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Concentration banding instability of a sheared bacterial suspension

Published online by Cambridge University Press:  06 October 2020

Laxminarsimharao Vennamneni Open the ORCID record for Laxminarsimharao Vennamneni [Opens in a new window] ,
Piyush Garg Open the ORCID record for Piyush Garg [Opens in a new window]  and
Ganesh Subramanian Open the ORCID record for Ganesh Subramanian [Opens in a new window]
Laxminarsimharao Vennamneni
Affiliation:
Engineering Mechanics Unit, JNCASR, Jakkur, Bangalore 560064, India
Piyush Garg
Affiliation:
Engineering Mechanics Unit, JNCASR, Jakkur, Bangalore 560064, India
Ganesh Subramanian*
Affiliation:
Engineering Mechanics Unit, JNCASR, Jakkur, Bangalore 560064, India
*
†Email address for correspondence: [email protected]
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Abstract

We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneous bacterial suspension, subject to a simple shear flow, is shown to be susceptible to exponentially growing layering perturbations in the shear rate and bacterial concentration. A semi-analytical expression for the growth rate of concentration perturbations is first obtained using the method of multiple scales, in the limit where the time scales characterizing the positional and orientation degrees of freedom are well separated. Next, the eigenspectrum obtained numerically from a full linear stability analysis is used to validate and extend the multiple scales result, and draw a contrast with the known orientation-shear instability. Finally, fully nonlinear simulations, but restricted to one-dimensional variations of the relevant fields (velocity, concentration and swimmer orientation distribution) show that the initial instability leads to gradient-banded velocity profiles, with a local depletion of bacteria at the interface between the homogeneous shear bands. Our results demonstrate that long-ranged hydrodynamic interactions serve as an alternate explanation for recent observations of shear bands in bacterial suspensions.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Non-Newtonian Flows: Rheology
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A7
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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