Force Dipole Interactions in Membranes with Odd Viscosity
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914379572707328 |
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| author | Krishnan, Sneha Maurya, Udaya Samanta, Rickmoy |
| author_facet | Krishnan, Sneha Maurya, Udaya Samanta, Rickmoy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07830 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Force Dipole Interactions in Membranes with Odd Viscosity Krishnan, Sneha Maurya, Udaya Samanta, Rickmoy Soft Condensed Matter Mathematical Physics Biological Physics Fluid Dynamics 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. |
| title | Force Dipole Interactions in Membranes with Odd Viscosity |
| topic | Soft Condensed Matter Mathematical Physics Biological Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2603.07830 |