The Effect of Flow Geometry on Shear-Induced Particle Segregation and Resuspension.

In this thesis, we investigate through theory and experiment the influence of the flow geometry on various shear-induced migration phenomena such as particle demixing, viscous resuspension and meniscus accumulation for a suspension of rigid, non-colloidal particles. The major focus of this thesis is the elucidation of a particle flux mechanism that has been ignored in the literature in the theoretical calculation of the concentration distribution in shear-induced migration phenomena. This mechanism is the convective flux due to the secondary currents arising from the non-Newtonian rheology of suspensions. Historically, suspensions have been modeled as Newtonian fluids with concentration dependent viscosities when calculating velocity distributions due to the tremendous simplification of the governing equations. The results presented in this thesis, however, demonstrate that it is critical to consider the complete rheology of a concentrated suspension when modeling flows in complex geometries. While the magnitude of the secondary currents is small, in many cases they are the dominant mechanism governing the resulting particle concentration distribution. In chapters 2 through 4, we investigate the impact of these secondary currents on the concentration profiles developed in suspension flow through conduits of arbitrary geometry, and in resuspension flow through a tube. In chapter 5, we examine the radial segregation of particles in the squeeze flow of concentrated suspensions. This flow is identical to that produced in loading suspensions on to a parallel plate viscometer and thus the concentration inhomogeneities generated during the loading phenomenon may play a role in the well known scatter of torque measurements in this system. We develop a criterion in terms of the experimental parameters in a parallel plate experiment for the onset of radial inhomogeneities. In the final investigation reported in this thesis, we develop a theoretical model for describing the droplet distribution in the Poiseuille flow of an emulsion through a tube. We show that the mathematical problem that results from this model is amenable to self-similar analysis via the trial function approach. The self-similar solution so obtained is used to evaluate oscillatory flows as a possible technique for separation of the dispersed phase from suspending fluid.