Abstract
In a recent paper, Tacher and co‐workers proposed an interesting numerical technique to generate granular porous media. In this contribution, we present a similar procedure based on a sedimentation algorithm, that is able to overcome some of the difficulties present in the former technique. These are: (a) the impossibility to choose a priori a grading curve for the generated medium while retaining a realistic stacking where each grain is connected to at least three of its neighbours, and, (b) he random pattern of the grains in the porous medium, arising from their location inside the remaining void space of a box according to an arbitrary space filling criterion. We propose to generate three‐dimensional granular media by simulating the deposition of spherical grains in a viscous fluid. We argue that the resulting chaotic grain pattern, by reflecting the actual generation process of sedimentary aggregates more closely, provides a better image of the complex topology of natural granular porous media. Although the generated medium is made up of spheres, it can be transformed, by changing the geometry of the grains through suitable domain mappings. The resulting three‐dimensional porous media provide a realistic boundary for the numerical solution of linearized Navier–Stokes equations.
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References
Adler, P. M.: 1992, Porous Media, Butterworth, Heinemann, London.
Allen, J. R. L.: 1985, Principles of Physical Sedimentology, George Allen & Unwin, London.
Bachmat, Y. and Bear, J.: 1986, Macroscopic modelling of transport phenomena in porous media: 1. The continuum approach, Transport in Porous Media 1, 213–240.
Bear, J.: 1988, Dynamics of Fluids in Porous Media, Dover, New York.
Buchalter, B. J. and Bradley, R. M.: 1994, Orientational order in amorphous packings of ellipsoids, Europhys. Lett. 26, 159.
Chen, S., Diemer, K., Doolen, G. D., Eggert, K., Fu, C., Gutman, S. and Travis, B. J.: 1991, Lattice gas automata for flow through porous media, Physica D 47, 72–84.
Coelho, D., Thovert, J.-F. and Adler, P. M.: 1997, Geometrical and transport properties of random packings of spheres and aspherical particles, Phys. Rev. E 55(2), 1959–1978.
Darcy, H. P. G.: 1856, Les fontaines publiques de la ville de Dijon, Dalmont, Paris.
DallaGiovanna, S. and Vitali, M.: 1996, Studio sperimentale sulla valutazione della conduttività idraulica degli ammassi sedimentari incoerenti, Tesi di Laurea, Politecnico di Milano.
Dexter, A. R. and Tanner, D.W.: 1972, Packing densities of mixtures of spheres with lognormal size distributions, Nature 238, 31–32.
Di Pietro, L. B., Melayah, A. and Zaleski, S.: 1994, Modeling water infiltration in unsaturated porous media by interacting lattice gas cellular automata, Water Resour. Res. 30(10), 2785–2792.
Garde, R. J.: 1972, Bed material characteristics of alluvial streams, J. Sedim. Geol. 7, 2.
Ghilardi, P., Menduni, G. and Rosso, R.: 1991, On the morphogenesis of scaling porous media, Excerpta 6, 207–227.
Ghilardi, P., Kai Kai A. and Menduni, G.: 1993, Self-similar heterogeneity in granular porous media at the representative elementary volume scale, Water Resour. Res. 29(4), 1205–1214.
Gray, W. A.: 1968, The Packing of Solid Particles, Chapman & Hall, London.
Haff, P. K., Anderson, R. S.: 1993, Grain scale simulations of loose sedimentary beds: the example of grain-bed impacts in aeolian saltation, Sedimentology 40, 175–198.
Heywood, H.: 1937, Numerical definitions of particle size and shape, Chemistry and Industry, 149–154.
Jiang, Z. and Haff, P. K.: 1993, Multiparticle simulation methods applied to the micromechanics of bed load transport, Water Resour. Res. 29(2), 399–412.
Jiang, Z.: 1995, The motion of sediment-water mixtures during intense bedload transport: computer simulations, Sedimentology 42, 935–945.
Jodrey, W. S. and Tory, E. M.: 1985, Computer simulation of close random packing of equal spheres, Phys. Rev. A 32, 2347.
Jullien, R. and Botet, R.: 1987, Aggregation and Fractal Aggregates, World Scientific, Singapore.
Jullien, R. and Meakin: 1987, Simple three-dimensional models for ballistic deposition with restructuring, P. Europhys. Lett. 4, 1385.
Katz, A. J. and Thompson, A. H.: 1986, Fractal sandstones pores: implications for conductivity and pore formation, Phys. Rev. Lett. 56(19), 2112.
Kothyari, U. C.: 1995, Frequency distribution of river bed materials, Sedimentology 42, 283–291.
Maier, R. S., Kroll, D. M., Kutsovsky, Y. E., Davis, H. T. and Bernard, R. S.: 1998, Simulation of flow through bead packs using the lattice Boltzmann method, Phys. Fluids 10(1), 60–74.
Martys, N. S., Torquato, S. and Bentz, D. P.: 1994, Universal scaling of fluid permeability for sphere packings, Phys. Rev. E 50(1), 403–408.
Meagher, D. J.: 1980, Octree encoding: a new technique for the representation, manipulation, and display of arbitrary three dimensional objects by computer, Technical Report IPL-TR-80-111, Image Processing Lab., Rensselaer Polytechnic Inst., Troy, N.Y.
Onoda, G. Y. and Liniger, E. G.: 1990, Random loose packings of uniform spheres and the dilatancy onset, Phys. Rev. Lett. 64, 2727.
Pilotti, M. and Menduni, G.: 1997, Application of lattice gas techniques to the study of sediment erosion and transport caused by laminar sheetflow, Earth Surface Processes and Landforms 22, 885–893.
Quintanilla J. and Torquato, S.: 1996, Clustering properties of d-dimensional overlapping spheres, Phys. Rev. E 54, 5331.
Ridgway, K. and Tarbuck, K. J.: 1966, Radial voidage variation in randomly packed beds of spheres of different sizes, J. Pharm. Pharmacol. 18(supplement).
Rothman, D.: 1988, Cellular automaton fluids: a model for flow in porous media, Geophysics 53(4), 509–518.
Rubinstein, J. and Torquato, S.: 1989, Flow in random porous media: mathematical formulation, variational principles and rigorous bounds, J. Fluid Mech. 206, 25.
Spencer, D. W.: 1963, The interpretation of grain size distribution curves of clastic sediments, J. Sedim. Petrol. 33, 180–190.
Tacher, L., Perrochet, P. and Parriaux, A.: 1997, Generation of granular media, Transport in Porous Media 26, 99–107.
Torquato, S.: 1987, Characterization of the microstructure of disordered media: a unified approach, Phys. Rev. B 35, 5385.
Torquato, S. and Lu, B.: 1990, Rigorous bounds on the fluid permeability: effect of polydispersivity in grain size, Phys. Fluids A 2, 487.
Torquato, S.: 1992, Connection between the morphology and effective properties of heterogeneous materials, In: S. Torquato and D. Krajcinovic (eds), Macroscopic Behavior of Heterogenous Materials from the Microstructure, American Society of Mechanical Engineers, AMD-Vol. 147, p. 53.
Torquato, S.: 1994, Macroscopic behavior of random media from the microstructure, Appl. Mech. Rev. 47.
Turcotte, D. L.: 1986, Fractals and fragmentation, J. Geophys. Res. 91(B2), 1921–1926.
Turcotte, D. L.: 1992, Fractals and Chaos in Geology and Geophysics, Cambridge University Press, Cambridge.
Vischer, G. S.: 1969, Grain size distribution and depositional processes, J. Sedim. Petrol. 39, 1074–1106.
Wakeman, R. J.: 1975, Packing densities of particles with lognormal size distributions, Powder Technol. 11, 297–299.
Witten, T. A. and Sander, L. M.: 1981, Diffusion limited aggregation, a kinetic critical phenomenon, Phys. Rev. Lett. 47, 1400–1403.
Wong P. Z., Howard, J. and Lin, J. S.: 1986, Surface roughening and the fractal nature of rocks, Schlumberger-Doll (Research Preprint).
Yerry, M. A. and Shephard, M. S.: 1984, Automatic three-dimensional mesh generation by the modified octree technique, Int. J. Num. Methods Engng. 20, 1965–1990.
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Pilotti, M. Generation of Realistic Porous Media by Grains Sedimentation. Transport in Porous Media 33, 257–278 (1998). https://doi.org/10.1023/A:1006598029153
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DOI: https://doi.org/10.1023/A:1006598029153