Force Dipole Interactions in Membranes with Odd Viscosity

TL;DR

This paper develops a hydrodynamic model for force dipole interactions in membranes with odd viscosity, revealing unique chiral behaviors and dynamical regimes influenced by odd-viscous effects.

Contribution

It introduces an exact Green tensor for membranes with odd viscosity, enabling analysis of dipole interactions and collective dynamics with novel chiral effects.

Findings

Identification of hydrodynamic screening scales

Discovery of chiral relative motion due to odd viscosity

Observation of distinct dynamical regimes

Abstract

We develop a hydrodynamic framework for the interactions and collective dynamics of force dipoles embedded in a compressible fluid membrane supported by a shallow viscous subphase. Starting from the generalized two-dimensional Stokes equations with shear, dilatational, and odd (Hall) viscosities, we derive an exact real-space Green tensor using Hankel transforms. The resulting tensor is characterized by three hydrodynamic screening scales associated with shear, compressional, and odd-viscous modes, and smoothly reduces to the standard limiting cases of incompressible membranes and compressible parity-symmetric membranes, while also capturing the chiral response generated by odd viscosity. Using this Green tensor we obtain the velocity and vorticity fields generated by a force dipole and formulate the dynamical system governing interacting dipoles. The analysis reveals several distinct dynamical regimes and identifies observables that isolate the antisymmetric odd-viscous contribution to dipole interactions, including transverse drift and chiral relative motion.