Role of symmetry in driven propulsion at low Reynolds number

Johannes Sachs, Konstantin I. Morozov, Oded Kenneth, Tian Qiu, Nico Segreto, Peer Fischer, and Alexander M. Leshansky
Phys. Rev. E 98, 063105 – Published 12 December 2018
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Abstract

We theoretically and experimentally investigate low-Reynolds-number propulsion of geometrically achiral planar objects that possess a dipole moment and that are driven by a rotating magnetic field. Symmetry considerations (involving parity P̂ and charge conjugation Ĉ) establish correspondence between propulsive states depending on orientation of the dipolar moment. Although basic symmetry arguments do not forbid individual symmetric objects to efficiently propel due to spontaneous symmetry breaking, they suggest that the average ensemble velocity vanishes. Some additional arguments show, however, that highly symmetrical (P̂-even) objects exhibit no net propulsion while individual less symmetrical (ĈP̂-even) propellers do propel. Particular magnetization orientation, rendering the shape ĈP̂-odd, yields unidirectional motion typically associated with chiral structures, such as helices. If instead of a structure with a permanent dipole we consider a polarizable object, some of the arguments have to be modified. For instance, we demonstrate a truly achiral (P̂- and ĈP̂-even) planar shape with an induced electric dipole that can propel by electrorotation. We thereby show that chirality is not essential for propulsion due to rotation-translation coupling at low Reynolds number.

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  • Received 3 August 2017
  • Revised 16 November 2018

DOI:https://doi.org/10.1103/PhysRevE.98.063105

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid DynamicsCondensed Matter, Materials & Applied PhysicsInterdisciplinary Physics

Authors & Affiliations

Johannes Sachs1,2, Konstantin I. Morozov3, Oded Kenneth4, Tian Qiu1, Nico Segreto2, Peer Fischer1,2,*, and Alexander M. Leshansky3,†

  • 1Max Planck Institute for Intelligent Systems, Heisenbergstraße 3 70569 Stuttgart, Germany
  • 2Institute of Physical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
  • 3Department of Chemical Engineering, Technion–IIT, Haifa, 32000, Israel
  • 4Department of Physics, Technion–IIT, Haifa, 32000, Israel

  • *fischer@is.mpg.de
  • lisha@technion.ac.il

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Issue

Vol. 98, Iss. 6 — December 2018

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