Swimming and pumping of rigid helical bodies in viscous fluids

Li, Lei; Spagnolie, Saverio E.

doi:10.1063/1.4871084

Cited by 9 publications

(12 citation statements)

References 65 publications

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“…Since we have neglected the rotational drag around the long axis of the filament locally, which scales as O(ε 2 ) as ε → 0, the rotation rate above tends towards infinity as b → 0. Nevertheless the coupling between the torque and the translational speed of such a filament does not vanish in this limit, instead it tends towards dependence on the wavenumber, k. A more detailed examination of this asymptotic regime shows that the model above amounts to a distinguished limit, accurate so long as εL/b is held fixed as b → 0 [51]. At leading order in c, the tensors above remain accurate; contributions which depend on the fixed value of εL/b enter at O(1).…”

Section: No Cell Body Prescribed Forces and Momentsmentioning

confidence: 95%

Helical trajectories of swimming cells with a flexible flagellar hook

Zou,

Lough,

Spagnolie

2021

Preprint

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The flexibility of the bacterial flagellar hook is believed to have substantial consequences for microorganism locomotion. Using a simplified model of a rigid flagellum and a flexible hook, we show that the paths of axisymmetric cell bodies driven by a single flagellum are generically helical. Phase-averaged resistance and mobility tensors are produced to describe the flagellar hydrodynamics, and a helical rod model which retains a coupling between translation and rotation is identified as a distinguished asymptotic limit. A supercritical Hopf bifurcation in the flagellar orientation beyond a critical ratio of flagellar motor torque to hook bending stiffness, which is set by the spontaneous curvature of the flexible hook, the shape of the cell body, and the flagellum geometry, can have a dramatic effect on the cell's trajectory through the fluid. Although the equilibrium hook angle can result in a wide variance in the trajectory's helical pitch, we find a very consistent prediction for the trajectory's helical amplitude using parameters relevant to swimming P. aeruginosa cells.

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Section: No Cell Body Prescribed Forces and Momentsmentioning

confidence: 95%

Helical trajectories of swimming cells with a flexible flagellar hook

Zou,

Lough,

Spagnolie

2021

Preprint

Self Cite

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“…(6), subject to the no-slip boundary conditions of Eq. (7). This solution is periodic in x, reflecting the symmetry of the underlying problem.…”

Section: Small-amplitude Swimming: Analytical Solutionmentioning

confidence: 98%

The mechanism of propulsion of a model microswimmer in a viscoelastic fluid next to a solid boundary

Ives

Morozov

2017

Physics of Fluids

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In this paper we study swimming of a model organism, the so-called Taylor's swimming sheet, in a viscoelastic fluid close to a solid boundary. This situation comprises natural habitats of many swimming microorganisms, and while previous investigations have considered the effects of both swimming next to a boundary and swimming in a viscoelastic fluid, seldom have both effects been considered simultaneously. We re-visit the small wave amplitude result obtained by Elfring and Lauga (Gwynn J. Elfring and Eric Lauga, in Saverio E. Spagnolie, editor, Complex Fluids in Biological Systems, Springer New York, New York, NY, 2015), and give a mechanistic explanation to the decoupling of the effects of viscoelasticity, which tend to slow the sheet, and the presence of the boundary, which tends to speed up the sheet. We also develop a numerical spectral method capable of finding the swimming speed of a waving sheet with an arbitrary amplitude and waveform.We use it to show that the decoupling mentioned above does not hold at finite wave amplitudes and that for some parameters the presence of a boundary can cause the viscoelastic effects to increase the swimming speed of microorganisms.

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“…A common feature in the modelling of microfluidic design, 1 the motion of particles with complex mixed stick-slip boundary conditions, 2 the motility of biological cells, 3 and the dynamics of cell-cell and cell-substrate interactions 4,5 are the needs to determine low-Reynolds-number Stokes flow in domains with boundaries having arbitrary shapes. In many applications, such boundaries may also deform as the quasi-static flow progresses, for instance, in modelling mobile deformable droplets or biological cells.…”

Section: Introductionmentioning

confidence: 99%

Boundary regularized integral equation formulation of Stokes flow

et al. 2015

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Single-phase Stokes flow problems with prescribed boundary conditions can be formulated in terms of a boundary regularized integral equation that is completely free of singularities that exist in the traditional formulation. The usual mathematical singularities that arise from using the fundamental solution in the conventional boundary integral method are removed by subtracting a related auxiliary flow field, w, that can be constructed from one of many known fundamental solutions of the Stokes equation. This approach is exact and does not require the introduction of additional cutoff parameters. The numerical implementation of this boundary regularized integral equation formulation affords considerable savings in coding effort with improved numerical accuracy. The high accuracy of this formulation is retained even in problems where parts of the boundaries may almost be in contact.

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Swimming and pumping of rigid helical bodies in viscous fluids

Cited by 9 publications

References 65 publications

Helical trajectories of swimming cells with a flexible flagellar hook

Helical trajectories of swimming cells with a flexible flagellar hook

The mechanism of propulsion of a model microswimmer in a viscoelastic fluid next to a solid boundary

Boundary regularized integral equation formulation of Stokes flow

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