Chaotic sedimentation of particle pairs in a vertical channel at low Reynolds number: multiple states and routes to chaos

TL;DR

This study numerically investigates the sedimentation behavior of particle pairs in a vertical channel at low Reynolds numbers, revealing multiple stable states, routes to chaos, and complex bifurcation phenomena beyond classical oscillatory regimes.

Contribution

It demonstrates the existence of chaotic sedimentation regimes and complex bifurcation structures for particle pairs, expanding understanding beyond traditional regular oscillations.

Findings

Chaotic sedimentation can occur at low Reynolds numbers.

Multiple stable states and hysteresis are observed.

A global bifurcation diagram illustrates complex behaviors.

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.