Theory of active suspensions

Active suspensions, of which a bath of swimming microorganisms is a paradigmatic example, denote large collections of individual particles or macromolecules capable of converting fuel into mechanical work and microstructural stresses. Such systems, which have excited much research in the last decade, exhibit complex dynamical behaviors such as large-scale correlated motions and pattern formation due to hydrodynamic interactions. In this chapter, we summarize efforts to model these systems using particle simulations and continuum kinetic theories. After reviewing results from experiments and simulations, we present a general kinetic model for a suspension of self-propelled rod-like particles and discuss its stability and nonlinear dynamics. We then address extensions of this model that capture the effect of steric interactions in concentrated systems, the impact of confinement and interactions with boundaries, and the effect of the suspending medium rheology. Finally, we discuss new active systems such as those that involve the interactions of biopolymers with immersed motor proteins, and surface-bound suspensions of chemically-powered particles.