UC San Diego

This thesis is devoted to understanding the effect of inter-particle interactions, external fields and confinement in active suspensions. Active suspensions, such as a bath of swimming micro-organisms, have microstructural elements which are motile and exert active stresses on the suspending fluid. The internally generated stresses in active suspensions lead to an intrinsic coupling between the swimmer configurations and the immersing fluid.

The first theme of the thesis focuses on hydrodynamically driven self-organization in active suspensions. We first study the dynamics of concentrated active suspensions in a 3D periodic domain using a coupled Smoluchowski-Stokes kinetic model and discover novel instabilities for both rear-actuated (pusher) and front-actuated (puller) swimmers, characterized by giant number density fluctuations, due to the coupled effects of hydrodynamic and steric interactions. Next, we incorporate chemotactic run-and-tumble effects in the kinetic model to study the dynamics in thin films of aerotactic bacteria. A transition to chaotic dynamics beyond a critical film thickness is reported, in agreement with experiments, and shown to be a consequence of the coupling between aerotactic response of bacteria and hydrodynamic disturbance flows.

The second theme focuses on the sole interplay between motility and confinement in dilute suspensions, ignoring the effect of inter-particle interactions. First, we investigate the dynamics of a confined suspension of Brownian swimmers using a simple kinetic model by prescribing a no-flux condition on the probability distribution function of particle configurations and explain several peculiar dynamics reported in experiments, viz., wall accumulation, as well as upstream swimming, centerline depletion and shear-trapping when a pressure-driven flow is imposed. Next, we calculate the swim pressure of non-Brownian run-and-tumble spherical swimmers using a kinetic model based on coupled bulk/surface probability density functions.

The third theme focuses on the effect of confinement on active self-organization. We discover a symmetry-breaking phase-transition to a spontaneous flowing state with net fluid pumping beyond a critical concentration in a strongly confined channel. The framework for studying confined active suspensions is also extended to explore geometric control of active self-organization in circular and other complex domains.