Non-equilibrium hydrodynamics of a rotating filament

Wada, Hirofumi; Netz, Roland R.

doi:10.1209/epl/i2006-10155-0

Cited by 47 publications

(61 citation statements)

References 15 publications

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“…As a final remark, we note that same sample we have sometimes observed two different devices moving in opposite directions according to th orientation, which rules out any suspected consequences field gradients. The Supplementary Movies show the dynam filament at two frame rates: 440 frames s 21 (Supplementar and 40 frames s 21 (Supplementary Movie 2), for which L f ¼ 10 Hz, B x ¼ 9 mT, B y ¼ 14.5 mT.…”

Section: Maximum Dimensional Speedmentioning

confidence: 99%

“…This behavior is consistent with low-Reynolds-number experiments with macroscale helical swimmers. 21,22 The maximum synchronized frequency is referred to as the step-out frequency. The Reynolds number of the ABF in Figure 2 is in the range of 10 -4 (the estimation of the Reynolds number of the ABFs are given in the Supporting Information) similar to the Reynolds number of bacteria in water.…”

Section: Maximum Dimensional Speedmentioning

confidence: 99%

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High-speed propulsion of flexible nanowire motors: Theory and experiments

et al. 2011

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Micro/nano-scale propulsion has attracted considerable recent attention due to its promise for biomedical applications such as targeted drug delivery. In this paper, we report on a new experimental design and theoretical modelling of high-speed fuel-free magnetically-driven propellers which exploit the flexibility of nanowires for propulsion. These readily prepared nanomotors display both high dimensional propulsion velocities (up to ≈ 21µm/s) and dimensionless speeds (in body lengths per revolution) when compared with natural microorganisms and other artificial propellers. Their propulsion characteristics are studied theoretically using an elastohydrodynamic model which takes into account the elasticity of the nanowire and its hydrodynamic interaction with the fluid medium. The critical role of flexibility in this mode of propulsion is illustrated by simple physical arguments, and is quantitatively investigated with the help of an asymptotic analysis for small-amplitude swimming. The theoretical predictions are then compared with experimental measurements and we obtain good agreement. Finally, we demonstrate the operation of these nanomotors in a real biological environment (human serum), emphasizing the robustness of their propulsion performance and their promise for biomedical applications.

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Section: Maximum Dimensional Speedmentioning

confidence: 99%

Section: Maximum Dimensional Speedmentioning

confidence: 99%

High-speed propulsion of flexible nanowire motors: Theory and experiments

et al. 2011

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“…Solving the transverse problem: Filament shape and swimming kinematics Let us now solve Eq. (29). Since the forcing is harmonic, we will solve these equations in Fourier space and write, for all variables, A(x, t) = ℜ{Â(x) exp(−it)}.…”

Section: F Nondimensionalization and Simplificationsmentioning

confidence: 99%

“…Related studies include the dynamics of magnetic filaments [23][24][25], the three-dimensional actuation and instabilities of flexible filaments [26][27][28][29] and the exploitation of symmetry-breaking to pump fluid in a channel [30].…”

Section: Introductionmentioning

confidence: 99%

Floppy swimming: Viscous locomotion of actuated elastica

2007

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Actuating periodically an elastic filament in a viscous liquid generally breaks the constraints of Purcell's scallop theorem, resulting in the generation of a net propulsive force. This observation suggests a method to design simple swimming devices -which we call "elastic swimmers" -where the actuation mechanism is embedded in a solid body and the resulting swimmer is free to move. In this paper, we study theoretically the kinematics of elastic swimming. After discussing the basic physical picture of the phenomenon and the expected scaling relationships, we derive analytically the elastic swimming velocities in the limit of small actuation amplitude. The emphasis is on the coupling between the two unknowns of the problems -namely the shape of the elastic filament and the swimming kinematics -which have to be solved simultaneously. We then compute the performance of the resulting swimming device, and its dependance on geometry. The optimal actuation frequency and body shapes are derived and a discussion of filament shapes and internal torques is presented. Swimming using multiple elastic filaments is discussed, and simple strategies are presented which result in straight swimming trajectories. Finally, we compare the performance of elastic swimming with that of swimming microorganisms. I. INTRODUCTIONThe fluid mechanics of microorganism locomotion, pioneered more than fifty years ago by G.I. Taylor, has become one of the most successful branches of biomechanics, with success in both the basic physical understanding of flow behavior and the quantitative prediction of kinematics and energetics of locomotion [1][2][3][4][5][6][7][8].Recent technical advances have led to ever more precise fabrication at small scales (microns or less), prompting both theorists [9-13] and experimentalists [14] to design and analyze a series of simple low-Reynolds number swimmers. The experiment of Dreyfus et al. [14], in particular, reported locomotion in a sperm-like micro-swimmer, composed of a cargo (red blood cell) and a slender flexible filament made of a series of paramagnetic beads. In that case, actuation by oscillating transverse magnetic fields led to the generation of bending waves propagating along the filament and resulted in the motion of the micro-swimmer. In this system, the right-left symmetry was broken by the presence of a cargo and led to a preferential tip-to-base propagation of the bending waves, resulting in locomotion in the direction base-to-tip.An alternative way to break the symmetry in a similar system would be to build-in the asymmetry in the actuation. In particular, if an elastic filament is periodically actuated at one of its extremities in a viscous liquid, the resulting motion will lead to the propagation of bending waves and, in general, propulsive forces. This idea was originally proposed by Edward Purcell [8]. Physically, actuating an elastic filament allows one to break the constraints of the "scallop theorem" -which states that a body performing a reciprocal motion at low Reynolds number cannot p...

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“…There is also a hydrodynamic torque per unit length distributed along the rod that tends to twist it [13,14,15]. However, the effects of this torque are smaller by a factor of (a/L) 2 relative to effects due to translation of the rod [13] and will henceforth be disregarded.…”

mentioning

confidence: 99%

Shape Transition and Propulsive Force of an Elastic Rod Rotating in a Viscous Fluid

2008

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The deformation of thin rods in a viscous liquid is central to the mechanics of motility in cells ranging from Escherichia coli to sperm. Here we use experiments and theory to study the shape transition of a flexible rod rotating in a viscous fluid driven either by constant torque or at constant speed. The rod is tilted relative to the rotation axis. At low applied torque, the rod bends gently and generates small propulsive force. At a critical torque, the rotation speed increases abruptly and the rod forms a helical shape with much greater propulsive force. We find good agreement between theory and experiment.PACS numbers: 87.16. Qp, 46.70.Hg Understanding how flagella and cilia work is a central aim of the field of cell motility. The problem may be split into two parts, both of which involve physics: the means of actuation, and the fluid-structure interaction. In this letter we consider the fluid-structure interaction for thin filaments in a viscous fluid. At micron scales, viscous effects dominate inertia, and the fluid-structure interaction problem simplifies because the Stokes equations governing the fluid motion are linear. Gray and Hancock used this linearity to develop a simple theory that successfully predicted the swimming speed of a sperm cell with a loadindependent pattern of bending waves propagating along the flagellum [1]. Soon after, Machin considered the fluid-structure interaction [2]. He argued that the motors must be distributed all along the length of the flagellum, since, for small amplitudes, a passive flexible rod waved at one end has an exponentially decaying envelop of deflection, whereas the amplitude of deflection in real flagellar bending waves increases slightly with distance from the head [2]. The shapes and propulsive forces of a passive rod actuated at one end have recently been examined theoretically [3,4] and experimentally [4]. Although sperm flagella are not passive, the results of [2,3,4] are important for modeling real flagella since the modes that Machin found also enter models in which the flagellum is actuated along its entire length [5].Rotating flagella are also common. For example, nodal cilia [6] have an internal structure similar to that of sperm flagella. However, instead of beating in a plane like most sperm flagella, nodal cilia rotate along the surface of an imaginary cone. The flow set up by these flagella has been implicated in the formation of left-right asymmetry in developing embryos (see [6] and references therein). Bacterial flagella provide another example. These flagella are helical, much thinner than eukaryotic flagella, and driven by a rotary motor embedded in the cell wall. Fluid-structure interactions are important for polymorphic transformations in swimming bacteria [7] and the bundling of multiple flagella [8].Complementary to the problem of understanding how biological flagella work is the problem of building an arti-

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Non-equilibrium hydrodynamics of a rotating filament

Cited by 47 publications

References 15 publications

High-speed propulsion of flexible nanowire motors: Theory and experiments

High-speed propulsion of flexible nanowire motors: Theory and experiments

Floppy swimming: Viscous locomotion of actuated elastica

Shape Transition and Propulsive Force of an Elastic Rod Rotating in a Viscous Fluid

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