Abstract
Monte Carlo simulations of point-like molecules in random and structured media are used to determine and characterize the effective diffusion coefficients of the molecules in the media. Simulations were carried out in 2D and 3D media. Monte Carlo simulation results in 2D and 3D media are compared with those obtained by analytical techniques. Simulation results indicate that for the structured, isotropic media the effective diffusivities can be characterized according to percolation thresholds in addition to porosity. The effective diffusivities in two isotropic media with the same porosity but different percolation thresholds can differ significantly. The effects of dimensionality on the effective diffusivities can also be significant. It is shown that in general the effective diffusion coefficients obtained from 2D simulation are not a good approximation to those of 3D, especially when the percolation thresholds of the 2D media and the 3D media are very different.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abbasi, M. H., Evans, J. W. and Abramson, I. S.: 1983, Diffusion of gases in porous solids: Monte Carlo Simulations in the Knudsen and Ordinary Regimes, AIChE J. 29, 617-624.
Anderson, T. B. and Jackson, R.: 1967, A fluid mechanical description of fluidized beds, Ind. Engng Chem. Fundam. 6, 527-533.
Baumgärtner, A. and Muthukumar, M.: 1987, A trapped polymer chain in random porous media, J. Chem. Phys. 87, 3082-3088.
Binder, K. and Heermann, D. W.: 1992, Monte Carlo Simulation in Statistical Physics, 2nd edn, Springer-Verlag.
Bird, R. B., Stewart, W. E. and Lightfoot, E. N.: 1960, Transport Phenomena, Wiley, p. 593.
Brenner, H. 1980, Dispersion resulting from flow through spatially periodic porous media, Phil. Trans. R. Soc. London A 297, 81-133.
Burganos, V. N. and Sotirchos, S. V.: 1988, Simulation of Knudsen diffusion in random networks of parallel pores, Chem. Engng Sci. 43, 1685-1694.
Burganos, V. N. and Sotirchos, S. V.: 1989, Of Knudsen diffusion in parallel, multidimensional or randomly oriented capillary structures, Chem. Engng Sci. 44, 2451-2462.
Currie, J. A. 1960: Gaseous diffusion in porous media. Part I - A non-steady state method, Brit. J. Appl. Phys. 11, 314-324.
Chang, H.-C.: 1982, Multiscale analysis of effective transport in periodic heterogeneous media, Chem. Engng Comm. 15, 83-91.
Edwards, D. A., Shapiro, M., Brenner, H. and Shapira, M.: 1991, Dispersion of inert solutes in periodic, two-dimensional model porous media, Transport in Porous Media 6, 337-358.
Einstein, A.: 1926, Investigations on the theory of Brownian movement, Dover, New York.
Evans, J. W., Abbasi, M.H. and Sarin, A.: 1980, A Monte Carlo simulation of the diffusion of gases in porous solid, J. Chem. Phys. 75, 2967.
Faley, T. L. and Strieder, W., 1987, Knudsen flow through a random bed of unidirectional fibers, J. Appl. Phys. 62, 4394-4396.
Faley, T. L. and Strieder, W.: 1988, The effect of random fiber orientation of Knudsen permeabilities J. Chem. Phys. 89, 6936-6940.
Hoogschagen, J.: 1955, Diffusion in porous catalysts and adsorbents, Ind. Engng Chem. 47, 906-913.
Kim, I. C., Torquato, S.: 1990, Determination of the effective conductivity of heterogeneous media by Brownian motion simulation, J. Appl. Phys. 68, 3892-3903.
Kim, J. H., Ochoa, J. A. and Whitaker, S.: 1987, Diffusion in anisotropic media, Transport in Porous Media 2, 327-356.
Maxwell, J. C.: 1881, A Treatise on Electricity and Magnetism I, 2nd edn, Claredon Press, Oxford, p. 440.
Monnier, A., Schuth, F., Huo, Q., Kumar, D., Margolese, D., Maxwell, R. S., Stucky, G. D., Krishnamurty, M., Petroff, P., Firouzi, A., Janicke, M. and Chmelka, B. F.: 1993, Cooperative formation of inorganic-organic interfaces in the synthesis of silicate mesostructures, Science 261, 1299-1303.
Muthukumar, M. and Baumgärtner, A.: 1989a, Effects of entropic barriers on polymer dynamics, Macromolecules 22, 1937-1941.
Muthukumar, M. and Baumgärtner, A.: 1989b, Diffusion of a polymer chain in random media, Macromolecules 22, 1941-1946.
Pandey, R. B., Stauffer, D., Margilina, A. and Zabolitzky, J. G.: 1984, Diffusion in three-dimensional random systems above, below and at their percolation threshold in two and three dimensions. J. Stat. Phys. 34, 427-450.
Quintard, M.: 1993, Diffusion in isotropic and anisotropic porous systems: three-dimensional calculations, Transport in Porous Media 11, 187-199.
Rayleigh, Lord: 1892, On the influence of obstacles arranged in rectangular order upon the properties of a medium, Phil. Mag. 34, 481-503.
Riley, R. M., Muzzio, F. J., Buettner, H. and Reyes, S. C.: 1995, Diffusion in heterogeneous media: application to immobilized cell systems, AIChE J. 41, 691-700.
R. L. Rill, Locke, B. R., Liu, Y., Dharia, J. and Van Winkle, D.: 1996, Protein electrophoresis in polyacrylamide gels with templated pores, Electrophoresis 17, 1304-1312.
R. L. Rill, Van Winkle, D. and Locke, B. R.: 1998, Templated pores in hydrogels for improved size selectivity in gel permeation chromatography, Anal. Chem. 70(13), 2433-2438.
Roman, H. E.: 1990, Diffusion in three-dimensional random system at their percolation threshold, J. Stat. Phys. 58, 375-382.
Rothman, D. H.: 1988, Cellular automata fluids: a model for flow in porous media, GeoPhysics 53, 509-518.
Ryan, D., Carbonell, R. G. and Whitaker, S.: 1981, A theory of diffusion and reaction in porous media, AIChE Symposium Series, 46-62.
Saez, A. E., Perfetti, J. C. and Rusinek, I.: 1991, Prediction of effective diffusivities in porous media using spatially periodic models, Transport in Porous Media 6, 143-157.
Sahimi, M. and Stauffer, D.: 1991, Efficient simulation of flow and transport in porous media, Chem. Engng Sci. 9, 2225-2233.
Sahimi, M.: 1992, Transport of molecules in porous media, J. Chem. Phys. 96, 4718-4728.
Sandry, T. D. and Stevenson, F. D.: 1970, Molecular conductance from a curved surface through a cylindrical hole by Monte Carlo methods, J. Chem. Phys. 53, 151.
Slattery, J. C.: 1969, Single-phase flow through porous media, AIChE J. 15, 866-872.
Sternberg, S. P. K., Cushman, J. H. and Greenkorn, R. A.: 1996, Random walks in prefractal porous media, AIChE J. 42, 921-926.
Stauffer, D.: 1992, Introduction to Percolation Theory, 2nd edn, Taylor & Francis, London.
Tomadakis, M. M. and Sotirchos, S. V.: 1991a, Effective Knudsen diffusivities in structures of randomly overlapping fibers, AIChE J. 37, 74-86.
Tomadakis, M. M. and Sotirchos, S. V.: 1991b, Knudsen diffusivities and properties of structures of unidirectional fibers, AIChE J. 37, 1175-1186.
Tomadakis, M. M. and Sotirchos, S. V.: 1993, Ordinary, transition, and Knudsen regime diffusion in random capillary structures, Chem. Engng Sci. 48, 3323-3333.
Transvalidou, F. and Sotirchos, S. V.: 1996, Effective diffusion coefficients in square arrays of filament bundles, AIChE J. 42, 2426-2438.
Weissberg, H. L.: 1963, Effective diffusion coefficients in porous media, J. Appl. Phys. 34, 297-303.
Whitaker, S.: 1967, Diffusion and dispersion in porous media, AIChE J., 420-427.
Whitaker, S.: 1969, Advances in theory of fluid motion in porous media, I.E.C. Res. 61, 14-28.
Yi, Xiaohua, Shing, K. S. and Sahimi, M.: 1996, Molecular Simulation of adsorption and diffusion in pillared clays, Chem. Engng Sci. 51, 3409-3426.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Trinh, S., Arce, P. & Locke, B.R. Effective Diffusivities of Point-Like Molecules in Isotropic Porous Media by Monte Carlo Simulation. Transport in Porous Media 38, 241–259 (2000). https://doi.org/10.1023/A:1006616009669
Issue Date:
DOI: https://doi.org/10.1023/A:1006616009669