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 twodimensional 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 (DraftingKissingTumbling), 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, perioddoubling 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 nondimensional 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:

arXiv eprints
 Pub Date:
 November 2016
 DOI:
 10.48550/arXiv.1611.09349
 arXiv:
 arXiv:1611.09349
 Bibcode:
 2016arXiv161109349V
 Keywords:

 Physics  Fluid Dynamics;
 Nonlinear Sciences  Chaotic Dynamics