Stability of active suspensions

Christel Hohenegger, Michael Shelley

Research output: Contribution to journalArticle

Abstract

We study theoretically the stability of "active suspensions," modeled here as a Stokesian fluid in which are suspended motile particles. The basis of our study is a kinetic model recently posed by Saintillan and Shelley where the motile particles are either "pushers" or "pullers." General considerations suggest that, in the absence of diffusional processes, perturbations from uniform isotropy will decay for pullers, but grow unboundedly for pushers, suggesting a possible ill-posedness. Hence, we investigate the structure of this system linearized near a state of uniform isotropy. The linearized system is nonnormal and variable coefficient, and not wholly described by an eigenvalue problem, in particular at small length scales. Using a high wave-number asymptotic analysis, we show that while long-wave stability depends on the particular swimming mechanism, short-wave stability does not and that the growth of perturbations for pusher suspensions is associated not with concentration fluctuations, as we show these generally decay, but with a proliferation of oscillations in swimmer orientation. These results are also confirmed through numerical simulation and suggest that the basic model is well-posed, even in the absence of translational and rotational diffusion effects. We also consider the influence of diffusional effects in the case where the rotational and translational diffusion coefficients are proportional and inversely proportional, respectively, to the volume concentration and predict the existence of a critical volume concentration or system size for the onset of the long-wave instability in a pusher suspension. We find reasonable agreement between the predictions of our theory and numerical simulations of rodlike swimmers by Saintillan and Shelley.

Original languageEnglish (US)
Article number046311
JournalPhysical Review E
Volume81
Issue number4
DOIs
StatePublished - Apr 20 2010

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Active Suspension
Isotropy
isotropy
planetary waves
Directly proportional
Decay
Perturbation
Numerical Simulation
perturbation
Ill-posedness
decay
Kinetic Model
Proliferation
Variable Coefficients
Asymptotic Analysis
Length Scale
Diffusion Coefficient
Eigenvalue Problem
eigenvalues
diffusion coefficient

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Stability of active suspensions. / Hohenegger, Christel; Shelley, Michael.

In: Physical Review E, Vol. 81, No. 4, 046311, 20.04.2010.

Research output: Contribution to journalArticle

Hohenegger, C & Shelley, M 2010, 'Stability of active suspensions', Physical Review E, vol. 81, no. 4, 046311. https://doi.org/10.1103/PhysRevE.81.046311
Hohenegger, Christel ; Shelley, Michael. / Stability of active suspensions. In: Physical Review E. 2010 ; Vol. 81, No. 4.
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