Dynamics of particles in fluids: effects of correlations and interactions

Abstract

Particles suspended in turbulent fluid flows are common in Nature and in technological applications. In some cases, the relative dynamics of spherical particles may be of interest. One example is small rain droplets in turbulent clouds. The dynamics of nearby droplets is correlated because they experience a correlated airflow. But their relative dynamics is influenced also by fluid-mediated droplet-droplet interactions, or by electrical forces due to charges which the droplets may carry. Heavy particles may detach from the fluid streamlines due to inertia and show inhomogeneities in their spatial distributions, known as clustering. In other cases, the angular dynamics of aspherical particles may be of interest, an example being long and slender fibres in wood pulp used for papermaking. In this thesis, we start by studying the separations and relative angles of non-interacting particles in turbulent flows. This is followed by two studies on the relative dynamics of interacting droplets in steady flows.

First, we analyse a discrete-time, toy model of inertial particles in turbulence. The simplicity of the model allows us to understand in detail how the distribution of inertial particles in turbulence depends on the particle inertia.

Second, we use a statistical model to study how slender rods align with the Lagrangian stretching direction in a turbulent channel flow. We show that the alignment is stronger near the channel wall, than near the channel center. Nevertheless, the rods show large excursions away from alignment. Our model explains the dynamics qualitatively near the channel center but quantitatively near the channel wall.

Third, we use dynamical systems theory to unravel the mechanisms leading to collisions of small, charged droplets in still air. We find that a saddle point with its associated stable manifold determines whether droplets collide or not. This mechanism causes the collision outcomes of droplets with large charges to become independent of non-continuum effects.

Finally, we perform a bifurcation analysis of hydrodynamically interacting neutral droplets settling in a straining flow. Our analysis explains a non-monotonic dependence of their collision rate upon the strength of the strain and that of gravity. We find that even for neutral droplets, there is a regime where the steady-state collision rate becomes independent of non-continuum effects. In addition, our analysis predicts strong inhomogeneities in the distribution of separations.