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Microswimmers typically operate in complex environments. In biologicalsystems, often diverse species are simultaneously present and interact witheach other. Here, we derive a (time-dependent) particle-scale statisticaldescription, namely a dynamical density functional theory, for suchmulti-species systems, extending existing works on one-component microswimmersuspensions. In particular, our theory incorporates the effect of externalpotentials, but also steric and hydrodynamic interactions between swimmers. Forthe latter, a previously introduced force-dipole-based minimal (pusher orpuller) microswimmer model is used. As a limiting case of our theory, mixturesof hydrodynamically interacting active and passive particles are captured aswell. After deriving the theory, we apply it to different planar swimmerconfigurations. First, these are binary pusher--puller mixtures in externaltraps. In the considered situations, we find that the majority species imposesits behavior on the minority species. Second, for unconfined binarypusher--puller mixtures, the linear stability of an orientationally disorderedstate against the emergence of global polar orientational order (and thusemergent collective motion) is tested analytically. Our statistical approachpredicts, qualitatively in line with previous particle-based computersimulations, a threshold for the fraction of pullers and for their propulsionstrength that lets overall collective motion arise. Third, we let drivenpassive colloidal particles form the boundaries of a shear cell, with confinedactive microswimmers on their inside. Driving the passive particles theneffectively imposes shear flows, which persistently acts on the insidemicroswimmers. Their resulting behavior reminds of the one of circle swimmers,though with varying swimming radii.

Multi-species dynamical density functional theory for microswimmers: derivation, orientational ordering, trapping potentials, and shear cells