Chaotic sedimentation of particle pairs in a vertical channel at low Reynolds number: multiple states and routes to chaos
Abstract
The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding to a maximum effective blockage ratio, and performing a quasiperiodic transition to chaos under increasing the particle weight. For less inertial regimes, the classical oblique doublet structure and its complex behavior (multiple stable states and hysteresis, period-doubling cascade and chaotic attractor) are recovered, in agreement with previous work [Aidun & Ding, Physics of Fluids 15(6), 2003]. As a consequence of these various behaviors, the link between the terminal Reynolds number and the non-dimensional driving force is complex: it contains several branches displaying hysteresis as well as various bifurcations. For the range of Reynolds number considered here, a global bifurcation diagram is given.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2016
- DOI:
- 10.48550/arXiv.1611.09349
- arXiv:
- arXiv:1611.09349
- Bibcode:
- 2016arXiv161109349V
- Keywords:
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- Physics - Fluid Dynamics;
- Nonlinear Sciences - Chaotic Dynamics