Validation of Pore-Scale Simulations of Hydrodynamic Dispersion in Random Sphere Packings
Siarhei Khirevich 1, Alexandra Holtzel 1, Ulrich Tallarek 1*1 Department of Chemistry, Philipps-Universitat Marburg, Hans-Meerwein-Strasse, 35032 Marburg, Germany.
Received 31 October 2011; Accepted (in revised version) 26 January 2012
Available online 29 August 2012
We employ the lattice Boltzmann method and random walk particle tracking to simulate the time evolution of hydrodynamic dispersion in bulk, random, monodisperse, hard-sphere packings with bed porosities (interparticle void volume fractions) between the random-close and the random-loose packing limit. Using Jodrey-Tory and Monte Carlo-based algorithms and a systematic variation of the packing protocols we generate a portfolio of packings, whose microstructures differ in their degree of heterogeneity (DoH). Because the DoH quantifies the heterogeneity of the void space distribution in a packing, the asymptotic longitudinal dispersion coefficient calculated for the packings increases with the packings' DoH. We investigate the influence of packing length (up to 150 d_p, where d_p is the sphere diameter) and grid resolution (up to 90 nodes per d_p) on the simulated hydrodynamic dispersion coefficient, and demonstrate that the chosen packing dimensions of 10 d_p X 10 d_p X 70 d_p and the employed grid resolution of 60 nodes per d_p are sufficient to observe asymptotic behavior of the dispersion coefficient and to minimize finite size effects. Asymptotic values of the dispersion coefficients calculated for the generated packings are compared with simulated as well as experimental data from the literature and yield good to excellent agreement.
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PACS: 47.56.+r, 81.05.Rm, 05.40.-a, 61.43.Bn, 02.60.Cb
Key words: Packing microstructure, degree of heterogeneity, packing algorithm, hydrodynamic dispersion, random sphere packings.
Email: firstname.lastname@example.org (S. Khirevich), email@example.com (A. Holtzel), firstname.lastname@example.org (U. Tallarek)