Scallop Theorem and Swimming at the Mesoscale

Hubert, Maxime; Trosman, Oleg; Collard, Ylona; Sukhov, Alexander; Harting, Jens; Vandewalle, Nicolas; Smith, Ana‐Sunčana

doi:10.1103/physrevlett.126.224501

Cited by 19 publications

(13 citation statements)

References 44 publications

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“…), the lower are the frequencies of the peak velocities leading to a better time resolution and the higher are the maximum velocity amplitudes. Finally, we note that since the swimmer velocity typically scales quadratically V ∼ A 2 [43,20,22,42] with the external driving amplitude A, this is also the way to tune up the velocity. With triangular magnetocapillary swimmers it has, however, a limitation at increasing field ratios, since at values |B(t)|/B ≈ 0.6 a dynamic transition from a triangular to a linear swimmer configuration occurs (Fig.…”

Section: Swimmer Velocitiesmentioning

confidence: 89%

“…It captures the whole complexity of the motion in terms of capillary and magnetic interactions (magnetocapillary potential), hydrodynamic interactions, the behaviour of the interface, triangular geometry of the swimmer and the effects associated with the inertia of the particles. Although there is a number of studies dealing with the physics of swimmer motion [5,6,40,41,20,22,42], it is hardly possible to include all the aforementioned effects in a single theoretical formalism. Studies relying on the force-based approach suggest that the maximum swimmer velocity should be centered around the frequencies associated with the harmonic potential controlling the arm length, e.g.…”

Section: Motion At Low Frequenciesmentioning

confidence: 99%

“…( 43)) or for a dumbbell swimmer including effects of inertia (ref. [42], eq. ( 2)): the lower the potential constant is (estimates in Appendix A yield k ≈ 10 −5 l.u.…”

Section: Swimmer Velocitiesmentioning

confidence: 99%

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Optimal motion of triangular magnetocapillary swimmers

Sukhov

Ziegler

Xie

et al. 2019

The Journal of Chemical Physics

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A system of ferromagnetic particles trapped at a liquid-liquid interface and subjected to a set of magnetic fields (magnetocapillary swimmers) is studied numerically using a hybrid method combining the pseudopotential lattice Boltzmann method and the discrete element method. After investigating the equilibrium properties of a single, two and three particles at the interface, we demonstrate a controlled motion of the swimmer formed by three particles. It shows a sharp dependence of the average center-of-mass speed on the frequency of the time-dependent external magnetic field. Inspired by experiments on magnetocapillary microswimmers, we interpret the obtained maxima of the swimmer speed by the optimal frequency centered around the characteristic relaxation time of a spherical particle. It is also shown that the frequency corresponding to the maximum speed grows and the maximum average speed decreases with increasing inter-particle distances at moderate swimmer sizes. The findings of our lattice Boltzmann simulations are supported by bead-spring model calculations.arXiv:1901.02241v2 [cond-mat.soft]

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Section: Swimmer Velocitiesmentioning

confidence: 89%

Section: Motion At Low Frequenciesmentioning

confidence: 99%

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Optimal motion of triangular magnetocapillary swimmers

Sukhov

Ziegler

Xie

et al. 2019

The Journal of Chemical Physics

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“…Hence the correction terms to particle interaction found here might allow for a rotation due to the viscosity gradient also for uniaxial swimmers (Najafi & Golestanian 2004; Dombrowski & Klotsa 2020; Hubert et al. 2021). Such a result would coincide with the recently reported viscotaxis for uniaxial squirmers (Datt & Elfring 2019; Shaik & Elfring 2021).…”

Section: Discussionmentioning

confidence: 85%

Hydrodynamic particle interactions in linear and radial viscosity gradients

Ziegler

Smith

2022

J. Fluid Mech.

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We present a versatile perturbative calculation scheme to determine the leading-order correction to the mobility matrix for particles in a low-Reynolds-number fluid with spatially variant viscosity. To this end, we exploit the Lorentz reciprocal theorem and the reflection method in the far field approximation. To demonstrate how to apply the framework to a particular choice of a viscosity field, we first study particles in a finite-size, interface-like, linear viscosity gradient. The extent of the latter should be significantly larger than the particle separation. Both situations of symmetrically and asymmetrically placed particles within such an odd symmetric viscosity gradient are considered. As a result, long-range flow fields are identified that decay by one order slower than their constant-viscosity counterparts. Self-mobilities for particle rotations and translations are affected, while for asymmetric placement, additional correction appears for the latter. The mobility terms associated with hydrodynamic interactions between the particles also need to be corrected, in a placement-specific manner. While the results are derived for the system of two particles, they apply also to many-particle systems. Furthermore, we treat the viscosity gradients induced by two particles with temperatures different from that of the surrounding fluid. Assuming a linear relation between fluid temperature and viscosity, we find that both the self-mobilities of the particles as well as the mobility terms for hydrodynamic interactions increase for hot particles and decrease for cold particles.

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“…Due to the scallop theorem 3 the mean swimming velocity vanishes in the Stokes limit of high viscosity in all three models. The behavior beyond this limit in the Oseen model was studied recently by Hubert et al 4 to second order in the amplitude of the stroke. We commented that the mean swimming velocity can be evaluated in a first harmonics approximation in close agreement with the exact result, and that when expanded to second order in the amplitude and for large center-to-center distance, this agrees with the second order expression 5 .…”

Section: Introductionmentioning

confidence: 82%

Optimizing the Mean Swimming Velocity of a Model Two-sphere Swimmer

Felderhof

2022

Preprint

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The swimming of a two-sphere system oscillating in a viscous fluid is studied on the basis of simplified equations of motion which take account of both friction and inertial effects. In the model the friction follows from an Oseen approximation to the mobility matrix, and the inertial effects follow from a dipole approximation to the added mass matrix. The resulting mean swimming velocity is evaluated analytically in a first harmonics approximation. For specific choices of the parameters this is compared with the exact result following from a numerical calculation including higher harmonics. The Oseen-Dipole model is compared with the simpler Oseen* model, in which the added mass effects are approximated by just the effective mass of the single spheres and dipole interactions are neglected. The expression for the mean swimming velocity can be reduced to a dimensionless scaling form. For given viscosity and mass density of the fluid the frequency of the stroke and the ratio of radii can be chosen such that the swimming velocity is optimized.

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Scallop Theorem and Swimming at the Mesoscale

Cited by 19 publications

References 44 publications

Optimal motion of triangular magnetocapillary swimmers

Optimal motion of triangular magnetocapillary swimmers

Hydrodynamic particle interactions in linear and radial viscosity gradients

Optimizing the Mean Swimming Velocity of a Model Two-sphere Swimmer

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