Using an accurate Lattice-Boltzmann scheme, the permeability and the hydrodynamic dispersivity tensor in two-dimensional flow around large random arrays of polygonal disks has been computed for porosities in the range 38% to 90%, Peclet numbers up to 100, and Reynolds number up to 16. In order to obtain statistically significant ensembles, a sufficiently large number of realizations are generated by repacking the domain and recomputing the interstitial fields for each dimensionless number. The effective dispersion coefficient is extracted by imposing a macroscopic uniform gradient of concentration parallel and normal to the applied pressure gradient. Random arrays results are compared with dispersion results for an inline, periodic array of polygonal cylinders for Peclet number up to 1000. These findings illuminate the role of inertia and disorder on permeability and dispersivity. The transition from the linear (Darcy) regime to the inertial (cubic and quadratic in velocity) regime is quantified. The high speed inclined jets of fluid which are formed in closely packed geometries by the impingement of streamwise jets on constricted regions give rise to much greater transverse dispersion than observed for higher porosity or ordered media. For longitudinal dispersion, disorder is shown to lead to a near linear increase in dispersivity with Peclet number in accordance with experimental findings. Comparison with (MRI) experimental data for interstitial flow and longitudinal and transverse dispersivity show good agreement suggesting that the physics of hydrodynamics dispersion in three-dimensional disordered media is recovered in the two-dimensional analogue considered here.
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