Taylor’s swimming sheet: Analysis and improvement of the perturbation series

Sauzade, Martin; Elfring, Gwynn J.; Lauga, Eric

doi:10.1016/j.physd.2011.06.023

Cited by 57 publications

(33 citation statements)

References 26 publications

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“…26 They found optimal speed is U v 0 ≈ 0.27 with m ≈ 1.9, which are about 20% greater than our RFT calculations. This difference however is not unexpected because for the infinitely thin filament there are no hydrodynamic interactions.…”

Section: Parametric Study Of Swimming Performancecontrasting

confidence: 56%

“…(25), the subscript v 0 in Eq. (26) indicates that the wave speed is constant. For small amplitude sine waves the work metric is…”

Section: Performance Criteriamentioning

confidence: 99%

“…Because Taylor's approach only is valid in the limit of small actuation, k x A 1, it is unsuitable for optimization studies. However, recently Sauzade, Elfring, and Lauga 26 improved on Taylor's work by developing a series approach that converges for k A O (10). They found the maximum swimming speed is for kA ≈ 2 and U ≈ 0.27v 0 .…”

Section: Introductionmentioning

confidence: 99%

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Pitching, bobbing, and performance metrics for undulating finite-length swimming filaments

2012

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We explore a simple (toy) model of undulating finite-length filaments swimming in viscous fluids, based on resistive force theory. The filaments are actuated by traveling waves, and we consider four different strategies: two smooth waveforms (cartesian and curvature sine waves) and two others with kinks (sawtooth and square waves). Analytical results in the limit of short filaments and/or small actuation parameters are provided. A new efficiency metric is proposed which takes into account that work expenditure is minimal when power consumption is maintained constant. This metric is particularly well-suited for short undulating filaments where power fluctuations for constant actuation rates can be substantial. Parametric studies are performed for a range of filament lengths and actuation parameters for the purpose of side-by-side comparisons. We give analytical expressions for swimming of arbitrary length filaments where the actuation is small. We describe “swimming resonances,” which are local maxima in performance that occur for certain values of the filament length, S, undulation wavelength, λ, and undulation amplitude. For the sawtooth and sinusoids these occur for undulation numbers Nλ = S/λ ≈ 3/2, 5/2, 7/2, …, whereas for the square wave strategy these occur at Nλ ≈ 1/2, 3/2, 2, 3, 4, …. We analyze swimming in terms of pitching as well as translation and bobbing, which are motion along and orthogonal to the net direction of translation, respectively. Resonances for the sawtooth and smooth waveforms occur when pitching is small and bobbing is near a local maximum. However, for square-wave actuation, most resonances occur when bobbing is small and pitching is near a local maximum.

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Section: Parametric Study Of Swimming Performancecontrasting

confidence: 56%

“…(25), the subscript v 0 in Eq. (26) indicates that the wave speed is constant. For small amplitude sine waves the work metric is…”

Section: Performance Criteriamentioning

confidence: 99%

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Pitching, bobbing, and performance metrics for undulating finite-length swimming filaments

2012

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“…The swimming speed found using a conventional sum of the first three terms of the perturbation series for a Newtonian fluid is inaccurate past ≈ 0.5 but by using the method of Padé approximants [44], with just three terms in the series, the P 1 1 ( ) approximant is accurate up to ≈ 1 (within 1% of the computational result determined using the boundary integral method) [43]. We follow the same tactic for the coefficients of the viscoelastic swimming speed based on the assumption that the Padé P 1 1 ( ) approximant is accurate for a larger range of amplitudes.…”

Section: B Large-amplitude Deformationsmentioning

confidence: 94%

“…In a Newtonian fluid the first two terms were found by Taylor [29], while the third was later derived by Drummond [42]. The series was recently resolved to arbitrarily high order by Sauzade et al [43] who showed that the series converges only for small , and then only slowly, but methods to accelerate convergence prove very effective enabling accurate prediction up of the swimming speed for order-one amplitudes.…”

Section: B Large-amplitude Deformationsmentioning

confidence: 99%

Theory of Locomotion Through Complex Fluids

Elfring

Lauga

2014

Complex Fluids in Biological Systems

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Microorganisms such as bacteria often swim in fluid environments that cannot be classified as Newtonian. Many biological fluids contain polymers or other heterogeneities which may yield complex rheology. For a given set of boundary conditions on a moving organism, flows can be substantially different in complex fluids, while non-Newtonian stresses can alter the gait of the microorganisms themselves. Heterogeneities in the fluid may also be characterized by length scales on the order of the organism itself leading to additional dynamic complexity. In this chapter we present a theoretical overview of small-scale locomotion in complex fluids with a focus on recent efforts quantifying the impact of non-Newtonian rheology on swimming microorganisms.

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Sperm Motility: Models for Dynamic Behavior in Complex Environments

Simons

Olson

2018

Modeling and Simulation in Science, Engineering and Technology

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Taylor’s swimming sheet: Analysis and improvement of the perturbation series

Cited by 57 publications

References 26 publications

Pitching, bobbing, and performance metrics for undulating finite-length swimming filaments

Pitching, bobbing, and performance metrics for undulating finite-length swimming filaments

Theory of Locomotion Through Complex Fluids

Sperm Motility: Models for Dynamic Behavior in Complex Environments

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