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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: [email protected]
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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
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Copyright
© 2016 Cambridge University Press 

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