Analytical solution for the hydrodynamic resistance of a disk in a compressible fluid layer with odd viscosity on a rigid substrate

TL;DR

This paper derives an exact analytical solution for the hydrodynamic resistance of a disk moving in a compressible fluid with odd viscosity, revealing symmetry-breaking effects and extending understanding of chiral active fluids.

Contribution

It provides the first exact analytical solution for the flow and resistance of a disk in a fluid with odd viscosity, accounting for compressibility and symmetry considerations.

Findings

Resistance coefficients break Onsager reciprocity

Solution applies to arbitrary disk size

Resistance coefficients satisfy Onsager-Casimir reciprocity

Abstract

Chiral active fluids can exhibit odd viscosity, a property that breaks the time-reversal and parity symmetries. Here, we examine the hydrodynamic flows of a rigid disk moving in a compressible 2D fluid layer with odd viscosity, supported by a thin lubrication layer of a conventional fluid. Using the 2D Green's function in Fourier space, we derive an exact analytical solution for the flow around a disk of arbitrary size, as well as its resistance matrix. The resulting resistance coefficients break the Onsager reciprocity, but satisfy the Onsager-Casimir reciprocity to any order in odd viscosity.