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Previous particle-based computer simulations have revealed a significantlymore pronounced tendency of spontaneous global polar ordering in puller(contractile) microswimmer suspensions than in pusher (extensile) suspensions.We here evaluate a microscopic statistical theory to investigate the emergenceof such order through a linear instability of the disordered state. For thispurpose, input concerning the orientation-dependent pair-distribution functionis needed, and we discuss corresponding approaches, particularly a heuristicvariant of the Percus test-particle method applied to active systems. Ourtheory identifies an inherent evolution of polar order in planar systems ofpuller microswimmers, if mutual alignment due to hydrodynamic interactionsovercomes the thermal dealignment by rotational diffusion. In the theory, thecause of orientational ordering can be traced back to the actively inducedhydrodynamic rotation--translation coupling between the swimmers. Conversely,disordered pusher suspensions remain linearly stable against homogeneous polarorientational ordering. We expect that our results can be confirmed inexperiments on (semi-)dilute active microswimmer suspensions, based, forinstance, on biological pusher- and puller-type swimmers.

Particle-scale statistical theory for hydrodynamically induced polar ordering in microswimmer suspensions