Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T23:10:44.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Stress relaxation in a dilute bacterial suspension

Published online by Cambridge University Press:  22 December 2016

Sankalp Nambiar ,
P. R. Nott  and
Ganesh Subramanian
Sankalp Nambiar
Affiliation:
Engineering Mechanics Unit, JNCASR, Jakkur, Bangalore 560064, India
P. R. Nott
Affiliation:
Department of Chemical Engineering, IISc, Bangalore 560012, India
Ganesh Subramanian*
Affiliation:
Engineering Mechanics Unit, JNCASR, Jakkur, Bangalore 560064, India
*
†Email address for correspondence: sganesh@jncasr.ac.in
Get access Rights & Permissions [Opens in a new window]

Abstract

In this communication, we offer a theoretical explanation for the results of recent experiments that examine the stress response of a dilute suspension of bacteria (wild-type E. coli) subjected to step changes in the shear rate (Lopez et al., Phys. Rev. Lett., vol. 115, 2015, 028301). The observations include a regime of negative apparent shear viscosities. We start from a kinetic equation that describes the evolution of the single-bacterium orientation probability density under the competing effects of an induced anisotropy by the imposed shear, and a return to isotropy on account of stochastic relaxation mechanisms (run-and-tumble dynamics and rotary diffusion). We then obtain analytical predictions for the stress response, at leading order, of a dilute bacterial suspension subject to a weak but arbitrary time-dependent shear rate profile. While the predicted responses for a step-shear compare well with the experiments for typical choices of the microscopic parameters that characterize the swimming motion of a single bacterium, use of actual experimental values leads to significant discrepancies. The incorporation of a distribution of run times leads to a better agreement with observations.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 41 - 64
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. A. 1970 Handbook of Mathematical Functions. Dover.Google Scholar
Aranson, A. & Sokolov, I. S. 2009 Reduction of viscosity in suspension of swimming bacteria. Phys. Rev. Lett. 103, 148101.Google Scholar
Batchelor, G. K. 1970a Slender-body theory for particles of arbitrary cross-section in stokes flow. J. Fluid Mech. 44, 791–810.CrossRefGoogle Scholar
Batchelor, G. K. 1970b The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.CrossRefGoogle Scholar
Berg, H. C. 1993 Random Walks in Biology. Princeton University Press.Google Scholar
Berg, H. C. 2004 E. coli in Motion. Springer.CrossRefGoogle Scholar
Berg, H. C. & Brown, D. A. 1972 Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature 239, 500–504.CrossRefGoogle ScholarPubMed
Berke, A. P., Turner, L., Berg, H. C. & Lauga, E. 2008 Hydrodynamic attraction of swimming microorganisms by surfaces. Phys. Rev. Lett. 101 (3), 038102.CrossRefGoogle ScholarPubMed
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids. Vol. 1 – Fluid Mechanics. Wiley.Google Scholar
Brenner, H. 1974 Rheology of a dilute suspension of axisymmetric brownian particles. Intl J. Multiphase Flow 1, 195–341.CrossRefGoogle Scholar
Darnton, N. C., Turner, L., Rojevsky, S. & Berg, H. C. 2007 On torque and tumbling in swimming. J. Bacteriol. 189, 1756–1764.CrossRefGoogle ScholarPubMed
Drescher, K., Dunkel, J., Cisneros, L. H., Ganguly, S. & Goldstein, R. E. 2011 Fluid dynamics and noise in bacterial cell–cell and cell–surface scattering. Proc. Natl Acad. Sci. USA 108 (27), 10940–10945.CrossRefGoogle ScholarPubMed
Elgeti, J. & Gompper, G. 2013 Wall accumulation of self-propelled spheres. Europhys. Lett. 101 (4), 48003.CrossRefGoogle Scholar
Elgeti, J. & Gompper, G. 2015 Run-and-tumble dynamics of self-propelled particles in confinement. Europhys. Lett. 109 (5), 58003.CrossRefGoogle Scholar
Gachelin, J., Rousselet, A., Lindner, A. & Clement, E. 2014 Collective motion in an active suspension of Escherichia coli bacteria. New J. Phys. 16, 025003.CrossRefGoogle Scholar
Ghosh, A., Samuel, J. & Sinha, S. 2012 A ‘gaussian’ for diffusion on the sphere. Eur. Phys. Lett. 98, 30003.CrossRefGoogle Scholar
Haines, B. M., Sokolov, A., Aranson, I. S., Berlyand, L. & Karpeev, D. A. 2009 Three-dimensional model for the effective viscosity of bacterial suspensions. Phys. Rev. E 80 (4), 041922.Google ScholarPubMed
Hatwalne, Y., Ramaswamy, S., Rao, M. & Simha, A. R. 2004 Rheology of active-particle suspensions. Phys. Rev. Lett. 92, 118101.CrossRefGoogle ScholarPubMed
Hernandez-Ortiz, J. P., Stoltz, C. G. & Graham, M. D. 2005 Transport and collective dynamics in suspensions of confined swimming particles. Phys. Rev. Lett. 95 (20), 204501.CrossRefGoogle ScholarPubMed
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161–179.Google Scholar
Karmakar, R., Gulvady, R., Tirumkudulu, M. S. & Venkatesh, K. V. 2014 Motor characteristics determine the rheological behavior of a suspension of microswimmers. Phys. Fluids 26 (7), 071905.CrossRefGoogle Scholar
Kasyap, T. V., Koch, D. L. & Wu, M. 2014 Hydrodynamic tracer diffusion in suspensions of swimming bacteria. Phys. Fluids 26 (8), 081901.CrossRefGoogle Scholar
Kirkwood, J. G. & Auer, P. L. 1951 The viscoelastic properties of solutions of rod-like macromolecules. J. Chem. Phys. 19, 231–283.CrossRefGoogle Scholar
Koch, D. L. & Subramanian, G. 2011 Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. 43, 637–659.CrossRefGoogle Scholar
Krishnamurthy, D. & Subramanian, G. 2015 Collective motion in a suspension of micro-swimmers that run-and-tumble and rotary diffuse. J. Fluid Mech. 781, 422–466.CrossRefGoogle Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.CrossRefGoogle Scholar
Leal, L. G. & Hinch, E. J. 1971 The effect of weak brownian rotations on particles in shear flow. J. Fluid Mech. 46, 685–703.CrossRefGoogle Scholar
Lopez, H. M., Gachelin, J., Douarche, C., Auradou, H. & Clement, E. 2015 Turning bacteria suspensions into superfluids. Phys. Rev. Lett. 115, 028301.CrossRefGoogle ScholarPubMed
Lovely, P. S. & Dahlquist, F. W. 1975 Statistical measures of bacterial motility and chemotaxis. J. Theor. Biol. 50, 477–496.CrossRefGoogle ScholarPubMed
Majumdar, S. & Sood, A. K. 2008 Nonequilibrium fluctuation relation for sheared micellar gel in a jammed state. Phys. Rev. Lett. 101, 078301.CrossRefGoogle Scholar
Marchetti, M. C. 2015 Soft matter: Frictionless fluids from bacterial teamwork. Nature 525, 37–39.CrossRefGoogle ScholarPubMed
Saintillan, D. 2010 The dilute rheology of swimming suspensions: a simple kinetic model. Exp. Mech. 50, 1275–1281.CrossRefGoogle Scholar
Saintillan, D. & Shelley, M. J. 2008 Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys. Rev. Lett. 100, 178103.CrossRefGoogle ScholarPubMed
Saintillan, D. & Shelley, M. J. 2012 Emergence of coherent structures and large-scale flows in motile suspensions. J. R. Soc. Interface 9, 571–585.CrossRefGoogle ScholarPubMed
Sandoval, M., Navaneeth, K. M., Subramanian, G. & Lauga, E. 2014 Stochastic dynamics of active swimmers in linear flows. J. Fluid Mech. 742, 50–70.CrossRefGoogle Scholar
Sokolov, A., Apodaca, M. M., Grzybowski, B. A. & Aranson, I. S. 2010 Swimming bacteria power microscopic gears. Proc. Natl Acad. Sci. USA 107, 969–974.CrossRefGoogle ScholarPubMed
Subramanian, G. & Koch, D. L. 2009 Critical bacterial concentration for the onset of collective swimming. J. Fluid Mech. 632, 359–400.CrossRefGoogle Scholar
Subramanian, G. & Nott, P. R. 2011 The fluid dynamics of swimming microorganisms and cells. IISc J. 91, 283–313.Google Scholar
Turner, L., Ryu, W. S. & Berg, H. C. 2000 Real-time imaging of fluorescent flagellar filaments. J. Bacteriol. 182, 2793–2801.CrossRefGoogle ScholarPubMed
Underhill, P. T. & Graham, M. D. 2011 Correlations and fluctuations of stress and velocity in suspensions of swimming microorganisms. Phys. Fluids 23, 121902.CrossRefGoogle Scholar
Underhill, P. T., Hernandez-Ortiz, J. P. & Graham, M. D. 2008 Diffusion and spatial correlations in suspensions of swimming particles. Phys. Rev. Lett. 100, 248101.CrossRefGoogle ScholarPubMed
Wu, X. L. & Libchaber, A. 2000 Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84, 3017–3020.CrossRefGoogle Scholar