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

Abstract

Previous particle-based computer simulations have revealed a significantly more 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 emergence of such order through a linear instability of the disordered state. For this purpose, input concerning the orientation-dependent pairdistribution function is needed, and we discuss corresponding approaches, particularly a heuristic variant of the Percus test-particle method applied to active systems. Our theory identifies an inherent evolution of polar order in planar systems of puller microswimmers, if mutual alignment due to hydrodynamic interactions overcomes the thermal dealignment by rotational diffusion. In the theory, the cause of orientational ordering can be traced back to the actively induced hydrodynamic rotation-translation coupling between the swimmers. Conversely, disordered pusher suspensions remain linearly stable against homogeneous polar orientational ordering. We expect that our results can be confirmed in experiments on (semi-)dilute active microswimmer suspensions, based, for instance, on biological pusher-and puller-type swimmers.

Particle-resolved lattice Boltzmann simulations of 3-dimensional active turbulence

“…[12][13][14][15] For front-actuated (puller) swimmers such as Chlamydomonas, no such collective behaviour is observed in 3-dimensional suspensions, 7,16 although instead a transition to a polar flocking state has been observed in simulations of puller stresslets confined to a 2-dimensional plane. 17,18 We also note that, in the case of squirmers, which swim by an imposed slip flow along the spherical [19][20][21] or elongated 22,23 swimmer body, such a polar state is found for pullers also in 3 dimensions, while no sign of collective behaviour is found in the corresponding pusher suspensions. 19,21 While squirmers is a more appropriate model for ciliated organisms such as Paramecium, these different collective behaviours highlight that the aspect ratio and seemingly subtle differences in the near-field flows can have large impacts on the non-equilibrium steady states.…”

Anisotropic mesoscale turbulence and pattern formation in microswimmer suspensions induced by orienting external fields

“…where 0 g is the strength of the interaction, and x 1 Q = ( ) for x 0  and zero otherwise. Note that this is a simplified ansatz that describes the polar alignment of neighboring swimmers due to near-field hydrodynamics interactions [72], an effect that has been observed experimentally [3]. Finally, the external potential for swimmer μ is given by Coming back to equations (A.1) and (A.2), far-field hydrodynamic interactions are taken into account by the coupling terms involving the average surrounding flow field u.…”

“…In earlier publications [18,19] we have shown that an equivalent hydrodynamic theory for the microswimmer velocity can be derived via a Fokker-Planck equation approach starting from a generic Langevin model (similar to [15,16]) for a system of microswimmers of length ℓ, diameter d and self-swimming speed v 0 with constant density ρ (see appendix A for a summary of the derivation). The Langevin model includes two types of interactions: first, there are short-range contributions stemming from an activity-driven polar interaction characterized by strength γ 0 and range r [72]. Second, far-field hydrodynamic effects are included via a coupling to the solvent flow field u.…”

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

“…159 Such order in the swimmer orientations naturally leads to collective motion, maintaining a common average propulsion direction. More-over, we have performed a corresponding linear stability analysis of our DDFT for planar pure (one-species) pusher or puller systems, with spontaneous ordering identified beyond a threshold active drive for pullers, 108 in contrast to pushers. We now address the corresponding two-species situation.…”

“…(69), were determined in Ref. 108 by a modified Percus test-particle method. For this purpose, hydrodynamic interactions were neglected and only the interplay of self-propulsion and steric interactions was evaluated.…”