Asymmetric and rough boundary effects on particle motions and fluid flows

Abstract

Particles immersed in a fluid will generally be carried along with that fluid as it flows. However, the resulting dynamics of the particles varies greatly depending on the geometry of the particles and other flow boundaries, as well as on the type and density of particles in the flow. Modeling the interactions of particles and fluids can take many forms, from describing the complicated trajectories of single particles, to modeling the distribution of Brownian particles in a suspension, to studying how the introduction of particles affects the macroscopic rheology of the bulk. In this dissertation I extend our understanding of particle and flow interactions in each of these three areas, focusing on the influence of boundary geometry and the effect of departures from idealized surface shapes. The first chapters of this dissertation explores the motion of single three-dimensional particles in two-dimensional flows. I enumerate all possible trajectories of particles of general shapes in shear flow and show that particles with certain body plans can drift across streamlines. I then explore the dynamics of rigid hinges and show that asymmetric hinges can adopt drifting trajectories. Finally, I introduce elasticity and show that elastic hinges can generate net drift in oscillating flows. Next, I explore the effects of a rough channel boundary geometry on the spreading of Brownian tracer particles in flow. I develop an asymptotic theory to describe the leading-order correction to classical Taylor-Aris dispersion and demonstrate that rough surfaces can induce particle drift. I show that our theory can be applied to surfaces of arbitrary roughness and validate our predictions using numerical simulation. Finally, I am motivated by a need to understand the rheology of complex biomolecular condensates to study micropipette aspiration as a tool for probing material properties of very small volumes of fluid. I develop a model that can be used to extract the surface tension and viscosity of fluids from a single set of experimental measurements without the need for calibration parameters. This lays the groundwork for developing models to extract more complicated viscoelastic properties from more complex fluids.