Quenched Dipole Pairs in Viscous Fluid Membranes across the Saffman Crossover: Integrable Hamiltonian Dynamics
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arXiv
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| Autori principali: | , , , , , , , , , |
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| Natura: | Preprint |
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2026
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| author | Bhattacharya, Satyagni Dey, Debdatta Jain, Samyak Khan, Yassir Mazumder, Tirthankar Seth, Aryaman Mihir Mogalapalli, Nikhil Tiwari, Divyansh Vemparala, Pravallika Samanta, Rickmoy |
| author_facet | Bhattacharya, Satyagni Dey, Debdatta Jain, Samyak Khan, Yassir Mazumder, Tirthankar Seth, Aryaman Mihir Mogalapalli, Nikhil Tiwari, Divyansh Vemparala, Pravallika Samanta, Rickmoy |
| contents | We investigate an analytic theory of force-dipole hydrodynamics in a viscous membrane coupled to an infinite surrounding fluid, focusing on quenched (orientation-fixed) dipoles. While the single-dipole flow exhibits the known Saffman crossover from a near-field $v\sim r^{-1}$ to a screened far-field $v\sim r^{-2}$, we show that this crossover induces a qualitatively new reorganization of dipole--dipole interactions. For two identical quenched dipoles, the near-field dynamics is exactly solvable and effectively one-dimensional, with a fixed line of centers and linear evolution of the squared separation. In the far field, the system remains integrable but becomes intrinsically two-dimensional, with coupled radial and angular dynamics and an exact first integral. For pullers, the angular dynamics drives alignment toward an attracting manifold, leading to universal late-time collapse $R\sim (t_c-t)^{1/3}$, in contrast to the near-field scaling $R\sim (t_c-t)^{1/2}$. The Saffman crossover thus reorganizes the Hamiltonian phase-space structure of dipolar interactions and produces a transition from effectively one-dimensional to fully coupled dynamics, providing a minimal framework for aggregation in viscous fluid membranes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23868 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quenched Dipole Pairs in Viscous Fluid Membranes across the Saffman Crossover: Integrable Hamiltonian Dynamics Bhattacharya, Satyagni Dey, Debdatta Jain, Samyak Khan, Yassir Mazumder, Tirthankar Seth, Aryaman Mihir Mogalapalli, Nikhil Tiwari, Divyansh Vemparala, Pravallika Samanta, Rickmoy Soft Condensed Matter Exactly Solvable and Integrable Systems Biological Physics Fluid Dynamics We investigate an analytic theory of force-dipole hydrodynamics in a viscous membrane coupled to an infinite surrounding fluid, focusing on quenched (orientation-fixed) dipoles. While the single-dipole flow exhibits the known Saffman crossover from a near-field $v\sim r^{-1}$ to a screened far-field $v\sim r^{-2}$, we show that this crossover induces a qualitatively new reorganization of dipole--dipole interactions. For two identical quenched dipoles, the near-field dynamics is exactly solvable and effectively one-dimensional, with a fixed line of centers and linear evolution of the squared separation. In the far field, the system remains integrable but becomes intrinsically two-dimensional, with coupled radial and angular dynamics and an exact first integral. For pullers, the angular dynamics drives alignment toward an attracting manifold, leading to universal late-time collapse $R\sim (t_c-t)^{1/3}$, in contrast to the near-field scaling $R\sim (t_c-t)^{1/2}$. The Saffman crossover thus reorganizes the Hamiltonian phase-space structure of dipolar interactions and produces a transition from effectively one-dimensional to fully coupled dynamics, providing a minimal framework for aggregation in viscous fluid membranes. |
| title | Quenched Dipole Pairs in Viscous Fluid Membranes across the Saffman Crossover: Integrable Hamiltonian Dynamics |
| topic | Soft Condensed Matter Exactly Solvable and Integrable Systems Biological Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2604.23868 |