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Lorentz Reciprocal Theorem in Fluids with Odd Viscosity

Yuto Hosaka1,*, Ramin Golestanian1,2,3,†, and Andrej Vilfan1,4,‡

  • 1Max Planck Institute for Dynamics and Self-Organization (MPI-DS), Am Fassberg 17, 37077 Göttingen, Germany
  • 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
  • 3Institute for the Dynamics of Complex Systems, University of Göttingen, 37077 Göttingen, Germany
  • 4Jožef Stefan Institute, 1000 Ljubljana, Slovenia

  • *yuto.hosaka@ds.mpg.de
  • †ramin.golestanian@ds.mpg.de
  • ‡andrej.vilfan@ds.mpg.de
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Phys. Rev. Lett. 131, 178303 – Published 25 October, 2023

DOI: https://doi.org/10.1103/PhysRevLett.131.178303

Abstract

The Lorentz reciprocal theorem—that is used to study various transport phenomena in hydrodynamics—is violated in chiral active fluids that feature odd viscosity with broken time-reversal and parity symmetries. Here, we show that the theorem can be generalized to fluids with odd viscosity by choosing an auxiliary problem with the opposite sign of the odd viscosity. We demonstrate the application of the theorem to two categories of microswimmers. Swimmers with prescribed surface velocity are not affected by odd viscosity, while those with prescribed active forces are. In particular, a torque dipole can lead to directed motion.

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References (65)

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Outline

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Phys. Rev. Lett. 131, 178303– Published 25 October, 2023
  • Received 24 May 2023
  • Accepted 29 September 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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