Laminar Transport of Solid Particles Suspended in Liquids

Abstract

Attention is focused on the laminar transport of non-colloidal, non-buoyant particles suspended in a continuous, Newtonian fluid. In the presence of a gravitational force field particles settle on the bottom of the conduit, while hydrodynamic diffusion acts against gravity and causes at least a part of the particles to be resuspended. Resuspension of heavy particles under the action of shear has been observed not only in turbulent flows but also when the Reynolds number is small. Since particle-particle interactions are important, an individual sphere will experience shear-induced diffusion. This phenomenon, which causes an upward flux of particles from regions of high concentrations to low is eventually balanced by the downward flux due to gravity. Several examples of uni-directional resuspension flows have been investigated in both theoretical and experimental levels. Experiments performed in a 2-D Hagen-Poiseuille channel show reasonable agreement with the theory for small flow rates of clear liquid. In certain parameter ranges, however, different flow instabilities were reported: When the flow rates were large the interface between the clear liquid and the suspension became unstable and the measured flow quantities were much different than theoretical predictions. Relatively heavy particles occasionally caused partial blocking of the channel and the clear fluid meandered through the stagnant sediment. Eventually, ripple-type instabilities were found in the case of a very thin layer of particles. A linear stability analysis for a 2-D Hagen-Poiseuille resuspension flow revealed that the interface is almost always unstable. The numerical solutions show that two branches contribute to the convective instability; i.e., long and short waves, which coexist in a certain range of parameters. Also, a large range exists where the flow is absolutely unstable. Finally, the entrance flow of an originally well mixed suspension flowing into a twodimensional channel and the propagation of a sediment layer can be investigated by applying a theory of kinematic waves.