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Hubert M, Trosman O, Collard Y, Sukhov A, Harting J, Vandewalle N, Smith AS. Scallop Theorem and Swimming at the Mesoscale. PHYSICAL REVIEW LETTERS 2021; 126:224501. [PMID: 34152187 DOI: 10.1103/physrevlett.126.224501] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 04/28/2021] [Indexed: 06/13/2023]
Abstract
By comparing theoretical modeling, simulations, and experiments, we show that there exists a swimming regime at low Reynolds numbers solely driven by the inertia of the swimmer itself. This is demonstrated by considering a dumbbell with an asymmetry in coasting time in its two spheres. Despite deforming in a reciprocal fashion, the dumbbell swims by generating a nonreciprocal Stokesian flow, which arises from the asymmetry in coasting times. This asymmetry acts as a second degree of freedom, which allows the scallop theorem to be fulfilled at the mesoscopic scale.
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Affiliation(s)
- M Hubert
- PULS Group, Department of Physics and Interdisciplinary Center for Nanostructured Films, FAU Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - O Trosman
- PULS Group, Department of Physics and Interdisciplinary Center for Nanostructured Films, FAU Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Y Collard
- GRASP, Research unit CESAM, Institute of Physics B5a, Université de Liège, 4000 Liège, Belgium
| | - A Sukhov
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, 90429 Nürnberg, Germany
| | - J Harting
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, 90429 Nürnberg, Germany
- Department of Chemical and Biological Engineering and Department of Physics, FAU Erlangen-Nürnberg, 90429 Nürnberg, Germany
| | - N Vandewalle
- GRASP, Research unit CESAM, Institute of Physics B5a, Université de Liège, 4000 Liège, Belgium
| | - A-S Smith
- PULS Group, Department of Physics and Interdisciplinary Center for Nanostructured Films, FAU Erlangen-Nürnberg, 91058 Erlangen, Germany
- Group for Computational Life Sciences, Division of Physical Chemistry, Ruđer Boskovic Institute, 10000 Zagreb, Croatia
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Felderhof BU. Collinear velocity relaxation of two spheres in a viscous incompressible fluid. Phys Rev E 2020; 101:043103. [PMID: 32422701 DOI: 10.1103/physreve.101.043103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2019] [Accepted: 03/18/2020] [Indexed: 11/07/2022]
Abstract
Collinear velocity relaxation of two spheres immersed in a viscous incompressible fluid is studied on the basis of an approximate expression for the retarded hydrodynamic interaction. After a sudden impulse applied to one sphere, the other one instantaneously starts to move as well, with amplitude determined by the added mass effect. The velocities of both spheres eventually decay with a t^{-3/2} long-time tail, but the relative velocity decays with a t^{-5/2} long-time tail. The three relaxation functions are approximated by simple expressions involving only a small number of poles in the complex square root of frequency plane.
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Affiliation(s)
- B U Felderhof
- Institut für Theorie der Statistischen Physik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
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