Hydrodynamics of Active Colloids

An active particle moving in a liquid medium will generate flows that extend into the surrounding medium. These particle-generated flows couple the active particles to each other and to any bounding surfaces or interfaces. Active hydrodynamic interactions are implicated in trapping of particles by solid surfaces, active clustering and active phase separation, and other topics of current interest in the active colloids community. In this chapter, we review active colloidal hydrodynamics, starting from foundational concepts of Stokes flow, and introducing some necessary mathematical formalism. We then cover the hydrodynamics of interfacially-driven microswimmers, including how to model the flow field sourced by a self-phoretic colloid. The latter part of this chapter focuses on developing the theory of the fundamental singularities of Stokes flow, as these can provide analytically tractable approximations for colloid/colloid and colloid/surface hydrodynamic interactions. We close with two outlooks on applications of concepts developed in this chapter to active colloids research.