Enhanced flagellar swimming through a compliant viscoelastic network in Stokes flow

Wróbel, Jacek K.; Lynch, Sabrina R.; Barrett, Aaron; Fauci, Lisa; Cortez, Ricardo

doi:10.1017/jfm.2016.99

Cited by 31 publications

(27 citation statements)

References 35 publications

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“…The activity parameter µ 1 allows the mean rate of working to take on negative values, suggesting that the tension/stresslet exerted by the fibres on the sheet may at times overcome the work the sheet does on the fluid to move. For some values of µ 1 , the mean swimming velocity may be negative, indicating a reversal of swimming direction; this change is dependent on the uniform orientation angle φ, a result also observed for rotated viscoelastic networks (Wróbel et al 2016). The inclusion of active behaviour dramatically changes the streamlines and flow field.…”

Section: Discussionmentioning

confidence: 70%

Viscous propulsion in active transversely isotropic media

2017

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Taylor's swimming sheet is a classical model of microscale propulsion and pumping. Many biological fluids and substances are fibrous, having a preferred direction in their microstructure; for example, cervical mucus is formed of polymer molecules which create an oriented fibrous network. Moreover, suspensions of elongated motile cells produce a form of active oriented matter. To understand how these effects modify viscous propulsion, we extend Taylor's classical model of small-amplitude zero-Reynolds-number propulsion of a 'swimming sheet' via the transversely isotropic fluid model of Ericksen, which is linear in strain rate and possesses a distinguished direction. The energetic costs of swimming are significantly altered by all rheological parameters and the initial fibre angle. Propulsion in a passive transversely isotropic fluid produces an enhanced mean rate of working, independent of the initial fibre orientation, with an approximately linear dependence of the energetic cost on the extensional and shear enhancements to the viscosity caused by fibres. In this regime, the mean swimming velocity is unchanged from the Newtonian case. The effect of the constant term in Ericksen's model for the stress, which can be identified as a fibre tension or alternatively a stresslet characterising an active fluid, is also considered. This stress introduces an angular dependence and dramatically changes the streamlines and flow field; fibres aligned with the swimming direction increase the energetic demands of the sheet. The constant fibre stress may result in a reversal of the mean swimming velocity and a negative mean rate of working if it is sufficiently large relative to the other rheological parameters.

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Section: Discussionmentioning

confidence: 70%

Viscous propulsion in active transversely isotropic media

2017

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“…Furthermore, the fact that w ex (t) does not overshoot its final value tells us that the helix does not regain any of the work it has supplied to the polymer when the polymer relaxes. This is in contrast to the observed enhancement of swimming due to the energetics of noiseless elastic surroundings [60,61]. In such systems, elastic networks or tubes which a swimmer swims through store elastic energy and transfer this energy back to during relaxation.…”

Section: Fluctuating Workmentioning

confidence: 75%

Biopolymer dynamics driven by helical flagella

et al. 2017

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Microbial flagellates typically inhabit complex suspensions of polymeric material which can impact the swimming speed of motile microbes, filter-feeding of sessile cells, and the generation of biofilms. There is currently a need to better understand how the fundamental dynamics of polymers near active cells or flagella impacts these various phenomena, in particular the hydrodynamic and steric influence of a rotating helical filament on suspended polymers. Our Stokesian dynamics simulations show that as a stationary rotating helix pumps fluid along its long axis, polymers migrate radially inwards while being elongated. We observe that the actuation of the helix tends to increase the probability of finding polymeric material within its pervaded volume. This accumulation of polymers within the vicinity of the helix is stronger for longer polymers. We further analyse the stochastic work performed by the helix on the polymers and show that this quantity is positive on average and increases with polymer contour length. Snapshots from a single simulation of a rotating helix and an advected polymer taken at times t0 < t1 < t2. A torque τ is distributed uniformly on the helix and, as it rotates, it generates a pumping flow. The polymer is drawn in radially and axially towards the helix, stretching in the process due to the induced shear flow. Once captured it winds around the helix and is pumped axially in the direction of the average flow.

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“…These models have wider relevance in the field of synthetic biology, with particular application to microscopic bacteriophage-based fibre sensors [26][27][28] and flexible filament microbots [29]. The proposed framework could be used to further investigate the dynamics of bundles of filaments [30], and additionally has applications in the multi-scale studies of complex polymeric fluids, and flagellar movement through them [31,32].…”

Section: Introductionmentioning

confidence: 99%

Efficient implementation of elastohydrodynamics via integral operators

et al. 2019

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The dynamics of geometrically non-linear flexible filaments play an important role in a host of biological processes, from flagella-driven cell transport to the polymeric structure of complex fluids. Such problems have historically been computationally expensive due to numerical stiffness associated with the inextensibility constraint, as well as the often non-trivial boundary conditions on the governing high-order PDEs. Formulating the problem for the evolving shape of a filament via an integral equation in the tangent angle has recently been found to greatly alleviate this numerical stiffness. The contribution of the present manuscript is to enable the simulation of nonlocal interactions of multiple filaments in a computationally efficient manner using the method of regularized stokeslets within this framework. The proposed method is benchmarked against a nonlocal bead and link model, and recent code utilizing a local drag velocity law. Systems of multiple filaments (1) in a background fluid flow, (2) under a constant body force, and (3) undergoing active self-motility are modeled efficiently. Buckling instabilities are analyzed by examining the evolving filament curvature, as well as by coarse-graining the body frame tangent angles using a Chebyshev approximation for various choices of the relevant non-dimensional parameters. From these experiments, insight is gained into how filament-filament interactions can promote buckling, and further reveal the complex fluid dynamics resulting from arrays of these interacting fibers. By examining active moment-driven filaments, we investigate the speed of worm-and sperm-like swimmers for different governing parameters. The MATLAB R implementation is made available as an open-source library, enabling flexible extension for alternate discretizations and different surrounding flows.

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Enhanced flagellar swimming through a compliant viscoelastic network in Stokes flow

Cited by 31 publications

References 35 publications

Viscous propulsion in active transversely isotropic media

Viscous propulsion in active transversely isotropic media

Biopolymer dynamics driven by helical flagella

Efficient implementation of elastohydrodynamics via integral operators

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