Hydrodynamic diffusion and mass transfer across a sheared suspension of neutrally buoyant spheres

Abstract

We present experimental, theoretical, and numerical simulation studies of the transport of fluid-phase tracer molecules from one wall to the opposite wall bounding a sheared suspension of neutrally buoyant solid particles. The experiments use a standard electrochemical method in which the mass transfer rate is determined from the current resulting from a dilute concentration of ions undergoing redox reactions at the walls in a solution of excess nonreacting ions that screen the electric field in the suspension. The simulations use a lattice-Boltzmann method to determine the fluid velocity and solid particle motion and a Brownian tracer algorithm to determine the chemical tracer mass transfer. The mass transport across the bulk of the suspension is driven by hydrodynamic diffusion, an apparent diffusive motion of tracers caused by the chaotic fluid velocity disturbances induced by suspended particles. As a result the dimensionless rate of mass transfer (or Sherwood number) is a nearly linear function of the dimensionless shear rate (Peclet number) at moderate values of the Peclet number. At higher Peclet numbers, the Sherwood number grows more slowly due to the mass transport resistance caused by a molecular-diffusion boundary layer near the solid walls. Fluid inertia enhances the rate of mass transfer in suspensions with particle Reynolds numbers in the range of 0.5–7.