## Abstract

We study the time and length scales of hydrodynamic dispersion in confined monodisperse sphere packings as a function of the conduit geometry. By a modified Jodrey-Tory algorithm, we generated packings at a bed porosity (interstitial void fraction) of ε = 0.40 in conduits with circular, rectangular, or semicircular cross section of area 100πd_{p} ^{2} (where d_{p} is the sphere diameter) and dimensions of about 20d_{p} (cylinder diameter) by 6553.6d_{p} (length), 25d_{p} by 12.5d_{p} (rectangle sides) by 8192d_{p} or 14.1d_{p} (radius of semicircle) by 8192d_{p}, respectively. The fluid-flow velocity field in the generated packings was calculated by the lattice Boltzmann method for Péclet numbers of up to 500, and convective-diffusive mass transport of 4 × 10^{6} inert tracers was modelled with a random-walk particle-tracking technique. We present lateral porosity and velocity distributions for all packings and monitor the time evolution of longitudinal dispersion up to the asymptotic (long-time) limit. The characteristic length scales for asymptotic behaviour are explained from the symmetry of each conduit's velocity field. Finally, we quantify the influence of the confinement and of a specific conduit geometry on the velocity dependence of the asymptotic dispersion coefficients.

Original language | English (US) |
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Pages (from-to) | 2485-2493 |

Number of pages | 9 |

Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 369 |

Issue number | 1945 |

DOIs | |

State | Published - Jun 28 2011 |

Externally published | Yes |

## Keywords

- Confined sphere packings
- Hydrodynamic dispersion
- Non-cylindrical packed beds
- Transcolumn velocity bias
- Wall effects

## ASJC Scopus subject areas

- General Mathematics
- General Engineering
- General Physics and Astronomy