Hydrodynamic diffusion near solid boundaries with applications to heat and mass transport into sheared suspensions and fixed-fibre beds

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Abstract
Heat and mass transport in the bulk of a suspension or fixed bed in the limit of high Péclet number is controlled by hydrodynamic diffusion. This hydrodynamic diffusion is caused by the stochastic velocity field induced by the randomly distributed particles. However, the no-slip boundary conditions require that the hydrodynamic diffusivity vanish at boundaries of the medium. Thus, molecular diffusion must aid the transport in a thin boundary layer near the solid boundary. Quantitative results are derived for the hydrodynamic diffusivity, boundary layer thickness, and net resistance to transport across a dilute fixed fibrous bed in the direction transverse to the mean flow. A scaling analysis is presented for transport in the direction of the gradient of the mean velocity in a sheared suspension of neutrally buoyant spheres. This scaling analysis is able to explain the qualitative variations of the transport resistance with the Péclet number and the ratio of the suspension thickness to the particle radius.