title: Hydrodynamic length-scale selection in microswimmer suspensions.
abstract: A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue, and active colloids, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent closure condition, the derivation shows that the vortex length scale is determined by the competition between local alignment forces, rotational diffusion, and intermediate-range hydrodynamic interactions. Vortex structures found in simulations of the theory agree with recent measurements in Bacillus subtilis suspensions. Moreover, our approach yields an effective viscosity enhancement (reduction), as reported experimentally for puller (pusher) microorganisms.
authors.affiliation: Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Heidenreich
authors.affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue E17-412, Cambridge, Massachusetts 02139-4307, USA.
authors.forename: Jörn
authors.initials: J
authors.lastname: Dunkel
authors.affiliation: Institute for Theoretical Physics, Technical University Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany.
authors.forename: Sabine H L
authors.initials: SH
authors.lastname: Klapp
authors.affiliation: Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Bär