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Stochastic kinetic theory for collective behavior of hydrodynamically interacting active particles

Yuzhou Qian1, Peter R. Kramer2, and Patrick T. Underhill1

  • 1Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
  • 2Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, New York 12180, USA

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Phys. Rev. Fluids 2, 043104 – Published 28 April, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.043104

Abstract

Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the hydrodynamic or kinetic equations. By incorporating stochastic fluxes into the mean field kinetic equation, we quantify the dynamics of a suspension of microswimmers in the parameter regime where the deterministic equation is stable. We can thereby compute nontrivial collective phenomena concerning spatial correlations of orientation and stress as well as the enhanced diffusion of tracer particles. Our analysis here focuses primarily on two-dimensional systems, though we also show how superdiffusion of tracers in three dimensions can occur by our framework.

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Outline

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Phys. Rev. Fluids 2, 043104– Published 28 April, 2017
  • Received 22 December 2016
Article part of CHORUS

©2017 American Physical Society

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