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This chapter covers models, in 2-D and 3-D, for simulating the development of microstructure and for probing the developing microstructure. These models include computing the curvature of digital surfaces, simulating sintering, and simulating mercury porosimetry.

This section discusses how to compute curvatures in 3D, and then applies the curvature algorithm to simulating sintering in 2D. The model is surface-attachment-limited in its kinetics, and used a square template method of measuring local curvature.

(1)
Cellular automaton algorithm for surface mass transport
due to curvature gradients: simulations of sintering.
(15 pages of text, 95K of figures)

This section discusses application of the digital-image based sintering model to three dimensions. It is surface-attachment-limited in its kinetics, and used a spherical template method of measuring local curvature.

(2)
Cellular automaton simulations of surface mass transport due to curvature
gradients: Simulations of sintering in 3-D.
(7 pages of text, 32K of figures)

This section examines the theoretical underpinnings of the template method of curvature computation, in 2D and 3D, for an arbitrary surface.

(3) Numerical methods for computing interfacial mean curvature (19 pages of text, 76K of figures)

This section discusses modelling of mercury injection in two dimensions. There is a description of the basic algorithm, and several applications.

(4) Digitized simulation of mercury intrusion porosimetry applications. (8 pages of text, 36K of figures)

This section discusses the validity of the Katz-Thompson approach for modelling the permeability of porous materials using parameters measured using mercury injection.

(5) Mercury porosimetry and effective networks for permeability calculations in porous materials. (9 pages of text, 6K of figures)

This section discusses obtaining three-dimensional brick microstructures from x-ray tomography, and then computing various transport properties to compare with experimental measurements, to see how well the tomographic image compares with real microstructure.

(6) Microstructure and transport properties of porous building materials II: Three-dimensional X-ray tomographic studies. (12 pages of text, 582K of figures)

This section discusses reconstruction techniques, wherein a 2-D slice of a material is used to generate a 3-D approximate image of the material. The limitations of this technique is explored used a 3-D model, whose microstructure is exactly known. The 3-D reconstructured microstructure is then compared to the known 3-D microstructure both visually, and using percolation and transport properties.

(7) Hydraulic radius and transport in reconstructed model three-dimensional porous media. (7 pages of text, 162K of figures)

Go to Part III Chapter 5. Conductivity

Go back to Part III Chapter 3. Percolation theory

References

(1) P.J.P. Pimienta, W.C. Carter, and E.J. Garboczi, Computational Materials Science **1**, 63-77 (1992).

(2) D.P. Bentz, P.J.P. Pimienta, E.J. Garboczi, and W.C. Carter, in *Synthesis and Processing of Ceramics: Scientific Issues*, edited by W.E. Rhine, T.M. Shaw, R.J. Gottschall, and Y. Chen (Materials Research Society Vol. 249, Pittsburgh, 1992), pp. 413-418.

(3) J.W. Bullard, E.J. Garboczi, W.C. Carter, and E.R. Fuller, Computational Materials Science **4**, 103-116 (1995).

(4) E.J. Garboczi and D.P. Bentz, in *Advances in Cementitious Materials*, edited by S. Mindess, Ceramics Transactions **16**, 365-380 (1991).

(5) E.J. Garboczi, Powder Technology **67**, 121 (1991).

(6) D.P. Bentz, D.A. Quenard, H.M. Kunzel, J. Baruchel, F. Peyrin,
N.S. Martys, and E.J. Garboczi, Materials and Structures, **33 **, 147-153 (2000).

(7) D.P. Bentz and
N.S. Martys, Transport in Porous Media **17**, 221-238 (1995).