Active suspensions and their nonlinear models

Active suspensions, such as suspensions of self-propelled microorganisms and related synthetic microswimmers, are known to undergo complex dynamics and pattern formation as a result of hydrodynamic interactions. In this review, we summarize recent efforts to model these systems using continuum kinetic theories. We first derive a basic kinetic model for a suspension of self-propelled rodlike particles and discuss its stability and nonlinear dynamics. We then present extensions of this model to analyze the effective rheology of active suspensions in external flows, the effect of steric interactions in concentrated systems, and the dynamics of chemotactically responsive suspensions in chemical fields.