Dynamical Density Functional Theory For Microswimmers

Abstract: Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on the one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state", which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.