Propulsion with a Rotating Elastic Nanorod

Manghi, Manoel; Schlagberger, Xaver; Netz, Roland R.

doi:10.1103/physrevlett.96.068101

Cited by 70 publications

(78 citation statements)

References 19 publications

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“…Figure 2 (d) shows the numerical data of η with the parabolic fit for ε = 0.1, which describes the date quite nicely. The highest efficiency is only of the order of 0.01%, which means that this self-propelling filament is quite inefficient compared to other known examples involving helices and other chiral objects [15], since most of the input power is dissipated by the axial spinning.…”

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confidence: 95%

Non-equilibrium hydrodynamics of a rotating filament

Wada

Netz

2006

Europhys. Lett.

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Abstract. -The nonlinear dynamics of an elastic filament that is forced to rotate at its base is studied by hydrodynamic simulation techniques; coupling between stretch, bend, twist elasticity and thermal fluctuations is included. The twirling-overwhirling transition is located and found to be strongly discontinuous. For finite bend and twist persistence length, thermal fluctuations lower the threshold rotational frequency, for infinite persistence length the threshold agrees with previous analytical predictions.The dynamics and morphology of elastic filaments are of interest in various fields encompassing systems on many different length scales [1]. Relevant examples are provided by biopolymes and bio-assemblies, including DNA, actin filaments, microtubules, and multicellular organisms like Bacillus subtilis [2]. Modern micro-manipulation techniques allow to observe and analyze filament dynamics on the single-molecule level [3], prompting a detailed understanding of the combined effects of fluctuations, hydrodynamics and elasticity. Static properties of elastic rods under external force loads have a long history of study, dating back to Euler [4]. Of current interest is the time-dependent behavior of such driven filaments and the possibility of shape bifurcations, especially on the biologically relevant nano-to-micro length scales, where viscous hydrodynamic dissipation dominates over inertia.In this Letter, we describe a hydrodynamic simulation technique for elastic filaments with arbitrary shape and rigidity and subject to external forces or boundary conditions, including full coupling between thermal, elastic and hydrodynamic forces in low-Reynolds-number flow. We apply our method to the whirling dynamics of a slender filament that is axially rotated at one end at frequency ω (while the other end is free). This model system has first been studied analytically by Wolgemuth et al. [5], who showed that a critical frequency ω c separates whirling (steady-state crankshafting motion with axial spinning) from twirling (diffusion-dominated simple axial rotation) by a supercritical Hopf bifurcation (i.e., a continuous shape transition). Subsequently, a zero-temperature simulation has been performed using the immersed boundary method [6], where the microscopic structure of the filament was modelled by interconnected springs. In contrast to analytic predictions, the filament was shown to undergo a subcritical (i.e. discontinuous) shape transition from twirling to a strongly bent state where the filament almost folds back on itself (termed overwhirling). The transition frequency ω c was found to be smaller by a factor of 3.5 compared to the analytic estimate. Using our simulation technique, we first map out the stability diagram in the absence c EDP Sciences

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confidence: 95%

Non-equilibrium hydrodynamics of a rotating filament

Wada

Netz

2006

Europhys. Lett.

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“…Refs. [11,12,13,14,15,16,17,18,19]) and of how their collective beating patterns, known as metachronal waves, occur (e.g. Refs.…”

Section: Introductionmentioning

confidence: 99%

Fluid transport at low Reynolds number with magnetically actuated artificial cilia

2008

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Abstract. By numerical modeling we investigate fluid transport in low-Reynolds-number flow achieved with a special elastic filament or artifical cilium attached to a planar surface. The filament is made of superparamagnetic particles linked together by DNA double strands. An external magnetic field induces dipolar interactions between the beads of the filament which provides a convenient way of actuating the cilium in a well-controlled manner. The filament has recently been used to successfully construct the first artificial micro-swimmer [R. Dreyfus at al., Nature 437, 862 (2005)]. In our numerical study we introduce a measure, which we call pumping performance, to quantify the fluid transport induced by the magnetically actuated cilium and identify an optimum stroke pattern of the filament. It consists of a slow transport stroke and a fast recovery stroke. Our detailed parameter study also reveals that for sufficiently large magnetic fields the artificial cilium is mainly governed by the Mason number that compares frictional to magnetic forces. Initial studies on multi-cilia systems show that the pumping performance is very sensitive to the imposed phase lag between neighboring cilia, i.e., to the details of the initiated metachronal wave.

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“…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%

“…Numerical simulations of the three-dimensional actuation (rotation) of the filament were presented by Manghi et al [26] using particle-based methods which include hydrodynamic interactions (similar to those used to study polymer dynamics). However, the simulations by Manghi et al obtain swimming even in the case where the body sizes shrink to zero, a fact which also violates torque balance for a torque-free swimmer at zero Reynolds number [33,34].…”

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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Propulsion with a Rotating Elastic Nanorod

Cited by 70 publications

References 19 publications

Non-equilibrium hydrodynamics of a rotating filament

Non-equilibrium hydrodynamics of a rotating filament

Fluid transport at low Reynolds number with magnetically actuated artificial cilia

Floppy swimming: Viscous locomotion of actuated elastica

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