Realization of the Najafi-Golestanian microswimmer

Grosjean, Galien; Hubert, Maxime; Lagubeau, Guillaume; Vandewalle, Nicolas

doi:10.1103/physreve.94.021101

Cited by 79 publications

(91 citation statements)

References 20 publications

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“…The triangular swimmer is composed of three spherical beads, each of radius a, connected by identical springs of equilibrium length L and spring constant k. All beads are placed in the x-z-plane with orientation θ the angle between the connection of bead 3 to the middle between bead 1 and 2 and the x-axis ( figure 3). Numerous experimental realizations of microswimmers rely on an external field, commonly an electric or magnetic one [11,5,2]. Therefore, we first consider here a toy model swimmer that is subject to an external force field which shall act in one direction only (without restriction of generality the x-direction) for the sake of simplicity.…”

Section: Triangular Swimmer 51 External Drivingmentioning

confidence: 99%

“…The locomotion of swimmers at small scales has been an active area of research in recent years [1], with a variety of microswimmer models being proposed, both experimental [2][3][4][5][6][7][8][9][10][11] and theoretical [12][13][14][15][16][17][18][19][20][21]. A number of these models aims at understanding the propulsion mechanisms of small organisms such as bacteria or algae cells, or at designing artificial microswimmers.…”

Section: Introductionmentioning

confidence: 99%

“…However, the perturbative calculations in [20,30,21] hold only in the limit of very large bead separations where the swimming velocity becomes extremely small. Especially since this limit is inaccessible in experiments (see [5,9]) as external disturbances become exuberant and can break the swimmer, an investigation of swimmers with smaller bead separations is required and still lacking.In this paper, we fill this gap by presenting a general perturbative framework to calculate the full behavior of arbitrarily shaped bead-spring swimmers, i.e. not only their stroke and swimming velocity, but also the average deformation and the produced flow field.…”

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A general perturbative approach for bead-based microswimmers reveals rich self-propulsion phenomena

et al. 2019

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Studies of model microswimmers have significantly contributed to the understanding of the principles of self-propulsion we have today. However, only a small number of microswimmer types have been amenable to analytic modeling, and further development of such approaches is necessary to identify the key features of these active systems. Here we present a general perturbative calculation scheme for swimmers composed of beads interacting by harmonic potentials and via hydrodynamics, driven by an arbitrary force protocol. The approach can be used with mobility matrices of arbitrary accuracy, and we illustrate it with the Oseen and Rotne-Prager approximations. We validate our approach by using 3 bead assemblies and comparing the results with the numerically obtained full-solutions of the governing equations of motion, as well as with existing analytic models for the linear and the triangular swimmer geometry. While recovering the relation between the force and swimming velocity, our detailed analysis and the controlled level of approximation allow us to find qualitative differences already in the far field flow of the devices. Consequently, we are able to identify a behavior of the swimmer that is richer than predicted in previous models. Given its generality, the framework can be applied to any swimmer geometry, driving protocol and bead interactions, as well as in problems involving many swimmers.Despite its immense usefulness, this model suffers from the constriction of all internal degrees of freedom by the swimming stroke, namely the internal dynamical behavior of the swimmer cannot react to its surrounding. This was overcome by replacing the arms with springs and prescribing the forces acting on the beads rather than the stroke itself [28,20]. Importantly, the responsive elastic degree of freedom, which is typically associated with the swimmer design, but which could also be in the fluid, is responsible for several interesting phenomena. For example, it is the source of the optimal driving frequency in the overdamped regime [29] and it promotes swimming based on the minimization of drag or enhancement of hydrodynamic interactions [20]. Furthermore, it is also responsible for the existence of a viscosity maximising the swimming velocity [30] and synchronization effects of the stroke [20]. Similar findings have been reported in investigations of bead-based swimmers in a visco-elastic fluid [31,32]. Recently, an altered version of the bead-spring model has been proposed, where the swimmer was driven by periodic changes in the equilibrium lengths of the springs [33,34].The boundedness of the linear swimmer to one dimension is broken in a triangular swimmer geometry, allowing for translational as well as rotational motion [35,14,16]. This geometry has also been used to model Chlamydomonas reinhardtii and investigate in particular the synchronization between the beating of its two flagella [18,36,19]. Experimentally, a triangular swimmer with intrinsic elasticity has been realized by placing ferromagnetic beads subject...

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Section: Triangular Swimmer 51 External Drivingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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A general perturbative approach for bead-based microswimmers reveals rich self-propulsion phenomena

et al. 2019

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“…if A=B and 0 a = , unlike the expression in equation (2.12). A similar swimmer, with symmetric driving but unequal spring stiffnesses, has been recently realized experimentally [63].…”

Section: A3 Velocity Expression For Unequal Spring Constantsmentioning

confidence: 99%

Setting the pace of microswimmers: when increasing viscosity speeds up self-propulsion

et al. 2017

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It has long been known that some microswimmers seem to swim counter-intuitively faster when the viscosity of the surrounding fluid is increased, whereas others slow down. This conflicting dependence of the swimming velocity on the viscosity is poorly understood theoretically. Here we explain that any mechanical microswimmer with an elastic degree of freedom in a simple Newtonian fluid can exhibit both kinds of response to an increase in the fluid viscosity for different viscosity ranges, if the driving is weak. The velocity response is controlled by a single parameter Γ, the ratio of the relaxation time of the elastic component of the swimmer in the viscous fluid and the swimming stroke period. This defines two velocity-viscosity regimes, which we characterize using the bead-spring microswimmer model and analyzing the different forces acting on the parts of this swimmer. The analytical calculations are supported by lattice-Boltzmann simulations, which accurately reproduce the two velocity regimes for the predicted values of Γ.

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“…23 As understanding of how physical stimuli affect biological responses is still developing, the ability to modify swimmer shape could prevent unnecessary inflammatory responses. In addition, physically linking the magnetic particles makes the magneto-elastic swimmer inherently more stable than swarm-type swimmers 24 and therefore less likely to break up in the turbulent and divergent flow conditions that exist within the blood stream. 25 Current research effort has largely concentrated on establishing structural designs capable of producing net translational motion either in purely unconstrained (bulk) fluids or purely along an interface (such that the interface does not impede motion).…”

Section: Introductionmentioning

confidence: 99%

Emergent propagation modes of ferromagnetic swimmers in constrained geometries

Bryan

Shelley

Parish

et al. 2017

Journal of Applied Physics

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Magnetic microswimmers, composed of hard and soft ferromagnets connected by an elastic spring, are modelled under low Reynolds number conditions in the presence of geometrical boundaries. Approaching a surface, the magneto-elastic swimmer's velocity increases and its trajectory bends parallel to the surface contour. Further confinement to form a planar channel generates new propagation modes as the channel width narrows, altering the magneto-elastic swimmer's speed, orientation and direction of travel. Our results demonstrate that constricted geometric environments, such as occur in microfluidic channels or blood vessels, may influence the functionality of magnetoelastic microswimmers for applications such as drug delivery.2

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Realization of the Najafi-Golestanian microswimmer

Cited by 79 publications

References 20 publications

A general perturbative approach for bead-based microswimmers reveals rich self-propulsion phenomena

A general perturbative approach for bead-based microswimmers reveals rich self-propulsion phenomena

Setting the pace of microswimmers: when increasing viscosity speeds up self-propulsion

Emergent propagation modes of ferromagnetic swimmers in constrained geometries

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