Pairwise hydrodynamic interactions of permeable particles and flow-induced structuring in dilute suspensions
Date of Award
Doctor of Engineering (DEng)
Chemical and Environmental Engineering (ENAS)
Loewenberg , Michael
The study of particle-level interactions in suspension flows enables a better understanding and control of systems where suspensions play a key role. Examples include the physiology of blood flow microcirculation, flow-induced segregation of polydisperse suspensions, particle aggregation in marine environments, and filtration processes, to name a few. In these systems, a detailed description of the hydrodynamic interactions between the particles and between the particles and fluid boundaries characterize the evolution of the suspension microstructure. Typically, the characteristic size of the particles is small compared to the imposed flow length scale, and hence low-Reynolds-number conditions usually apply. In the dilute regime, pair-interactions between smooth, rigid and spherical particles yield symmetric particle trajectories with zero net cross-flow displacements and thus no structuring. However, short-range phenomena including material specific forces, e.g., electrostatic repulsion and van der Waals attraction, and physical properties of the particles, e.g., particle permeability, surface roughness, and interface mobility, break the symmetry of particle trajectories resulting in net particle displacements and hence particle structuring. This thesis contains a detailed analysis of the near-contact motion of permeable particles in the limit of weak surface permeability where Darcy's law is used to describe the flow in the permeable medium. A full set of resistance and mobility functions that relates particle motion to forces, torques, and stresslets acting on the particles are calculated. Results show that non-zero values of particle permeability qualitatively alter the near-contact particle motion, removing the classical lubrication resistance between approaching smooth impermeable spheres that prevents particle contact under the action of a finite force without the need for nonhydrodynamic interparticle forces (van der Waals attraction). Particle permeability also qualitatively alters the tangential motion of particles, providing access to non-singular rolling motion of particles along walls. This analysis may help to predict the capacity for crossflow filtration devices. Analytical closed-form expressions are derived for binary collision rates for permeable particles in Brownian motion, gravity sedimentation, uniaxial straining, and shear flow. Here, the solution of the analogous problem of binary collision rates of particles with small-amplitude surface roughness provide accurate approximations for the collision rates of permeable particles for all aggregation mechanisms considered herein. Finally, a pairwise hydrodynamic theory is presented for flow-induced particle distributions in dilute polydisperse suspensions. Diffusive fluxes and a drift velocity in non-homogeneous shear flows are obtained from a Boltzmann-like master equation. A boundary-layer analysis in regions of vanishing shear rates (e.g., centerline of a channel flow) overcomes the failure of the current theories that predict aphysical singular behavior. The analysis presented herein yields non-singular particle distributions that qualitatively resemble experimental results in the literature. Results for bidisperse suspensions show that size segregation occurs in Poiseuille flow leading to relative enrichment of larger or smaller species at the centerline, depending on the size ratio, relative number densities, and physical properties of the particles.
Reboucas, Rodrigo Bento, "Pairwise hydrodynamic interactions of permeable particles and flow-induced structuring in dilute suspensions" (2021). Yale Graduate School of Arts and Sciences Dissertations. 396.