A Hamiltonian formulation for the motion of an active spheroidal particle suspended in laminar straight duct flow
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arXiv
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| Format: | Preprint |
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2025
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| author | Harding, Brendan Valani, Rahil N. Stokes, Yvonne M. |
| author_facet | Harding, Brendan Valani, Rahil N. Stokes, Yvonne M. |
| contents | We analyse a generalisation of Zöttl and Stark's model of active spherical particles [Phys. Rev. Lett. 108, 218104 (2012)] and prolate spheroidal particles [Eur. Phys. J. E 36(1), 4 (2013)] suspended in cylindrical Poiseuille flow, to particle dynamics in an arbitrary unidirectional steady laminar flow through a straight duct geometry. Our primary contribution is to describe a Hamiltonian formulation of these systems and provide explicit forms of the constants of motions in terms of the arbitrary fluid velocity field. The Hamiltonian formulation provides a convenient and robust approach to the computation of particle orbits whilst also providing new insights into the dynamics, specifically the way in which orbits are trapped within basins defined by a potential well. In addition to considering spherical and prolate spheroidal particles, we also illustrate that the model can be adapted to oblate spheroidal particles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_11388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hamiltonian formulation for the motion of an active spheroidal particle suspended in laminar straight duct flow Harding, Brendan Valani, Rahil N. Stokes, Yvonne M. Fluid Dynamics Dynamical Systems Chaotic Dynamics 37N10, 37N25, 70H99, 76T20 We analyse a generalisation of Zöttl and Stark's model of active spherical particles [Phys. Rev. Lett. 108, 218104 (2012)] and prolate spheroidal particles [Eur. Phys. J. E 36(1), 4 (2013)] suspended in cylindrical Poiseuille flow, to particle dynamics in an arbitrary unidirectional steady laminar flow through a straight duct geometry. Our primary contribution is to describe a Hamiltonian formulation of these systems and provide explicit forms of the constants of motions in terms of the arbitrary fluid velocity field. The Hamiltonian formulation provides a convenient and robust approach to the computation of particle orbits whilst also providing new insights into the dynamics, specifically the way in which orbits are trapped within basins defined by a potential well. In addition to considering spherical and prolate spheroidal particles, we also illustrate that the model can be adapted to oblate spheroidal particles. |
| title | A Hamiltonian formulation for the motion of an active spheroidal particle suspended in laminar straight duct flow |
| topic | Fluid Dynamics Dynamical Systems Chaotic Dynamics 37N10, 37N25, 70H99, 76T20 |
| url | https://arxiv.org/abs/2506.11388 |