Particle dispersion is the flow-induced long-time collective particle diffusion. It is different from the short-time or long-time self-diffusion of particles (Brady 1994) for there is no particle dispersion in a suspension at rest. The contradiction of the dispersivity among different experimental settings reported in the literature is resolved. Applying volume-and-time averaging concepts in analyzing suspension flow, we are able to relate the particle 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 addition, bulk flow itself and the rotation of particles also cause particle random movement in concentrated suspensions. Thus, there is a pure bulk flow-induced particle dispersion. A constitutive equation for computing particle 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 experimental data for suspension flows in concentric cylinders.
The particle concentration distribution in a flow field is greatly influenced by the particle size d Q and average concentration in addition to the details of the flow field. The two parts of the particle dispersion, flow-induced dispersion and shear-induced particle migration, have opposing effects on particle concentration distribution. Shear-induced particle migration causes particles to concentrate in the low shear region, while flow-induced particle dispersion causes particles to spread evenly in the flow field. The shear-induced particle migration is proportional to d Q . The two parts in the flow-induced particle dispersion, particle dispersion due to translational flow and particle dispersion due to rotational flow, have different degrees of dependence on the particle size. The particle dispersion due to translational flow is directly proportional to d Q and the particle dispersion due to rotational flow is proportional to d Q . Thus, suspension of smaller particles tends to have more even distribution of particles in flow. Since the particles cannot concentrate more than the random packing limit, the average particle concentration also influences the particle concentration distribution.