Maximum in density heterogeneities of active swimmers

Abstract: Suspensions of unicellular microswimmers such as flagellated bacteria or motile algae exhibit spontaneous density heterogeneities at large enough concentrations. Based on the relative location of the biological actuation appendages i.e. flagella or cilia) microswimmers' propulsion mechanism can be classified into two categories: (i) pushers, like \textit{E. coli} bacteria or spermatozoa, that generate thrust in their rear, push fluid away from them and propel themselves forward; (ii) pullers, like the microalgae \textit{Chlamydomonas reinhardtii}, that have two flagella attached to their front, pull the fluid in and thereby generate thrust in their front. We introduce a novel model for biological microswimmers that creates the flow field of the corresponding microswimmers, and takes into account the shape anisotropy of the swimmer's body and stroke-averaged flagella. By employing multiparticle collision dynamics, we directly couple the swimmer's dynamics to the fluid's. We characterize the nonequilibrium phase diagram, as the filling fraction and P\'eclet number are varied, and find density heterogeneities in the distribution of both pullers and pushers, due to hydrodynamic instabilities. We find a maximum degree of clustering at intermediate filling fractions and at large P\'eclet numbers resulting from a competition of hydrodynamic and steric interactions between the swimmers. We develop an analytical theory that supports these results. This maximum might represent an optimum for the microorganisms' colonization of their environment.