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Lorentz Reciprocal Theorem in Fluids with Odd Viscosity.

Yuto Hosaka¹, Ramin Golestanian^1,2,3, Andrej Vilfan^1,4

¹Max Planck Institute for Dynamics and Self-Organization (MPI-DS), Am Fassberg 17, 37077 Göttingen, Germany.

Physical Review Letters

|November 13, 2023

Summary

This summary is machine-generated.

The Lorentz reciprocal theorem is violated in chiral active fluids but can be generalized by using an auxiliary problem. This generalized theorem applies to microswimmers, revealing how odd viscosity affects their motion, particularly those with active forces.

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Area of Science:

Hydrodynamics
Active Matter Physics
Non-equilibrium Statistical Mechanics

Background:

The Lorentz reciprocal theorem is fundamental for studying transport phenomena in hydrodynamics.
Chiral active fluids with odd viscosity break time-reversal and parity symmetries, violating the standard theorem.
Understanding these violations is crucial for modeling complex fluid behaviors.

Purpose of the Study:

To generalize the Lorentz reciprocal theorem for chiral active fluids with odd viscosity.
To investigate the impact of odd viscosity on microswimmer dynamics.
To provide a theoretical framework for analyzing active fluid systems.

Main Methods:

Formulating a generalized Lorentz reciprocal theorem by introducing an auxiliary problem with opposite odd viscosity.
Analyzing two categories of microswimmers: those with prescribed surface velocity and those with prescribed active forces.
Applying the generalized theorem to specific microswimmer models, including those with torque dipoles.

Main Results:

The Lorentz reciprocal theorem can be successfully generalized to include odd viscosity.
Microswimmers with prescribed surface velocity are unaffected by odd viscosity.
Microswimmers with prescribed active forces are influenced by odd viscosity, with torque dipoles inducing directed motion.

Conclusions:

The generalized Lorentz reciprocal theorem offers a powerful tool for active fluid research.
Odd viscosity plays a significant role in the locomotion of certain active matter systems.
This work advances the understanding of non-reciprocal phenomena in chiral active fluids.