Transient and asymptotic dispersion in confined sphere packings with cylindrical and non-cylindrical conduit geometries

Siarhei Khirevich, Alexandra Höltzel, Ulrich Tallarek*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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 100πdp 2 (where dp is the sphere diameter) and dimensions of about 20dp (cylinder diameter) by 6553.6dp (length), 25dp by 12.5dp (rectangle sides) by 8192dp or 14.1dp (radius of semicircle) by 8192dp, 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 × 106 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 languageEnglish (US)
Pages (from-to)2485-2493
Number of pages9
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1945
StatePublished - Jun 28 2011


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

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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