Optimal Swimming at Low Reynolds Numbers

Avron, J. E.; Gat, Omri; Kenneth, Oded

doi:10.1103/physrevlett.93.186001

Cited by 161 publications

(157 citation statements)

References 22 publications

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“…They are thus very expedient to use for synthetic nanomotors whose mechanical degrees of freedom are hard to control. In contrast to the efficiency of molecular motors [10] or other swimming mechanisms at low Reynolds numbers [11][12][13], the efficiency of surface-driven propulsion has, to our knowledge, received no attention so far. However, this question becomes relevant when energy resources are limited by the environment of the swimmer.…”

mentioning

confidence: 96%

Efficiency of Surface-Driven Motion: Nanoswimmers Beat Microswimmers

Sabass

Seifert

2010

Phys. Rev. Lett.

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Surface interactions provide a class of mechanisms which can be employed for propulsion of microand nanometer sized particles. We investigate the related efficiency of externally and self-propelled swimmers. A general scaling relation is derived showing that only swimmers whose size is comparable to, or smaller than, the interaction range can have appreciable efficiency. An upper bound for efficiency at maximum power is 1/2. Numerical calculations for the case of diffusiophoresis are found to be in good agreement with analytical expressions for the efficiency.

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mentioning

confidence: 96%

Efficiency of Surface-Driven Motion: Nanoswimmers Beat Microswimmers

Sabass

Seifert

2010

Phys. Rev. Lett.

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“…In dimensions D > 2 the translational part of the gauge potential can be determined by the condition that the net force on the swimmer vanish. In two dimensions, however, the net force vanishes identically [24] and so one must instead determine the translational part of the gauge potential by requiring that the fluid velocity vanish at infinity [25]. We discuss this condition in more detail in Section V.…”

Section: Equations Of Motion Force and Torquementioning

confidence: 99%

“…The swimmer feels no net force (a generic result for Stokes flows in two dimensions [24]) and the total torque is…”

Section: Equations Of Motion Force and Torquementioning

confidence: 99%

Swimming at low Reynolds number in fluids with odd, or Hall, viscosity

Lapa

Hughes

2014

Phys. Rev. E

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We apply the geometric theory of swimming at low Reynolds number to the study of nearly circular swimmers in two-dimensional fluids with non-vanishing Hall, or "odd", viscosity. The Hall viscosity gives an off-diagonal contribution to the fluid stress-tensor, which results in a number of striking effects. In particular, we find that a swimmer whose area is changing will experience a torque proportional to the rate of change of the area, with the constant of proportionality given by the coefficient η o of odd viscosity. After working out the general theory of swimming in fluids with Hall viscosity for a class of simple swimmers, we give a number of example swimming strokes which clearly demonstrate the differences between swimming in a fluid with conventional viscosity and a fluid which also has a Hall viscosity. A number of more technical results, including a proof of the torque-area relation for swimmers of more general shape, are explained in a set of appendices.The theory of swimming in classical fluids at low Reynolds number [1,2] is remarkable because of the connections it makes between seemingly disparate fields [3]. For example, the motion of swimmers with cyclic swimming strokes is determined purely from classical fluid dynamics, but it can be re-cast into an elegant geometric formulation reminiscent of Berry's phase physics and gauge fields [3][4][5]. In fact, the motion of tiny organisms in fluids with high viscosity can be captured by a "gauge-theory" of shapes. Since the initial work on the geometric formulation of swimming there have been generalizations to swimmers in quantum fluids [6] and even to swimmers in fluids on curved spaces [7,8]. The theory has also been successfully applied in practice to describe the swimming of robots [9] and microbots [10,11].In this article we focus on swimmers in 2D fluids with broken time-reversal symmetry, for example, fluids in magnetic fields or rotating fluids. We are not interested in the specific source of time-reversal breaking, but instead just consider a classical fluid with a microscopic source of local angular momentum (on a much smaller scale than the size of the swimmer) that gives rise to a non-vanishing Hall (or odd) viscosity coefficient [12,13] in addition to the usual isotropic viscosity coefficients. The Hall viscosity is an off-diagonal viscosity term that is dissipationless and produces forces perpendicular to the direction of the fluid flow. It can have a quantum mechanical origin in, for example, systems exhibiting the quantum Hall effect [12][13][14][15][16][17][18][19][20][21][22], or a classical origin in plasmas at finite-temperature [23].We will not focus on the microscopic origin of the Hall viscosity coefficient, but only assume it to be non-vanishing in conjunction with the usual viscosity coefficients. From this assumption we will determine the motion of swimmers at low Reynolds number in the presence of Hall viscosity. Specifically, we will consider the problem of swimmers with circular boundaries that move via deformations of thei...

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“…Recent technical advances have led to ever more precise fabrication at small scales (microns or less), prompting both theorists [9][10][11][12][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.…”

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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Optimal Swimming at Low Reynolds Numbers

Cited by 161 publications

References 22 publications

Efficiency of Surface-Driven Motion: Nanoswimmers Beat Microswimmers

Efficiency of Surface-Driven Motion: Nanoswimmers Beat Microswimmers

Swimming at low Reynolds number in fluids with odd, or Hall, viscosity

Floppy swimming: Viscous locomotion of actuated elastica

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