4 results
Enhanced velocity fluctuations in interacting swimmer suspensions
- Sankalp Nambiar, Piyush Garg, Ganesh Subramanian
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- Journal:
- Journal of Fluid Mechanics / Volume 907 / 25 January 2021
- Published online by Cambridge University Press:
- 25 November 2020, A26
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This paper characterizes the nature of velocity fluctuations in swimmer suspensions by determining the fluid velocity variance and the diffusivity of immersed passive tracers in dilute suspensions of hydrodynamically interacting slender microswimmers. The swimmers considered include straight-swimmers whose orientations change only on account of hydrodynamic interactions, and run-and-tumble particles (RTPs) whose orientations change in addition due to tumble events obeying Poisson statistics. In a dilute non-interacting swimmer suspension, the fluid velocity variance is finite and the covariance is short ranged, decaying for distances larger than the swimmer length. In contrast, we show, for a suspension of interacting straight-swimmers, that pair interactions lead to a non-decaying velocity covariance, and a variance that diverges logarithmically with system size. For suspensions of RTPs, the aforementioned divergence is arrested due to tumbling. While the variance remains finite, and the covariance short ranged, for suspensions of interacting rapid tumbling RTPs (short run lengths), the underlying straight-swimmer divergence manifests as a logarithmic increase of the variance with the swimmer run length for persistent RTPs (long run lengths), with a correspondingly long-ranged covariance. The tracer mean squared displacement undergoes an increasingly broad crossover from the ballistic to the diffusive regime for persistent RTPs, with the tracer diffusivity exhibiting a stronger linear increase with the swimmer run length. Our analysis explains the bifurcation of the velocity variance and tracer diffusivities between pusher and puller suspensions, as well as numerous observations of a volume-fraction-dependent crossover time for passive tracer dynamics.
Shear-induced migration of microswimmers in pressure-driven channel flow
- Laxminarsimharao Vennamneni, Sankalp Nambiar, Ganesh Subramanian
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- Journal:
- Journal of Fluid Mechanics / Volume 890 / 10 May 2020
- Published online by Cambridge University Press:
- 12 March 2020, A15
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We study shear-induced migration in a dilute suspension of microswimmers (modelled as active Brownian particles or ABPs) subject to plane Poiseuille flow. For wide channels characterized by $U_{s}/HD_{r}\ll 1$, the separation between time scales characterizing the swimmer orientation dynamics (of $O(D_{r}^{-1})$) and those that characterize migration across the channel (of $O(H^{2}D_{r}/U_{s}^{2})$), allows for use of the method of multiple scales to derive a drift-diffusion equation for the swimmer concentration profile; here, $U_{s}$ is the swimming speed, $H$ is the channel half-width and $D_{r}$ is the swimmer rotary diffusivity. The steady state concentration profile is a function of the Péclet number, $Pe=U_{f}/(D_{r}H)$ ($U_{f}$ being the channel centreline velocity), and the swimmer aspect ratio $\unicode[STIX]{x1D705}$. Swimmers with $\unicode[STIX]{x1D705}\gg 1$ (with $\unicode[STIX]{x1D705}\sim O(1)$), in the regime $1\ll \text{Pe}\ll \unicode[STIX]{x1D705}^{3}$ ($Pe\sim O(1)$), migrate towards the channel walls, corresponding to a high-shear trapping behaviour. For $Pe\gg \unicode[STIX]{x1D705}^{3}$ ($Pe\gg 1$ for $\unicode[STIX]{x1D705}\sim O(1)$), however, swimmers migrate towards the centreline, corresponding to a low-shear trapping behaviour. Interestingly, within the low-shear trapping regime, swimmers with $\unicode[STIX]{x1D705}<2$ asymptote to a $Pe$-independent concentration profile for large $Pe$, while those with $\unicode[STIX]{x1D705}\geqslant 2$ exhibit a ‘centreline collapse’ for $Pe\rightarrow \infty$. The prediction of low-shear trapping, validated by Langevin simulations, is the first explanation of recent experimental observations (Barry et al., J. R. Soc. Interface, vol. 12 (112), 2015, 20150791). We organize the high-shear and low-shear trapping regimes on a $Pe{-}\unicode[STIX]{x1D705}$ plane, thereby highlighting the singular behaviour of infinite-aspect-ratio swimmers.
Stress relaxation in a dilute bacterial suspension: the active–passive transition
- Sankalp Nambiar, Phanikanth S., P. R. Nott, Ganesh Subramanian
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- Journal:
- Journal of Fluid Mechanics / Volume 870 / 10 July 2019
- Published online by Cambridge University Press:
- 15 May 2019, pp. 1072-1104
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This paper follows a recent article of Nambiar et al. (J. Fluid Mech., vol. 812, 2017, pp. 41–64) on the linear rheological response of a dilute bacterial suspension (e.g. E. coli) to impulsive starting and stopping of simple shear flow. Here, we analyse the time dependent nonlinear rheology for a pair of linear flows – simple shear (a canonical weak flow) and uniaxial extension (a canonical strong flow), again in response to impulsive initiation and cessation. The rheology is governed by the bacterium orientation distribution which satisfies a kinetic equation that includes rotation by the imposed flow, and relaxation to isotropy via rotary diffusion and tumbling. The relevant dimensionless parameters are the Péclet number $Pe\equiv \dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D70F}$, which dictates the importance of flow-induced orientation anisotropy, and $\unicode[STIX]{x1D70F}D_{r}$, which quantifies the relative importance of the two intrinsic orientation decorrelation mechanisms (tumbling and rotary diffusion). Here, $\unicode[STIX]{x1D70F}$ is the mean run duration of a bacterium that exhibits a run-and-tumble dynamics, $D_{r}$ is the intrinsic rotary diffusivity of the bacterium and $\dot{\unicode[STIX]{x1D6FE}}$ is the characteristic magnitude of the imposed velocity gradient. The solution of the kinetic equation is obtained numerically using a spectral Galerkin method, that yields the rheological properties (the shear viscosity, the first and second normal stress differences for simple shear, and the extensional viscosity for uniaxial extension) over the entire range of $Pe$. For simple shear, we find that the stress relaxation predicted by our analysis at small $Pe$ is in good agreement with the experimental observations of Lopez et al. (Phys. Rev. Lett., vol. 115, 2015, 028301). However, the analysis at large $Pe$ yields relaxations that are qualitatively different. Upon step initiation of shear, the rheological response in the experiments corresponds to a transition from a nearly isotropic suspension of active swimmers at small $Pe$, to an apparently (nearly) isotropic suspension of passive rods at large $Pe$. In contrast, the computations yield the expected transition to a nearly flow-aligned suspension of passive rigid rods at high $Pe$. We probe this active–passive transition systematically, complementing the numerical solution with analytical solutions obtained from perturbation expansions about appropriate base states. Our study suggests courses for future experimental and analytical studies that will help understand relaxation phenomena in active suspensions.
Stress relaxation in a dilute bacterial suspension
- Sankalp Nambiar, P. R. Nott, Ganesh Subramanian
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- Journal:
- Journal of Fluid Mechanics / Volume 812 / 10 February 2017
- Published online by Cambridge University Press:
- 22 December 2016, pp. 41-64
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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.