2025/06/13 by Brendan Harding, Harding, Brendan, Rahil N. Valani +3
Engineering · Physics and Astronomy · #37N10 #37N25 #70H99 #76T20 #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #Experimental and Theoretical Physics Studies #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Micro and Nano Robotics #Particle Dynamics in Fluid Flows
paper · pdf · doi:10.48550/arxiv.2506.11388
openalex publication_date 2025/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.