Secondary convection due to second normal stress differences: A new mechanism for the mass transport of solutes in pressure-driven flows of concentrated, non-colloidal suspensions

Abstract

A mechanism for enhancement in the mass transfer rates of solutes in flowing, concentrated suspensions that is often cited in the literature is the self-diffusion of particles arising from shear-induced interparticle interactions. Recently, it was demonstrated by Zrehen and Ramachandran (Phys. Rev. Lett., 2013, 110, 018306) that the pressure-driven flow of suspensions through non-axisymmetric geometries is not unidirectional; the main flow is accompanied by secondary currents within the cross-section of the conduit, driven by second normal stress differences. This secondary convection represents a new and heretofore unexplored, advective mechanism for the mass transfer of solutes normal to the primary streamlines in flowing suspensions, and is investigated in this paper via simulations. For small particle sizes, the enhancement of solute diffusivity by shear-induced self-diffusion is weak. However, the magnitude of the secondary currents is unaffected by particle size. Thus, for suspensions with particles much smaller than the conduit size, secondary convection, and not shear-induced self-diffusion, can be the dominant mechanism for shear-induced enhancement of mass transfer. In the limit where shear-induced self-diffusion is the dominant diffusive mode of mass transfer, secondary convection can, for some geometries and conditions, double the augmentation of mass transfer over that expected from self-diffusion alone. The relevance of this new mechanism of mass transfer is in the improved modeling of the transport of solutes for which the dominant mass transfer resistance is in the suspension phase. This mechanism also suggests the possibility of exploiting conduit geometry to improve the mass transfer rate of solutes.