Up: Main Previous: Acknowledgements
References
- 1
- P. Hirsch, J.D. Birchall, D.D. Double, A. Kelly, G.K. Moir,
and C.D. Pomeroy, Technology in the 1990's: Developments in the science
and technology of hydraulic cements, Phil. Trans. Roy. Soc. Lond. 310,
1-207 (1983).
- 2
- R.L. Coble and W.D. Kingery, Effect of porosity on physical
properties of sintered alumina, J. Amer. Ceram. Soc. 39, 377-385 (1956).
- 3
- J. Rodel and A.M. Glaeser, Production of controlled-morphology
pore arrays: Implications and opportunities, J. Amer. Ceram. Soc. 70,
C172-C175 (1987).
- 4
- R.L. Johnson, J.A. Cherry, and J.F. Pankow, Diffusive contaminant
transport in natural clay: A field example and implications for clay-lined
waste disposal sites, Environ. Sci. Technol. 23, 340-349 (1989).
- 5
- R.L. Smith and S.D. Collins, Porous silicon formation mechanisms,
J. Appl. Phys. 71, R1-R2 (1992).
- 6
- F.A.L.Dullien, Porous Media: Fluid Transport and
Pore Structure
2nd Edition(Academic Press, San Diego, 1992).
- 7
- M. Sahimi, Transport, reaction, and fragmentation in evolving
porous media, Phys. Rev. A 43, 5367-5376 (1991).
- 8
- M. Sahimi, Flow and Transport in Porous Media
and Fractured Rock (VCH, New York, 1996).
- 9
-
(a) M.A. Biot, Mechanics of deformation and acoustic propagation
in porous media, J. Appl. Phys. 33, 1482-1498 (1962);
(b) M.A. Biot, Generalized theory of acoustic propagation in porous
dissipative media, J. Acoust. Soc. Am. 34, 1254-1264 (1962).
-
10
-
E.J. Garboczi,
Mercury porosimetry and effective networks for
transport calculations in porous media, Powder Tech. 67, 121-130 (1991).
- 11
- B.E. Hornby, L.M. Schwartz, and J.A. Hudson, Anisotropic
effective-medium modeling of the elastic properties of shales, Geophysics
59, 1570-1583 (1994).
- 12
-
K.A. Snyder, E.J. Garboczi, and A.R. Day, The elastic
moduli of random two-phase composites: Computer simulation and effective
medium theory, J. Appl. Phys. 72, 5948-5955 (1992).
- 13
- C. Kittel, Introduction to Solid State Physics 5th Edition
(John Wiley and Sons, New York, 1979).
- 14
-
E.J. Garboczi, M.F. Thorpe, M.S. DeVries, and A.R. Day,
Universal conductivity curve for a plane containing random holes, Phys.
Rev. A 43, 6473-6482 (1991).
- 15
-
N.Martys and E.J. Garboczi,
Length scales relating the fluid
permeability and electrical conductivity in random two-dimensional model
porous media, Phys. Rev. B 46, 6080-6090 (1992).
- 16
- J. Berryman, E. Garboczi, and N. Martys, unpublished.
- 17
- B. Lu and S. Torquato, Local volume fraction fluctuations in
heterogeneous media, J. Chem. Phys. 93, 3452-3459 (1990).
- 18
- K.R. Castleman, Digital Image Processing (Prentice-
Hall, Englewood Cliffs, 1981).
- 19
- E.E. Underwood, Quantitative Stereology (Addison
-Wesley, Reading, Massachusetts, 1970).
- 20
- R.T. DeHoff and F.N. Rhines, Quantitative Microscopy
(McGraw-Hill, New York, 1968).
- 21
- John C. Russ, The Image Processing Handbook (CRC Press,
Cleveland, 1994).
- 22
- V. Cantoni, S. Levialdi, and G. Musso, eds. Image
Analysis and Processing (Plenum Press, New York, 1986).
- 23
- J. Serra, Image Analysis and Mathematical Morphology
(Academic Press, London, 1982);
J. Serra, Image Analysis and Mathematical Morphology
Volume II: Theoretical Advances(Academic Press, London, 1988).
- 24
- B.B. Mandelbrot, The Fractal Geometry of
Nature (W.H. Freeman and Company, New York, 1983).
- 25
- P. Wong, The statistical physics of sedimentary rock, Phys.
Today 41, 24-25 (1988).
- 26
- P. Wong, Scattering by inhomogeneous systems with rough
internal surfaces: Porous solids and random-field Ising systems,
Phys. Rev. B 32, 7417-7424 (1985).
- 27
- P. Wong and A.J. Bray, Small-angle scattering by rough and
fractal surfaces, J. Appl. Cryst. 21, 786-794 (1988).
- 28
- P. Wong and Q. Cao, Correlation function and structure factor
for a mass fractal bounded by a surface fractal, Phys. Rev. B 45,
7627-7632 (1992).
- 29
- H.E. Stanley and N. Ostrowsky, eds., Random Fluctuations
and Pattern Growth (Kluwer Academic Publilshers, Dordrecht, 1988).
- 30
- T. Vicsek, Fractal Growth Phenomena (World Scientific,
Singapore, 1989).
- 31
- F. Family and T. Vicsek, eds., Dynamics of Fractal
Surfaces (World Scientific, Singapore, 1991).
- 32
- J. Feder, Fractals (Plenum, New York, 1988).
- 33
- A.H. Thompson, A.J. Katz,, and C.E. Krohn, The microgeometry and
transport properties of sedimentary rock, Adv. in Phys. 36, 625-694
(1987).
- 34
- D.W. Schaefer and K.D. Keefer, Structure of random porous materials:
Silica aerogel, Phys. Rev. Letts. 56, 2199-2202 (1986).
- 35
- D.N. Winslow, J.M. Bukowski, and J.F. Young, The fractal
arrangement of hydrated cement paste, Cement and Concrete Research 25
(1), 147-156, 1995.
- 36
- R. Lemaitre and P.M. Adler, Fractal Porous Media IV:
Three-dimensional Stokes flow through random media and regular fractals,
Transport in Porous Media 5, 325-340 (1990).
- 37
- J.K. Williams and R.A. Dawe, Fractals -- An overview
of potential
applications to transport in porous media, Transport in Porous Media 1,
201-209 (1986).
- 38
- S. Torquato and G. Stell, J. Chem. Phys. 79, 1505 (1983).
- 39
- J.G. Berryman, Measurement of spatial correlation functions
using image processing techniques, J. Appl. Phys. 57, 2374-2384 (1985).
- 40
- P. Debye, H.R. Anderson, and H. Brumberger,
J. Appl. Phys. 28,679 (1957).
- 41
- J.G. Berryman, Relationship between
specific surface area and
spatial correlation functions for anisotropic porous media, J. Math. Phys.
28, 244-245 (1987).
- 42
- J.G. Berryman and S.C. Blair, Use of digital image
analysis to estimate fluid permeability of porous materials: Application
of two-point correlation functions, J. Appl. Phys. 60, 1930-1938 (1986).
- 43
- D.A. Coker and S. Torquato, Extraction of
morphological quantities
from a digitized medium, J. Appl. Phys. 77, 6087-6099 (1995).
- 44
- D.A. Coker and S. Torquato, Simulation of diffusion
and trapping
in digitized heterogeneous media, J. Appl. Phys. 77, 955-964 (1995).
- 45
- S. Torquato, Random heterogeneous media: Microstructure and
improved bounds on effective properties, Appl. Mech. Rev. 44,
37-76 (1991).
- 46
- Z. Hashin, Analysis of composite materials: A Survey, J.
Appl. Mech. 50, 481-505 (1983).
- 47
- W.F. Brown, Solid mixture permitivitties, J. Chem. Phys.
23, 1514-1517 (1955).
- 48
- S. Torquato, Effective stiffness tensor of composite media
--I. Exact series expansions, J. Mech. Phys. Solids 45, 1421-1448 (1997).
- 49
- J.G. Berryman and G.W. Milton, Normalization constraint for
variational bounds on fluid permeability, J. Chem. Phys. 83, 754-760
(1985).
- 50
- J. Rubinstein and S. Torquato, J. Fluid Mech. 206,
25-46 (1989).
- 51
- S. Torquato, Relationship between permeability and diffusion-
controlled trapping constant of porous media, Phys. Rev. Letts. 64, 2644-
2646 (1990).
- 52
- M. Avellaneda and S. Torquato, Rigorous link between fluid
permeability, electrical conductivity, and relaxation times for transport
in porous media, Phys. Fluids A 3, 2529-2540 (1991).
- 53
- D. Stauffer, Percolation Theory (Taylor and Francis,
London, 1985).
- 54
-
D.P. Bentz and E.J. Garboczi,
Percolation of phases in
a three-dimensional cement paste microstructural model, Cem. Conc. Res.
21, 325-344 (1991).
- 55
- R. Zallen, The Physics of Amorphous Solids (J. Wiley and
Sons, New York, 1983), Chapter 4.
- 56
- N.S. Martys, S. Torquato, and D.P. Bentz, Universal
Scaling of Fluid Permeability for Sphere Packings, Phys. Rev. E, 50
(1), 403-408, 1994 (PDF version).
- 57
-
E.J. Garboczi,
Finite element and finite difference codes
for computing the linear electrical and elastic properties of digital images
of random materials, National Institute of Standards and Technology Internal
Report 6269 (1998).
- 58
- M.J. Graf, C.A. Huber, T.E. Huber, and A.P. Salzberg,
Indium-impregnated
porous glass: Magnetotransport and superconducting transition,
in MRS Proc. Vol. 195 Physical Phenomena in Granular Materials, edited by
G.D. Cody, T.H. Geballe, and P. Sheng, pp. 397-402.
- 59
- K. Kendall, Electrical conductivity of ceramic powders and
pigments, Powder Technology 62, 1147-154 (1990).
- 60
- C.B. Millikan, On the steady motion of viscous, incompressibole fluids; with particular reference to a variation principle, Phil. Mag. S. 7.
7, 641-662 (1929).
- 61
- H. Helmholtz, Wiss. Abh. 1, 223-230 (1868); J.B. Keller,
L.A. Rubenfeld, and J.E. Molyneux, Extremum principles for slow viscous flows
with applications to suspensions, J. Fluid Mech. 30, 97-125 (1967).
- 62
-
E.J. Garboczi and D.P. Bentz,
Computer simulation of the
diffusivity of cement-based materials, J. Mater. Sci. 27, 2083-2092
(1992).
- 63
- M.A. Ioannidis, M.J. Dwiecien, and I. Chatzis,
Electrical conductivity and percolation aspects of statistically
homogeneous porous media, Transport in Porous Media 29, 61-83 (1997).
- 64
- A.E. Scheidegger, The Physics of Flow Through Porous
Media,(University of Toronto Press, Toronto, 1974).
- 65
- R. Peyret and T.D. Taylor, Computational Methods for
Fluid Flow (Springer-Verlag, New York, 1983).
- 66
- L.M. Schwartz, N.S. Martys, D.P. Bentz, E.J. Garboczi,
and S. Torquato, Cross property relations and permeability estimation in model
porous media, Phys. Rev. E 48, 4584-4591 (1993).
- 67
- S. Whitaker, Flow in porous media: A theoretical
derivation of Darcy's law, Trans. Porous Media 1, 3 (1986).
- 68
- D.L. Johnson, J. Koplik, and L.M. Schwartz, Phys. Rev. Letts.
57, 2564 (1986).
- 69
- A.J. Katz and A.H. Thompson, Phys. Revv. B 34, 8179 (1986);
J. Geopys. Res. 92, 599 (1987).
- 70
- L.D. Landau and E.M. Lifshitz, Theory of Elasticity, 3rd Ed.
(Pergamon Press, Oxford, 1986).
- 71
- J. Poutet, D. Manzoni, F. Hage-Chehade, C.J. Jacquin,
M.J. Bouoteca, J.-F. Thovert, and P.M. Adler, The effective mechanical
properties of reconstructed porous media, Int. J. Rock Mech. Min. Sci. and
Geomech. Abstr. 33, 409-15 (1996);
J. Poutet, D. Manzoni, F. Hage-Chehade, C.J. Jacquin,
M.J. Bouoteca, J.-F. Thovert, and P.M. Adler, The effective mechanical
properties of random porous media, J. Mech. Phys. Solids 44, 1587-1620
(1996).
- 72
-
E.J. Garboczi and A.R. Day,
An algorithm for computing the
effective linear elastic properties of heterogeneous materials: 3-D results
for composites with equal phase Poisson's ratios, J. Phys. Mech. Solids
43, 1349-1362 (1995).
- 73
- R.D. Cook, D.S. Malkus, and M.E. Plesha, Concepts and
Applications of Finite Element Analysis, 3rd Edition (J. Wiley and Sons,
New York, 1989).
- 74
- S.P. Timoshenko and J.N. Goodier, Theory of Elasticity 3rd
Ed. (McGraw-Hill Book Co., New York, 1970), 90-97.
- 75
-
D.P. Bentz, E.J. Garboczi and D.A. Quenard,
Modelling drying shrinkage
in porous materials using image reconstruction: Application to porous
Vycor glass, Model. and Sim. in Mater. Sci. and Eng. 6, 211-236, (1998).
- 76
-
E.J. Garboczi and D.P. Bentz,
Digitized simulation of
mercury intrusion porosimetry, Ceramics Trans. 16,
365-379 (1991).
- 77
- J.A. Lewis, M.A. Galler, and D.P. Bentz, Computer simulation
of binder removal from 2-D and 3-D model particulate bodies, J. Amer. Ceram.
Soc. 79, 1377-1388 (1996).
- 78
-
D.P. Bentz, D.A. Quenard, V. Baroghel-Bouny, E.J. Garboczi,
and H.M. Jennings,
Modelling drying shrinkage of cement paste and mortar:
Part I. Structural models from nanometres to millimetres, Materials and
Structures 28, 450-458 (1995).
- 79
- J.F. Thovert, J. Salles, and P.M. Adler, Computerized
characterization of the geometry of real porous media: Their discretization,
analysis, and interpretation, J. Microscopy 170, 65-79 (1993).
- 80
- D.A. Quenard, D.P. Bentz, and E.J. Garboczi, Capillary
condensation, hystersis, and image analysis, in Drying 92,
Ed. A.S. Mudjumdar, Elsevier Press, Pt. A 252-262, 1992.
- 81
- J. van Brakel, S. Modry, and M. Svata, Mercury porpsimetry:
State of the art, Powder Technology 29, 1-12 (1981). This is the first
article
in a special issue devoted to mercury poroisimetry.
- 82
- D.H. Rothman, Geophysics 53, 509 (1988);
D.H. Rothman and S. Zaleski, Lattice-gas models of phase
separation: Interfaces, phase transitions, and multiphase flow, Rev. Mod.
Phys. 66, 1417-1479 (1994).
- 83
- N.S. Martys and H. Chen, Simulation of multi-component fluids
in complex three-dimensional geometries by the lattice Boltzmann method,
Phys. Rev. E 53, 743-750 (1996)
PDF Version.
- 84
- R. Benzi, S. Succi, and M. Vergassola, The lattice Boltzmann
equation: Theory and applications, Phys. Rep. 222, 145-197 (1992).
- 85
- P.E. Stutzman, Serial Sectioning of Hardened Cement Paste for
Scanning Electron Microscopy, Ceramic Transactions 16, 237, 1991.
- 86
- B.P. Flannery, H.W. Deckman, W.G. Roberge, and K.L. D'Amico,
Three-Dimensional X-ray Microtomography, Science 237, 1439-1444 (1987).
- 87
-
D.P. Bentz, N.S. Martys, P. Stutzman, M.S. Levenson,
E.J. Garboczi, J. Dunsmuir, and L.M. Schwartz,
X-ray microtomography of an
ASTM C-109 mortar exposed to sulfate attack, in Microstructure of Cement-
Based Systems/Bonding and Interfaces in Cementitious Materials, edited by
S. Diamond et al. (Materials Research Society Vol. 370, Pittsburgh, 1995),
77-82.
- 88
- F.M. Auzerais, J. Dunsmuir, B.B. Ferreol, N. Martys,
J. Olson, T.S. Ramakrishman, D.H. Rothman, and L.M. Schwartz, Transport
in sandstone: A study based on three dimensional microtomography, Geophysical
Researach Letters 23, 705-708 (1996)
PDF Version.
- 89
- M. Joshi, A Class of Stochastic Models for Porous Media,
Ph. D. Thesis, Univ. of Kansas, 1974.
- 90
- J.A. Quiblier, A New Three-Dimensional
Modeling Technique for
Studying Porous Media, J. Colloid and Interface Science 98
84-102 (1984).
- 91
- P.M. Adler, C.G. Jacquin, and J.A. Quiblier, Flow in
Simulated Porous Media, Int. J. Multiphase Flow 16, 691-
712 (1990).
- 92
- P.M. Adler, C.G. Jacquin, and J.F. Thovert, The Formation
Factor of Reconstructed Porous Media, Water Resources Research
28, 1571-1576 (1992).
- 93
- D.P. Bentz and N.S. Martys,
Hydraulic radius
and transport in reconstructed model three-dimensional porous media,
Transport in Porous
Media 17, 221-238 (1994).
- 94
- D.A. Quenard, K. Xu, H.M.
Kunzel, D.P. Bentz, and N.S. Martys, Microstructure and transport properties
of porous building materials, Materials and Structures,
31 (209), 317-324, 1998
(PDF Version).
- 95
- D.A. Young and E.M. Corey, Lattice models of biological growth,
Phys. Rev. A 41, 7024-7032 (1990).
- 96
- M.B. Isichenko, Rev. Mod. Phys. 64, 961 (1992).
- 97
- J.W. Essam, Percolation Theory, Rep. Prog. Phys. 43, 833-
912 (1980).
- 98
- J.M. Hammersley and D.J. A. Welsh, Percolation theory and its
ramifications, Contemp. Phys. 21, 593-605 (1980).
- 99
- P. Renault, The effect of spatially correlated blocking-up
of some bonds or nodes of a network on the percolation threhold, Transport
in Porous Media 6, 451-468 (1991).
- 100
- S. Kirkpatrick, Percolation and conduction, Rev. Mod. Phys.
45, 574-588 (1973).
- 101
-
E.J. Garboczi, K.A. Snyder, J.F. Douglas, and M.F. Thorpe,
Geometrical percolation threshold of overlapping ellipsoids, Phys. Rev. E
52, 819-828 (1995).
- 102
- W. Xia and M.F. Thorpe, Phys. Rev. A 38, 2650-2655 (1988).
- 103
- I. Balberg, Recent developments in continuum percolation,
Phil. Mag. B 56, 991-1003 (1987).
- 104
- P. Salatino and L. Massimilla, Modeling fragmentation
by percolation in combustion of carbons, Powder Technology 66, 47-52
(1991).
- 105
- M. Yanuka, Prediction of the capillary hysteresis loop from
geometrical and topological information of the pore space, J. Coll. Inter.
Sci. 127, 48-58 (1989).
- 106
- L.M. Schwartz and S. Kimminau, Analysis of electrical
conduction in the grain consolidation model, Geophysics 52, 1402-1411
(1987).
- 107
- L.M. Schwartz, D.L. Johnson, and S. Feng, Phys. Rev. Letts.
52, 831-834 (1984).
- 108
- R. Lenormand, Proc. Roy. Soc. London A 423, 159
(1989).
- 109
- M. Blunt and P. King, Macroscopic parameters from simulations
of pore scale flow, Phys. Rev. A 42, 4780-4787 (1990).
- 110
- P. Wong, J. Koplik, and J.P. Tomanic, Phys. Rev. B 30,
6066 (1984).
- 111
- P.A. Crossley, L.M. Schwartz, and J.R. Banavar,
Image-based models
of porous media: Application to VycorTM glass and carbonate rocks,
Appl. Phys. Lett. 59, 3553-3555 (1991).
- 112
- R. Blumenfeld and S. Torquato, Coarse-graining procedure to
generate and analyze heterogeneous materials: Theory, Phys. Rev. E 48,
4492-4500 (1993).
- 113
- A.P. Roberts and M.A. Knackstedt, Mechanical and transport
properties of model foamed solids, J. Mater. Sci. Letts. 14, 1357-1359
(1995).
- 114
- A.P. Roberts and M. Teubner,
Transport properties of heterogeneous
materials derived from Gaussian random fields: Bounds and simulation, Phys.
Rev. E 51, 4141-4154 (1995).
- 115
- A.P. Roberts and M.A. Knackstedt, Effective properties of
composites with model
microstructures: Two level-cut Gaussian random fields and overlapping
hollow spheres, Phys. Rev. E 54, 2313 (1996).
- 116
- H.F.W. Taylor, Cement Chemistry (Academic Press, London,
1990).
- 117
- D.P. Bentz, P.V. Coveney, E.J. Garboczi, M.F. Kleyn, and
P.E. Stutzman,
Cellular
automaton simulations of cement hydration and
microstructure development, Modelling Simul. Mater. Sci. Eng. 2, 783-808
(1994).
- 118
- D.P. Bentz,
Three-dimensional computer simulation
of portland cement hydration and microstructure development, J. Amer. Ceram.
Soc. 80, 3-21 (1997).
- 119
- D.P. Bentz, E. Schlangen, and E.J. Garboczi, Computer
simulation of interfacial zone microstructure and its effect on the properties
of cement-based materials, in Materials Science of Concrete IV, edited
by J. Skalny and S. Mindess (American Ceramic Society, Westerville, Ohio, 1995).
- 120
-
D.P. Bentz, P.E. Stutzman, and E.J. Garboczi,
Experimental and
simulation studies of the interfacial zone in concrete, Cement and Concrete
Research, 22 (5), 891-902 (1992).
- 121
- W.D. Kingery, H.K. Bowen, and D.R. Uhlman, Introduction
to Ceramics, 2nd ed. (J. Wiley and Sons, New York, 1976).
- 122
-
P. Pimeinta, W.C. Carter, and E.J. Garboczi,
Cellular
automaton simulations of surface mass transport due to curvature gradients,
Comp. Mater. Sci. 1, 63-77 (1992).
- 123
-
J.W. Bullard, E.J. Garboczi, W.C. Carter, and E.R. Fuller,
Numerical methods for computing interfacial mean curvature, Comp. Mater.
Sci.
4, 103-116 (1995).
- 124
- J.C. Russ, Automatic methods for the measurement of
curvature of lines, features, and feature alignment in images, J. Computer-
Assisted Microscopy 1, 39-77 (1989).
- 125
- G. Polya and G. Szego, Isoperimetric Inequalities
in Mathematical Physics (Princeton University Press, Princeton, NJ, 1951).
- 126
- J.W. Bullard and W.C. Carter, Numerical determination of
critical strain rate for neck rupture for evaporation-condensation sintering
of isotropic particles, in Sintering Technology, edited by R.M. German,
G.L. Messing, and R.G. Cornwall (Marcel Dekker, New York, 1996), 45-52.
- 127
- J.W. Bullard, Digital-image-based models of 2D
microstructural evolution by surface diffusion and vapor transport, J. Appl.
Phys. 81, 159-168 (1997).
Up: Main Previous: Acknowledgements