Collective Behaviours: Theory

This chapter reviews some examples of simulation work to illustrate the collective behavior in active colloidal systems using established numerical methods. Thereby, it illustrates how to apply these methods. First, we consider interacting active Brownian particles and explore the properties of an active bath. Then, we add non-reciprocal orientational and social interactions to explore phenomena such as flocking and swirling, respectively. Second, we add interactions mediated by chemical fields, which are particularly relevant for active colloids driven by self-diffusiophoresis. Monodisperse systems exhibit dynamic clustering and in a bidisperse system active particles act as seeds to induce a cluster of passive particles. Finally, we show how hydrodynamic interactions between active colloids influence their collective behavior. Using hydrodynamic multipoles, we demonstrate that active particles in a parabolic potential form an active pump. Furthermore, we illustrate explicit simulations of the flow field with the mesoscopic method of multi-particle collision dynamics. The flow fields are generated by a collection of squirmer model microswimmers. Under gravity they show a variety of dynamic structure formations, while squirmer rods made from several spherical squirmers allow us to investigate the emergent collective dynamics of elongated microswimmers including the active turbulence of pusher rods.