Hamiltonian formulation for the motion of an active spheroidal particle suspended in laminar straight duct flow
Date
2025
Authors
Harding, B.
Valani, R.N.
Stokes, Y.M.
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Journal article
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Physical Review E, 2025; 112(5):054125-1-054125-19
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Brendan Harding, Rahil N. Valani, Yvonne M. Stokes
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Abstract
We analyze a generalization 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, 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 while 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.
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©2025 American Physical Society.