PRESSURE; HARTMAN NUMBER; HOMOGENIZATION; ONSAGER RELATIONS; POISSON-BOLTZMANN PROBLEM; STREAMING CURRENT; SWELLING CLAY;

CLAY;

CLAY; ELECTROCHEMISTRY; ELECTROHYDRODYNAMICS; ELECTROLYTES; ELECTROMIGRATION; ELECTROOSMOSIS; FLOW INTERACTIONS; MATHEMATICAL MODELS; PRESSURE EFFECTS; SOLUTIONS; SWELLING;

CLAY MINERAL; EXPANSIVE SOIL; SWELLING;

EID: 33644546366     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-005-1290-8     Document Type: Article

References (81)

1. G. Achari R. C. Joshi L. R. Bentley S. Chatterji 1999 Prediction of the hydraulic conductivity of clays using the electric double layer theory Canad. Geotech. J. 35 783-792
2. S. Allison 1996 Modeding the electrophoresis of rigid polyions: inclusion of ion relaxation Macromolecules 29 7391-7941 10.1021/ma960890w
3. A. Anandarajah 1997 Influence of particle orientation on ono-dimensional compression of montmorillonite J. Colloid Interface Sci. 194 44-52 10.1006/jcis.1997.5068
4. J. L. Auriault 1991 Heterogeneous media: Is an equivalent homogeneous description always possible? Int. J. Engng. Sci. 29 785-795 10.1016/ 0020-7225(91)90001-J
5. J. L. Auriault 1990 Behavior of porous saturated deformable media, geomaterials F. Darve Constitutive Equations and Modeling Elsevier New York 311-328
6. J. L. Auriault P. M. Adler 1995 Taylor dispersion in porous media: analysis by multiple scale expansions Adv. Water Resour. 18 4 217-226 10.1016/0309-1708(95)00011-7
7. J. L. Auriault E. Sanchez-Palencia 1977 Etude du comportement macroscopique d'un milieu poreux saturé déformable J. Mécanique 16 4 575-603
8. J. L. Auriault T. Strzelecki J. Bauer S. He 1990 Porous deformable media saturated by a very compressible fluid: Quasi-statics Eur. J. Mech. A:SOlids 4 373-392
9. S. L. Barbour D. G. Fredlund 1989 Mechanisms of osmotic flow and volume changes in clay soils Canad. Geotech. J. 26 551-562
10. L. S. Bennethum J. H. Cushman 2002 Multicomponent, multiphase thermodynamics of swelling porous media with electroquasistatics: Parts I-II Transport Porous Media 47 3 309-362
11. L. S. Bennethum M. A. Murad J. H. Cushman 2000 Macroscale thermodynamics and the chemical potential for swelling porous media Transport Porous Media 39 187-225 10.1023/A:1006661330427
12. S. G. Bike C. Prieve 1992 Electrohydrodynamics of thin double layers: A model for the streaming potential profile J. Colloid Interface Sci. 154 1 87-96 10.1016/0021-9797(92)90080-6
13. M. Biot D. G. Willis 1957 The elastic coefficients of the theory of consolidation J. Appl. Mech. 79 594-601
14. H. Callen 1985 Thermodynamics and an Introduction to Thermostatics Wiley New York
15. D. Coelho M. Shapiro J. F. Thovert P. M. Adler 1996 Electroosmotic phenomena in porous media J. Colloid Interface Sci. 181 169-190 10.1006/ jcis.1996.0369
16. K. Dahnert D. Huster 1999 Comparison of the Poisson-Boltzmann model and the Donnan equilibrium of a polyelectrolyte in salt solution J. Colloid Interface Sci. 215 131-139 10.1006/jcis.1999.6238
17. B. V. Derjaguin N. V. Churaev V. M. Muller 1987 Surface Forces Plenum Press New York
18. F. G. Donnan 1924 The theory of membrane equilibria Chem. Rev. 1 73-90 10.1021/cr60001a003
19. L. Dormieux P. Barboux O. Coussy P. Dangla 1995 A macroscopic model of the swelling phenomenon of a saturated clay Eur. Mech. A/Solids 14 981-1004
20. L. Dormieux E. Lemarchand O. Coussy 2003 Macroscopic and micromechanical approaches to the modelling of the osmotic swelling in clays Transport Porous Media 50 75-91 10.1023/A:1020679928927
21. Eringen A. C. and Maugin, G. A.: 1989, Electrodynamics of Continua, Springer-Verlag.
22. J. C. Fair J. F. Osterlé 1971 Reverse electrodialysis in charged capillary membranes J. Chem. Phys. 54 8 3307-3316 10.1063/1.1675344
23. W. G. Gray S. M. Hassanizadeh 1989 Averaging theorems and averaged equations for transport of interface properties in multiphase systems Int. J. Multiphase Flow 15 81-95 10.1016/0301-9322(89)90087-6
24. S. R. Groot de P. G. Mazur 1962 Non-Equilibrium Thermodynamics North-Holland Amsterdam
25. R. J. Gross J. F. Osterlé 1968 Membrane transport characteristics of ultrafine capillaries J. Chem. Phys. 49 1 228-234 10.1063/1.1669814
26. W. Y. Gu W. M. Lai V. C. Mow 1998 A triphasic analysis of negative osmotic flows through charged hydrated tissues J. Biomech. 30 1 71-78
27. W. Y. Gu W. M. Lai V. C. Mow 1998 A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: Passive transport and swelling behaviors J. Biomech. Engng. 120 169-180
28. S. M. Hassanizadeh W. G. Gray 1990 Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries Adv. Water Resour. 13 169-186 10.1016/0309-1708(90)90040-B
29. W. K. Heidug S. W. Wong 1996 Hydration swelling of water-adsorbing rocks: A constitutive model Int. J. Numer. Anal. Methods Geomech. 20 403-430 10.1002/ (SICI)1096-9853(199606)20:6<403::AID-NAG832>3.0.CO;2-7
30. E. J. Hinch J. D. Sherwood 1983 The primary electroviscous effect in a suspension of spheres with thin double layers J. Fluid Mech. 132 337-347
31. T. Hueckel 1992 On effective stress concepts and deformation in clays subjected to environmental loads Canad. Geotech. J. 29 1120-1125
32. J. M. Huyghe J. D. Janssen 1997 Quadriphasic mechanics of swelling incompressible porous media Int. J. Eng. Sci. 25 8 793-802
33. R. J. Hunter 1981 Zeta Potential in Colloid Science: Principles and Applications Academic Press New York
34. R. J. Hunter 1994 Introduction to Modern Colloid Science Oxford University Press Oxford
35. J. Israelachvili 1991 Intermolecular and Surfaces Forces Academic Press New York
36. D. J. Kim J. Diels J. Feyen 1992 Water movement associated with overburden potential in a shrinking marine clay soil J. Hydrol. 133 179-200 10.1016/0022-1694(92)90254-S
37. W. M. Lai J. S. Hou V. C. Mow 1991 A triphasic theory for the swelling and deformation behaviors of articular cartilage J. Biomech. Engng. 113 245-258
38. T. W. Lambe 1960 A mechanistic picture of shear strength in clay Boulder Colorado 503-532 Proc. ASCE Research Conference on Shear Strength of Cohesive Soils
39. L. D. Landau E. M. Lifchitz 1960 Electrodynamics of Continuous Media Pergamon Press Oxford
40. E. Lee Y. S. Lee F. Y. Yen J. P. Hsu 2000 Electroosmotic flow of a general electrolyte solution through a fibrous medium J. Colloid Interface Sci. 223 223-228 10.1006/jcis.1999.6626
41. B. Loret T. Hueckel A. Gajo 2002 Chemo-mechanical coupling in saturated porous media: Elastic-plasic behavior of homoionic expansive clays Int. J. Solids Struct. 39 2773-2806
42. D. Lydzba J. F. Shao 2000 Study of poroelasticity material coefficients as response of microstructure Mech. Cohesive-Frictional Mater. 5 171-194
43. P. F. Low 1987 Structural component of the swelling pressure of clays Langmuir 3 18-25 10.1021/la00073a004
44. J. Lyklema 1993 Fundamentals of Colloid and Interface Science Academic Press London
45. W. Macevoy M. Avellaneda 1997 Electroosmotic coupling: Incorporating larger surface effects with a new length scale J. Colloid Interface Sci. 188 139-149 10.1006/jcis.1996.4742
46. Melcher, J. R.: 1981, Continuum Electromechanics, MIT Press.
47. N. A. Mishchuk P. V. Takhistov 1998 Electroosmosis of the second kind Colloids Surfaces A: Physicochem. Eng. Aspects 95 119-131
48. J. K. Mitchell 1993 Fundamentals of Soil Behaviour Wiley New York
49. C. Moyne M. Murad 2002 Electro-chemo-mechanical couplings in swelling clays derived from a micro/macro homogenization procedure Int. J. Solids Struct. 39 6159-6190
50. C. Moyne M. Murad 2003 Macroscopic behavior of swelling porous media derived from micromechanical analysis Transport Porous Media 50 127-151 10.1023/A:1020665915480
51. Moyne, C. and Murad, M.: 2006, A Two-scale model for coupled electro-chemo-mechanical phenomena and Onsager's reciprocity relations in expansive clays: II Computational validation, Transport Porous Media, In press.
52. M. A. Murad J. C. Cushman 1997 A multiscale theory of swelling porous media: II Dual porosity models for consolidation of clays incorporating physicochemical effects. Transport Porous Media 28 1 69-108
53. M. A. Murad J. C. Cushman 2000 Thermomechanical theories for swelling porous media with microstructure Int. J. Engng. Sci. 38 5 517-564 10.1016/S0020-7225(99)00054-3
54. M. A. Murad C. Moyne 2002 Micromechanical computational modeling of expansive porous media C. R. Mecanique 330 865-870
55. J. S. Newman 1973 Electrochemical Systems Prentice-Hall Englewood Cliffs, N.J.
56. J. A. Ochoa-Tapia P. J. Antoniodel Rio S. Whitaker 1993 Bulk and surface diffusion in porous media: An application of the surface-averaging theorem Chem. Engng. Sci. 48 2061-2082
57. Olphen Van 1977 An Introduction to Clay Colloid Chemistry: For Clay Technologists, Geologists, and Soil Scientists Wiley New York
58. J. Philip 1969 Hydrostatics and hydrodynamics in swelling soils Water Resour. Res. 143 1070-1077
59. I. Prigogine 1967 Thermodynamics of Irreversible Processes Wiley New York
60. A. S. Rathore C. S. Horvath 1997 Capillary electrochromatography: theories on electroosmotic flow in porous media J. Chromatogr. A 781 185-195 10.1016/S0021-9673(97)00627-4
61. L. Ren D. Li M. Qu 2001 Electro-Viscous effects on liquid flow in microchannels J. Colloid Interface Sci. 233 12-22 10.1006/jcis.2000.7262
62. A. Revil 1999 Ionic diffusivity, electrical conductivity, membrane and thermoelectric potentials in colloids and granular porous media: A Unified model J. Colloid Interface Sci. 212 503-522 10.1006/ jcis.1998.6077
63. F. J. Rubio-Hernndez E. Ruiz-Reina A. I. Gomez-Merino 1998 The influence of a dynamic stern layer on the primary electroviscous effect J. Colloid Interface Sci. 206 334-337
64. E. Samson J. Marchand J. Robert J. Bournauel 1999 Modeling ion diffusion mechanisms in porous media Int. J. Numer. Methods Eng. 46 2043-2060 10.1002/(SICI)1097-0207(19991230)46:12<2043::AID-NME795>3.0.CO;2-7
65. E. Samson J. Marchand 1999 Numerical solution of the extended Nernst-Planck model J. Colloid Interface Sci. 215 1-8 10.1006/ jcis.1999.6145
66. E. Sanchez-Palencia 1980 Non-Homogeneous Media and Vibration Theory Springer New York Lectures Notes in Phys.
67. V. Sasidhar E. Ruckenstein 1981 Electrolyte osmosis through capillaries J. Colloid Interface Sci. 82 2 439-457
68. V. Sasidhar E. Ruckenstein 1982 Anomalous effects during electrolyte osmosis across charged porous membranes J. Colloid Interface Sci. 85 2 332-361 10.1016/0021-9797(82)90003-0
69. J. Q. Shang 1997 Zeta potential and electroosmotic permeability of clay soils Canadian Geotech. J. 34 627-631
70. J. D. Sherwood 1980 The primary electroviscous effect in a suspension of spheres J. Fluid Mech. 101 3 609-629
71. J. D. Sherwood 1992 Ionic motion in a compacting filtercake Proc. Roy. Soc. Lond. A 437 607-627
72. J. D. Sherwood 1994 A model for the flow of water and ions into swelling shale Langmuir 10 2480-2486 10.1021/la00019a075
73. J. D. Sherwood F. J. Rubio-Hernandez E. Ruiz-Reina 2000 The primary electroviscous effect: Thin double layers and a stern layer J. Colloid Interface Sci. 228 7-13 10.1006/jcis.2000.6935
74. Slattery, J.C. (1999). Advanced Transport Phenomena, In: Cambridge Ser. Chemical Engineering, Cambridge University Press, New York.
75. D. E. Smiles M. J. Rosenthal 1968 The movement of water in swelling materials Aust. J. Soil. Res. 6 237-248 10.1071/SR9680237
76. A. Sridharan G. V. Rao 1973 Mechanisms controlling volume change of saturated clays and the role of the effective stress concept Geotechnique 23 3 359-382
77. A. Szymczyk B. Aoubiza P. Fievet J. Pagetti 1999 Electrokinetic phenomena in homogeneous cylindrical pores J. Colloid Interface Sci. 216 285-296 10.1006/jcis.1999.6321
78. K. Terada T. Ito N. Kikuchi 1998 Characterization of the mechanical behaviors of solid-fluid mixture by the homogenization method Comput. Meth. Appl. Mech. Engng. 153 223-257 10.1016/S0045-7825(97)00071-6
79. C. Yang D. Li 1998 Analysis of electrokinetic effects on the liquid flow in rectangular microchannels Colloids Surfaces A: Physicochem. Eng. Aspects 143 339-353
80. A. T. Yeung J. K. Mitchell 1993 Coupled fluid, electrical and chemical flows in soil Geotechnique 43 1 121-134
81. Whitaker, S. (1999) The method of volume averaging, In: Theory and Applications of Transport in Porous Media, Kluwer Academic Publishers.