Force Dipole Interactions in Membranes with Odd Viscosity

Sneha Krishnan; Udaya Maurya; Rickmoy Samanta

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arXiv · 2603.07830

Force Dipole Interactions in Membranes with Odd Viscosity

Sneha Krishnan·Udaya Maurya·Rickmoy Samanta

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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.

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Sneha Krishnan, Udaya Maurya, Rickmoy Samanta. 2026-03-08. Force Dipole Interactions in Membranes with Odd Viscosity. https://arxiv.org/abs/2603.07830

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