UC San Diego

The primary objective of this thesis is to develop and provide a theoretical framework based on hydrodynamic theory and statistical mechanics that furthers our physical understanding of active suspensions at a macroscopic level. These non-equilibrium systems are comprised of interacting units that extract and consume free energy from their environment, usually via chemical reactions, to produce directed motion. Examples include synthetic swimmers, biomimetic materials and living systems and their motile constituents. An intrinsic property of these active particles, biological and artificial, is the display of an enhanced diffusion in the absence of external fields, here termed "active diffusion", which leads to an additional pressure contribution as a consequence of their self-propulsion. During their motion, active particles additionally generate stresses that get transmitted to the surrounding medium, creating long-range hydrodynamic interactions that, along with steric and chemical effects, often lead to striking macroscopic features and highly correlated large-scale motions.

We first present a continuum model based on generalized Taylor dispersion theory, complemented by Langevin simulations, to predict the long-time asymptotic transport of active Brownian particles in periodic crowded media, when subjected to an applied flow and chemical fields. We start from a micro-continuum level approach and show that the overall behavior of a dilute cloud of cells can be described by an obstacle-free advection-diffusion equation, whose effective long-time mean particle velocity and dispersivity dyadic are determined through a set of boundary value problems. The intrinsic complexity of particle transport arises from the activity of the swimmers, and the complex geometry of the flow paths, which originates from the mixing and re-splitting of streams at pore junctions. We unravel the roles of particle motility, applied fluid flow, chemotactic fields and porous lattice geometry on asymptotic particle transport properties, and provide a physical explanation for the trends observed. Particularly, we show that obstacles behave predominantly as entropic barriers at low flow rates and as regions of shear production at high flow rates, and find that shear-induced polarization as well as activity-driven cross-stream migration affect the axial particle dispersion. Our mathematical framework gives new insights and provides a simple approach to control the spreading of active particles in structured crowded environments.

We additionally study the mechanical force per unit area exerted by these active particles on confining boundaries. We also quantify and characterize the effect of these biological microorganisms on the suspension viscosity as well as on the onset of self-generated spontaneous flows in confinement. Our work captures the main qualitative patterns observed in experiments, and a close quantitative agreement is achieved between the developed theory and existing experiments. In particular, we capture and explain the superfluidity regime of rear-actuated suspensions, recently observed in experiments, a state of matter in which the suspension behaves as a frictionless fluid. This superfluidity regime has remarkable consequences on the onset of internally generated flows and the subsequent formation of coherent structures, most of them observed in past experiments and caused by bacterial activity and confinement, such as: the formation of bacterial vortices, bacterial traveling waves, chaotic dynamics, stabilization of inverted bacterial fluid films, unidirectional fluid pumping in channels, and control of the magnitude and direction of the self-generated flows upon simple application of uniform magnetic fields. Our theoretical and computational models enable us to reproduce and elucidate these phenomena within a single integrated framework.

The understanding, control and manipulation of the transport of active particles have important consequences in human health as well as in microbial ecology. Applications include the spreading of contaminants in soils and groundwater aquifers, design of medical devices, bacterial filtering, and biodegradation-bioremediation processes. The theoretical framework developed in this thesis provides the scientific community with powerful tools that enable a better understanding of complex microbial systems, thus paving the way for the conceptual development of new revolutionary devices and processes involving active particles. A lot of progress needs to be done, a great diversity of challenges need to be faced, and many applications are yet to be discovered.