Three-dimensional sedimentation patterns of two interacting disks in a viscous fluid

TL;DR

This study investigates the complex three-dimensional sedimentation behaviors of two flat disks in a viscous fluid using simulations and experiments, revealing how shape and flow conditions influence their motion patterns.

Contribution

It introduces a phase diagram classifying ten distinct sedimentation patterns based on disk shape and flow conditions, advancing understanding of disk interactions in viscous fluids.

Findings

Sedimentation patterns depend on disk shape and Reynolds number.

High Re promotes chaotic three-dimensional rotation.

Contact likelihood increases with smaller I* and Re.

Abstract

The sedimentation of two spherical solid objects in a viscous fluid has been extensively investigated and well understood. However, a pair of flat disks (in three dimensions) settling in the fluid shows more complex hydrodynamic behaviors. The present work aims to improve understanding of this phenomenon by performing Direct Numerical Simulations (DNS) and physical experiments. The present results show that the sedimentation processes are significantly influenced by disk shape, characterized by a dimensionless moment of inertia I*, and Reynolds number of the leading disk Re. For the flatter disks with smaller I*, steady falling with enduring contact transits to periodic swinging with intermittent contacts as Re increases. The disks with larger I* tend to fall in a Drafting-Kissing-Tumbling (DKT) mode at low Re and to remain separated at high Re. Based on I* and Re, a phase diagram is created to classify the two-disk falling into ten distinctive patterns. The planar motion or three-dimensional motion of the disks is determined primarily by Re. Turbulent disturbance flows at a high Re contribute to the chaotic three-dimensional rotation of the disks. The chance for the two disks to contact is increased when I* and Re are reduced.