Pressure-driven flow of a suspension: Buoyancy effects

Dynamic simulation of pressure-driven flow of a non-neutrally buoyant suspension has been performed by Stokesian Dynamics. Channel flow at zero Reynolds number of a monodisperse non-Brownian suspension of spheres in a monolayer was studied for a range of three parameters: bulk particle area fraction phi(A)(b), dimensionless gravitational parameter B = (U-0/[u])(H/a)(2), and dimensionless channel width H/a. Here, U-0 is the Stokes settling velocity of an isolated sphere, [u] is the mean velocity of the suspension, H is the channel width, and a is the particle radius. From an initially uniform distribution, a range of behavior in the fully-developed flow is observed depending upon the value of B. For small B, shear-induced migration dominates buoyancy effects, and a layer at large phi(A) is formed in the center of the channel. For sufficiently strong gravitation, particles settle rapidly to form a concentrated layer that is transported along the bottom of the channel by shearing. At intermediate values of B, shear-induced migration of particles to the center of the channel occurs simultaneously with gravitational settling. In the lower portion of the channel, these fluxes are opposed and lead to nonmonotonic variation of particle fraction, with phi(A) increasing away from the lower wall to a maximum near or even above the centerline and then rapidly decreasing, typically vanishing to leave clear fluid adjacent to the upper wall. These results are in qualitative agreement with the small amount of experimental data in the literature on such systems. The flow has been modeled using macroscopic balance equations presented previously; the predictions agree well with simulations. (C) 1997 Elsevier Science Ltd.