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A universal characteristic of mesoscale turbulence in active suspensions isthe emergence of a typical vortex length scale, distinctly different from thescale-invariance of turbulent high-Reynolds number flows. Collectivelength-scale selection has been observed in bacterial fluids, endothelialtissue and active colloides, yet the physical origins of this phenomenon remainelusive. Here, we systematically derive an effective fourth-order field theoryfrom a generic microscopic model that allows us to predict the typical vortexsize in microswimmer suspensions. Building on a self-consistent closurecondition, the derivation shows that the vortex length scale is determined bythe competition between local alignment forces and intermediate-rangehydrodynamic interactions. Vortex structures found in simulations of the theoryagree with recent measurements in Bacillus subtilis suspensions. Moreover, ourapproach correctly predicts an effective viscosity enhancement (reduction), asreported experimentally for puller (pusher) microorganisms.

Hydrodynamic length-scale selection and effective viscosity in microswimmer suspensions