The swimming of animalcules

Felderhof, B. U.

doi:10.1063/1.2204633

Cited by 76 publications

(105 citation statements)

References 17 publications

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“…Recently, Leshansky et al [17] have considered the remarkably efficient locomotion of an elongated treadmilling body, which can propel itself at nearly the same velocity of the surface motion. Other simple means of propulsion proposed for locomotion at zero Reynolds number include a deformable two-dimensional loop [18], systems of two [19,20], three [21,22] or N spheres [23], flapping near deformable interfaces [24], a rehinging swimmer [25], and a jellyfish-inspired bilayer vesicle [26]. For a more complete list of references we refer the reader to Ref.…”

Section: Introductionmentioning

confidence: 99%

Jet propulsion without inertia

Spagnolie

Lauga

2010

Physics of Fluids

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A body immersed in a highly viscous fluid can locomote by drawing in and expelling fluid through pores at its surface. We consider this mechanism of jet propulsion without inertia in the case of spheroidal bodies, and derive both the swimming velocity and the hydrodynamic efficiency. Elementary examples are presented, and exact axisymmetric solutions for spherical, prolate spheroidal, and oblate spheroidal body shapes are provided. In each case, entirely and partially porous (i.e. jetting) surfaces are considered, and the optimal jetting flow profiles at the surface for maximizing the hydrodynamic efficiency are determined computationally. The maximal efficiency which may be achieved by a sphere using such jet propulsion is 12.5%, a significant improvement upon traditional flagella-based means of locomotion at zero Reynolds number. Unlike other swimming mechanisms which rely on the presentation of a small cross section in the direction of motion, the efficiency of a jetting body at low Reynolds number increases as the body becomes more oblate, and limits to approximately 162% in the case of a flat plate swimming along its axis of symmetry. Our results are discussed in the light of slime extrusion mechanisms occurring in many cyanobacteria.

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Section: Introductionmentioning

confidence: 99%

Jet propulsion without inertia

Spagnolie

Lauga

2010

Physics of Fluids

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“…(2.2) the nature of the forces {F j } need not be specified. In an earlier calculation [12] we have considered microswimmers with internal harmonic interactions, driven by actuating forces. The forces are of the form…”

Section: Harmonic Interactions and Actuating Forcesmentioning

confidence: 99%

“…Numerical calculations have shown that the equations of Stokesian dynamics for a set of spheres lead to numerical instability of the solution, unless the spheres are subject to attractive direct interactions keeping them together [12]. For simplicity one can assume harmonic elastic interactions between the spheres, bound harmonically to sites on a given equilibrium structure.…”

Section: Introductionmentioning

confidence: 99%

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Swimming of an assembly of rigid spheres at low Reynolds number

Felderhof

2014

Eur. Phys. J. E

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A matrix formulation is derived for the calculation of the swimming speed and the power required for swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent. The spheres may have arbitrary radii and may interact with elastic forces. The analysis is based on the Stokes mobility matrix of the set of spheres, defined in low Reynolds number hydrodynamics. For small amplitude swimming optimization of the swimming speed at given power leads to an eigenvalue problem. The method allows straightforward calculation of the swimming performance of structures modeled as assemblies of interacting rigid spheres.

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“…The model with three linked spheres, presented by Najafi and Golestanian [7], has three spheres connected via two deformable rods(see also [8]). Examples of propulsion motion, characteristic for bacterial motions and involving cilia waves or rotation of flagella, have been considered [9][10][11][12][13][14][15][16][17].…”

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Propulsion hydrodynamics of a butterfly micro-swimmer

Iima

Mikhailov

2009

Europhys. Lett.

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Abstract. -Propulsion motion of a simple mechanical model at low Reynolds numbers is considered. The model consists of two spheroids (wings) connected by a hinge. Its non-reciprocal operation cycles represent combinations of flapping motions of the wings and of their rotations, resembling conformational motions characteristic for real protein machines and similar to the propulsion pattern of a butterfly. The net generated velocity and the net stall force, exhibited by an immobilized machine on its support, are calculated and their dependence on the model parameters is discussed.Introduction. -It is well known that bacteria and other microorganisms can swim through fluids by periodically changing their shape. The only restriction, imposed by the laws of hydrodynamics at low Reynolds numbers, has been pointed out by Purcell [1] in the form of the "scallop theorem": a purely reciprocal cyclic motion, such as opening and closing of a scallop's shell, cannot generate net propulsion. General analysis of propulsion effects of an object cyclically changing its shape is available [2,3].Several theoretical models of propulsion have been considered to achieve non-reciprocal motion. The Purcell's three-link swimmer, a simplest model swimmer, consists of three rigid rods connected at two hinges each of which has one degree of freedom: the relative angle between two rods [1,[4][5][6]. The model with three linked spheres, presented by Najafi and Golestanian [7], has three spheres connected via two deformable rods(see also [8]). Examples of propulsion motion, characteristic for bacterial motions and involving cilia waves or rotation of flagella, have been considered [9][10][11][12][13][14][15][16][17].Not only microorganisms, but even individual macromolecules operating as protein machines can cyclically change their shapes while being immersed into a fluid. Typically, a protein machine receives energy in the chemical form, with an ATP or other molecule binding to it as a ligand. This leads to a gradual change of the protein shape, representing a process of conformational relaxation of the protein-ligand complex to its equilibrium state . At some stage, the ligand is converted into a product (such as the ADP molecule) which then leaves the protein. After product detachment, the free protein molecule undergoes conformational relaxation back to its equilibrium state. Thus, the cycle of a machine consists of two relaxational motions, the forward one induced by ligand binding and the backward

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The swimming of animalcules

Cited by 76 publications

References 17 publications

Jet propulsion without inertia

Jet propulsion without inertia

Swimming of an assembly of rigid spheres at low Reynolds number

Propulsion hydrodynamics of a butterfly micro-swimmer

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