Shape matters: a Brownian microswimmer in a channel

Chen, Hongfei; Thiffeault, Jean-Luc

doi:10.1017/jfm.2021.144

Cited by 23 publications

(18 citation statements)

References 131 publications

(175 reference statements)

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“…Researches investigating the complex behaviours of micro-swimmers near boundaries are hot-spots recently (Li et al 2008;Kantsler et al 2013;Bianchi et al 2019), however, less is developed for the continuum description of the behaviours and further works regarding this are welcome. In addition, assuming the micro-swimmers to be point-size is also not accurate for very narrow channel Chen & Thiffeault 2021).…”

Section: Discussionmentioning

confidence: 99%

Gyrotactic trapping of micro-swimmers in simple shear flows: a study directly from the fundamental Smoluchowski equation

2022

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Thin phytoplankton layers with vertically compressed structures found in stratified lakes and coastal water bodies have been a hot-spot in marine science and fluid mechanics. Although extensive efforts have been made to explore gyrotactic trapping as a possible mechanism, obvious inconsistencies remain there between the generalised Taylor dispersion method and individual-based model. In this work, a study directly from the fundamental Smoluchowski equation is carried out on the gyrotactic trapping mechanism in representative simple shear flows. With no approximation made to the fundamental equation and applying a biorthogonal expansion to the local moments of the probability density function, the evolution and steady state of the transport process are in good agreement with results of individual-based model, thus removing the gap between the continuum approach and individual-based model. The influences of strongly varying shear rate and boundary effect are reasonably scrutinised. The average swimming orientation with fixed local shear is highlighted as time-dependent rather than steady as previously assumed. The variations of characteristic time of the transient thin layer as functions of the flow intensity, gyrotaxis intensity and swimming ability are characterised. Sedimentation of the micro-swimmers is considered in some cases to reflect that micro-organisms are possibly negatively buoyant, with corresponding boundary conditions devised. A steady thin layer can be realised in the solution by adding a small settling speed to counteract the gravitactic focusing at the upper surface.

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Section: Discussionmentioning

confidence: 99%

Gyrotactic trapping of micro-swimmers in simple shear flows: a study directly from the fundamental Smoluchowski equation

2022

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“…In this paper, we study a model of an elongated swimmer in a planar Kolmogorov flow and elucidate the connection between the swimmer trajectories with noise and the swimmer density in phase space. We choose to study the planar Kolmogorov flow-that is, a spatially periodic, alternating shear flow-rather than the channel flow, because this allows us to ignore the effect of boundary conditions on the swimmer dynamics, which can be quite complex and system dependent [16]. We calculate the steady-state distributions of swimmers in the flow numerically, which exhibit nonuniform concentration profiles in the cross-stream direction that are similar to those observed in channel flows.…”

Section: Introductionmentioning

confidence: 99%

Noise-Induced Aggregation of Swimmers in the Kolmogorov Flow

et al. 2022

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We investigate a model for the dynamics of ellipsoidal microswimmers in an externally imposed, laminar Kolmogorov flow. Through a phase-space analysis of the dynamics without noise, we find that swimmers favor either cross-stream or rotational drift, depending on their swimming speed and aspect ratio. When including noise, i.e., rotational diffusion, we find that swimmers are driven into certain parts of phase space, leading to a nonuniform steady-state distribution. This distribution exhibits a transition from swimmer aggregation in low-shear regions of the flow to aggregation in high-shear regions as the swimmer’s speed, aspect ratio, and rotational diffusivity are varied. To explain the nonuniform phase-space distribution of swimmers, we apply a weak-noise averaging principle that produces a reduced description of the stochastic swimmer dynamics. Using this technique, we find that certain swimmer trajectories are more favorable than others in the presence of weak rotational diffusion. By combining this information with the phase-space speed of swimmers along each trajectory, we predict the regions of phase space where swimmers tend to accumulate. The results of the averaging technique are in good agreement with direct calculations of the steady-state distributions of swimmers. In particular, our analysis explains the transition from low-shear to high-shear aggregation.

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“…(It is prevented from entering the wall by the noflux boundary condition on p.) Hence, the steady solution to Eq. (I.6) is not uniform: particles tend to accumulate near boundaries, in a manner similar to the filter example above [9][10][11].…”

Section: Nonuniform Mixingmentioning

confidence: 93%

Nonuniform mixing

Thiffeault

2021

Preprint

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Fluid mixing usually involves the interplay between advection and diffusion, which together cause any initial distribution of passive scalar to homogenize and ultimately reach a uniform state. However, this scenario only holds when the velocity field is nondivergent and has no normal component to the boundary. If either condition is unmet, such as for active particles in a bounded region, floating particles, or for filters, then the ultimate state after a long time is not uniform, and may be time dependent. We show that in those cases of nonuniform mixing it is preferable to characterize the degree of mixing in terms of an f -divergence, which is a generalization of relative entropy, or to use the L 1 norm. Unlike concentration variance (L 2 norm), the f -divergence and L 1 norm always decay monotonically, even for nonuniform mixing, which facilitates measuring the rate of mixing. We show by an example that flows that mix well for the nonuniform case can be drastically different from efficient uniformly mixing flows.

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Shape matters: a Brownian microswimmer in a channel

Abstract: Abstract

Cited by 23 publications

References 131 publications

Gyrotactic trapping of micro-swimmers in simple shear flows: a study directly from the fundamental Smoluchowski equation

Gyrotactic trapping of micro-swimmers in simple shear flows: a study directly from the fundamental Smoluchowski equation

Noise-Induced Aggregation of Swimmers in the Kolmogorov Flow

Nonuniform mixing

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