Particle dispersion for suspension flow

Particle dispersion is the flow-induced long-time collective particle diffu sion. It is different from the short-time or long-time self-diffusion of pa rticles (Brady 1994) for there is no particle dispersion in a suspension at rest. The contradiction of the dispersivity among different experimental s ettings reported in the literature is resolved. Applying volume-and-time av eraging concepts in analyzing suspension flow, we are able to relate the pa rticle dispersion with bulk flow velocity field. Non-uniformity in particle force dipole strength gives rise to particle collision-deflection induced particle migration or shear-induced particle migration (dispersion). In add ition, bulk flow itself and the rotation of particles also cause particle r andom movement in concentrated suspensions. Thus, there is a pure bulk flow -induced particle,dispersion. A constitutive equation for computing particl e concentration and velocity profiles is proposed. The model parameters are drawn from fluidization, flow in porous media, sedimentation and granular flow down a rectangular channel. The model predictions agree well with expe rimental data for suspension flows in concentric cylinders. The particle concentration distribution in a flow field is greatly influenc ed by the particle size d(s), and average concentration in addition to the details of the flow field. The two parts of the particle dispersion, flow-i nduced dispersion and shear-induced particle migration, have opposing effec ts on particle concentration distribution. Shear-induced particle migration causes particles to concentrate in the low shear region, while flow-induce d particle dispersion causes particles to spread evenly in the flow field. The shear-induced particle migration is proportional to d(s)(2). The two pa rts in the flow-induced particle dispersion, particle dispersion due to tra nslational flow and particle dispersion due to rotational flow, have differ ent degrees of dependence on the particle size. The particle dispersion due to translational flow is directly proportional to d(s), and the particle d ispersion due to rotational flow is proportional to d(s)(2). Thus, suspensi on of smaller particles tends to have more even distribution of particles i n flow. Since the particles cannot concentrate more than the random packing limit, the average particle concentration also influences the particle con centration distribution. (C) 1999 Elsevier Science Ltd. All rights reserved .