Active colloids are micron-sized particles that self-propel through viscous fluids by converting energy extracted from their environment into mechanical motion. The origin or mechanism of their locomotion can be either biological or synthetic ranging from motile bacteria to artificial phoretic particles. Owing to their ability to self-propel, active colloids are out of thermodynamic equilibrium and exhibit interesting macroscopic or collective dynamics. In particular, active colloids exhibit accumulation at confining boundaries, upstream swimming in Poiseuille flow, and a reduced or negative apparent shear viscosity. My work has been focused on a theoretical and computational understanding of the dynamics of active colloids under the influence of confinement and external fluid flows, which are ubiquitous in biological processes. I consider the transport of active colloids in channel flows, the microrheology of active colloids, and lastly I propose and study a vesicle propulsion system based on the learned principles.

A generalized Taylor dispersion theory is developed to study the transport of active colloids in channel flows. I show that the often-observed upstream swimming can be explained by the biased upstream reorientation due to the flow vorticity. The longitudinal dispersion of active colloids includes the classical shear-enhanced dispersion and an active swim diffusivity. Their coupling results in a non-monotonic variation of the dispersivity as a function of the flow speed. To understand the effect of particle shape on the transport of active colloids, a simulation algorithm is developed that is able to faithfully resolve the inelastic collision between an ellipsoidal particle and the channel walls. I show that the collision-induced rotation for active ellipsoids can suppress upstream swimming. I then investigate the particletracking microrheology of active colloids. I show that active colloids exhibit a swimthinning microrheology and a negative microviscosity can be observed when certain hydrodynamic effects are considered. I show that the traditional constant-velocity probe model is not suitable for the quantification of fluctuations in the suspension. To resolve this difficulty, a generalized microrheology model that closely mimicks the experimental setup is developed. I conclude by proposing a microscale propulsion system in which active colloids are encapsulated in a vesicle with a semi-permeable membrane that allows water to pass through. By maintaining an asymmetric number density distribution, I show that the vesicle can self-propel through the surrounding viscous fluid.