From random sphere packings to regular pillar arrays: Analysis of transverse dispersion

Anton Daneyko, Dzmitry Hlushkou, Siarhei Khirevich, Ulrich Tallarek*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

80 Scopus citations


We study the impact of microscopic order on transverse dispersion in the interstitial void space of bulk (unconfined) chromatographic beds by numerical simulations of incompressible fluid flow and mass transport of a passive tracer. Our study includes polydisperse random sphere packings (computer-generated with particle size distributions of modern core-shell and sub-2. μm particles), the macropore space morphology of a physically reconstructed silica monolith, and computer-generated regular pillar arrays. These bed morphologies are analyzed by their velocity probability density distributions, transient dispersion behavior, and the dependence of asymptotic transverse dispersion coefficients on the mobile phase velocity. In our work, the spherical particles, the monolith skeleton, and the cylindrical pillars are all treated as impermeable solid phase (nonporous) and the tracer is unretained, to focus on the impact of microscopic order on flow and (particularly transverse) hydrodynamic dispersion in the interstitial void space. The microscopic order of the pillar arrays causes their velocity probability density distributions to start and end abruptly, their transient dispersion coefficients to oscillate, and the asymptotic transverse dispersion coefficients to plateau out of initial power law behavior. The microscopically disordered beds, by contrast, follow power law behavior over the whole investigated velocity range, for which we present refined equations (i.e., Eq. (13) and the data in Table 2 for the polydisperse sphere packings; Eq. (17) for the silica monolith). The bulk bed morphologies and their intrinsic differences addressed in this work determine how efficient a bed can relax the transverse concentration gradients caused by wall effects, which exist in all confined separation media used in chromatographic practice. Whereas the effect of diffusion on transverse dispersion decreases and ultimately disappears at increasing velocity with the microscopically disordered chromatographic beds, it dominates in the pillar arrays. The pillar arrays therefore become the least forgiving bed morphology with macroscopic heterogeneities and the engendered longitudinal dispersion in chromatographic practice. Wall effects in pillar arrays and the monolith caused by their confinement impact band broadening, which is traditionally observed on a macroscopic scale, more seriously than in the packings.

Original languageEnglish (US)
Pages (from-to)98-115
Number of pages18
JournalJournal of Chromatography A
StatePublished - Sep 28 2012


  • Microscopic order
  • Packed beds
  • Pillar arrays
  • Silica monoliths
  • Transverse dispersion
  • Wall effects

ASJC Scopus subject areas

  • Analytical Chemistry
  • Biochemistry
  • Organic Chemistry


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