Dynamics of two disks settling in a two-dimensional narrow channel: From periodic motion to vertical chain in Oldroyd-B fluid

TL;DR

This study numerically investigates how two disks settle in a narrow channel filled with Oldroyd-B fluid, revealing periodic interactions and chain formations influenced by elasticity and Mach numbers.

Contribution

It introduces a detailed numerical analysis of two-disk dynamics in Oldroyd-B fluids, highlighting conditions for periodic motion and chain formation based on elasticity and Mach numbers.

Findings

Periodic disk interactions occur without elastic force.

Chain formation depends on elasticity and Mach numbers.

Tilted or vertical chains are observed based on parameters.

Abstract

In this article we present a numerical study of the dynamics of two disks settling in a narrow vertical channel filled with Oldroyd-B fluid. Two kinds of particle dynamics are obtained: (i) periodic interaction between two disks and (ii) the chain formation of two disks. For the periodic interaction of two disks, two different motions are obtained: (a) two disks stay far apart and interact periodically and (b) two disks interact closely and then far apart in a periodic way, like the drafting, kissing and tumbling of two disks sedimenting in Newtonian fluid, due to the lack of strong enough elastic force. For the formation of two disk chain occurred at higher values of the elasticity number, it is either a tilted chain or a vertical chain. The tilted chain can be obtained for either that the elasticity number is less than the critical value for having the vertical chain or that the Mach number is greater than the critical value for a long body to fall broadside-on. Hence the values of the elasticity number and the Mach number determine whether the the chain can be formed and the orientation of the chain.