Dispersion of a passive tracer in the pressure-driven flow of a non-colloidal suspension

Abstract

This paper numerically quantifies the dispersion of a solute, and in particular, the Taylor dispersion, in the pressure-driven flow of a non-colloidal suspension at moderately high volume fractions (0.2 to 0.5) through conduits of different cross-sectional shapes. An obvious intuition is that the Taylor dispersivity should increase owing to a decrease in the molecular diffusivity of the solute in the presence of particles impermeable to the solute; however, this is true only at low volume fractions. At higher volume fractions, three other physical effects become important, all of which lead to a reduction in Taylor dispersivity relative to a Newtonian fluid. The first is the blunting of the velocity profile resulting from particle migration into the low shear-stress regions, an effect that has been alluded to in the past by Roht et al. [J. Contam. Hydrol., 2013, 14, 10] and is important only at low Péclet numbers (Pe). At higher Pe, the two stronger effects are shear-induced solute self-diffusion, which arises due to shear-induced particle–particle interactions, and secondary convection, which is observed in non-axisymmetric cross-sections as a result of the second normal stress differences exhibited by concentrated suspensions. For a given volume fraction and cross-sectional geometry, a regime map, developed using a scaling analysis, delineates five regimes of dispersion involving one or a combination of the mass transfer mechanisms mentioned above. Our analysis also suggests that the cross-sectional shape can be exploited to enhance or suppress solute dispersion by modifying the secondary current strength and profile.