Impact of conduit geometry and bed porosity on flow and dispersion in noncylindrical sphere packings

The three-dimensional velocity field and corresponding hydrodynamic dispersion in pressure-driven flow through fixed beds of solid (impermeable), uniformly sized, spherical particles are studied by quantitative numerical analysis for conduits with different cross-sectional geometries. Packings with average interparticle porosities (bed porosities) of 0.40 ≤ ∈ ≤ 0.50 were generated in conduits with circular, quadratic, rectangular, and semicircular cross sections utilizing a parallel collective-rearrangement algorithm. The lateral dimensions of the generated packings were chosen to represent typical values encountered in miniaturized liquid chromatography (LC) systems. The interparticle velocity field was calculated using the lattice-Boltzmann (LB) method, and a random-walk particle-tracking method was employed to model advective-diffusive transport of an inert tracer in the LB velocity field. We present the morphologies and corresponding flow patterns for these packings and demonstrate that the porosity distribution and velocity profiles of noncylindrical packings deviate significantly from those of conventional cylindrical packings. This deviation becomes more pronounced at higher bed porosities. Extended regions of high local porosity in the corners of noncylindrical conduits give rise to the formation of fluid channels of advanced flow velocity. The differences in the flow velocity distributions of cylindrical and noncylindrical packings are analyzed, and their impact on the axial hydrodynamic dispersion coefficient is shown. The presented data support the conclusion that LC performance depends critically on the conduit geometry and bed porosity. Our results have particular relevance for microchip-LC, where noncylindrical conduit geometries are prevalent.