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This chapter covers general models for simulating complex fluid flow, including lattice Boltzmann algorithms and applications. "Complex" means having more than one fluid present in a porous media, and having a variety of boundary conditions between the fluids and between the fluids and the solid backbone.

This section discusses modelling of electrical conductivity and fluid flow in two dimensions. The relationship between the electrical conductivity, fluid permeability, and various length scales, including lambda, the Katz-Thompson parameter, and the hydraulic radius, is studied.

(1) Length scales relating the fluid permeability and electrical conductivity in random two-dimensional porous media. (15 pages of text, 991K of figures)

This section presents a study of the polarizability (intrinsic conductivity) and the intrinsic viscosity for a very wide range of shapes. It is found that for a very wide range of shapes, the intrinsic conductivity, in the conducting limit, is proportional to the intrinsic viscosity in the vanishing shear limit.

(2) Intrinsic viscosity and polarizability of particles having a wide range of shapes (57 pages of text, 46K of figures)

(3) Large scale simulations of single and multi-component flow in porous media (14 pages of text, 112K of figures)

This section presents computations of the diffusivity through partially saturated porous media. These partially saturated media were formed using the Lattice Boltzmann fluid flow algorithm.

(4) Diffusion in partially-saturated porous materials (12 pages of text, 425K of figures)

This section presents a derivation of how to build in energy conservation into the discrete Boltzmann equation in non-ideal systems.

(5) Energy conserving discrete Boltzmann equation for non-ideal systems (14 pages of text, 60K of figures)

This section presents how basic equilibrium properties of lattice Boltzmann fluid mixtures are calculated to characterize the critical phenomena occurring in these model liquids and to establish a reduced variable description allowing a comparison with real fluid mixtures.

(6a) Critical properties and phase separation in lattice Boltzmann fluid mixtures (18 pages of text, 726K of figures)

(6b) Breakup of a fluid thread in a confined geometry: droplet-plug transition, perturbation sensitivity, and kinetic stabilization with confinement (18 pages of text, 325K of figures)Results from large scale simulations of single and multi-component fluid flow through digitized Fontainebleau sandstone, generated by X-Ray microtomography, are given. Reasonably good agreement was found when compared to experimentally determined values of permeability for similar rocks. Modification of the lattice Boltzmann equations, to describe flow in microporous materials, is described. The potential for modeling flows in other microstructures of interest to concrete technology will be discussed.

(7a) Multiscale modeling of fluid transport in heterogeneous materials using discrete Boltzmann methods (9 pages of text, 183.5K of figures)

We show that accurate numerical micropermeametry can be performed on three-
dimensional (3D) digitized images of sedimentary rock. The sample size can be
very small, making it possible to predict properties from core material not
suited for laboratory testing (e.g., drill cuttings, sidewall core and
damaged core plugs). Simulation of fluid permeability on microtomographic images of
Fontainbleau sandstone on sample sizes of less than 1 mm^{3} are in
good agreement with experimental measurements over a wide range of porosities.

We investigate the stability of a polymer thread imbedded in a matrix that is
confined between two parallel plates. Utilizing a combination of experiments,
numerical simulations (lattice-Boltzmann), and surface area calculations, we
find substantial deviations from the classical results when the diameter of the
thread (*D*_{0} is comparable to the height (*H*) of the
matrix.

(8) Suppression of Capillary Instability of a Polymeric Thread via Parallel Plate Confinement (9 pages of text, 572K of figures)

A thermodynamic model is developed of the free energy of gas-filled voids formed within cavities on solid surfaces covered by a liquid. Capillary effects are assumed to be the only important contributions to the free energy, and expressions are derived for the free energy of the system as a function of the void size, the relative surface free energy densities involved, and the geometry of the cavity.

(9) Stability of voids formed in cavities at liquid-solid interfaces (9 pages of text, 96.1K of figures)Go back to Part III Chapter 5: Conductivity

References

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(2) J.F. Douglas and E.J. Garboczi, Advances in Chemical Physics **91**, 85-153 (1995).

(3) N.S. Martys, J.G. Hagedorn, D. Goujon, and J.E. Devaney, SPIE (1999).

(4) N.S. Martys, Materials and Structures **32**, 555-562 (1999).

(5) N.S. Martys, Int. J. Mod. Phys. **10**, 1367-1382 (1999).

(6a) N.S. Martys, J.F. Douglas, Physical Review E, **63** (2001).

(6b) J.G. Hagedorn, N.S. Martys and J.F. Douglas, Physical Review E, **69**
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(7a) N.S. Martys and J.G. Hagedorn, Materials and Structures **35**,
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(7b) C.H. Arns, M.A. Knackstedt, V.W. Pinczewski and N.S. Martys, Journal of
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