Active particle motion in Poiseuille flow through rectangular channels
arxiv(2024)
摘要
We investigate the dynamics of a point-like active particle suspended in
fluid flow through a straight channel. For this particle-fluid system, we
derive a constant of motion for a general unidirectional fluid flow, and apply
it to an approximation of Poiseuille flow through rectangular cross-sections.
For a given rectangular cross-section, this results in a 4D nonlinear
conservative dynamical system with one constant of motion and a dimensionless
parameter as the ratio of maximum flow speed to intrinsic active particle
speed. We observe a diverse set of active particle trajectories with variations
in system parameters and initial conditions which we classify into different
types of swinging, trapping, tumbling and wandering motion. Regular
(periodic/quasiperiodic) motion as well as chaotic active particle motion are
observed for these trajectories and quantified using largest Lyapunov
exponents. We explore the transition to chaotic motion using Poincaré maps
and show “sticky" chaotic tumbling trajectories that have long transients near
a periodic state. Outcomes of this work may have implications for dynamics of
natural and artificial microswimmers in experimental microfluidic channels that
typically have rectangular cross-sections.
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