Lorentz Reciprocal Theorem in Fluids with Odd Viscosity

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.Received 24 May 2023Accepted 29 September 2023DOI:https://doi.org/10.1103/PhysRevLett.131.178303Published 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.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChiralityLow Reynolds number flowsPhysical SystemsLiving matter & active matterMicroswimmersPropertiesViscosityFluid Dynamics

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