Settling of an asymmetric dumbbell in a quiescent fluid

TL;DR

This paper analyzes how an asymmetric dumbbell settles in a quiescent fluid, revealing that size differences and fluid inertia influence its orientation and settling behavior at small Reynolds numbers.

Contribution

It provides a detailed computation of the hydrodynamic torque on an asymmetric dumbbell, elucidating how size disparity and inertia determine its settling orientation.

Findings

Larger sphere leads to vertical settling when sizes differ greatly.

Small size differences cause a competition between size and Reynolds number affecting orientation.

Equal-sized spheres result in horizontal settling due to fluid inertia.

Abstract

We compute the hydrodynamic torque on a dumbbell (two spheres linked by a massless rigid rod) settling in a quiescent fluid at small but finite Reynolds number. The spheres have the same mass densities but different sizes. When the sizes are quite different the dumbbell settles vertically, aligned with the direction of gravity, the largest sphere first. But when the size difference is sufficiently small then its steady-state angle is determined by a competition between the size difference and the Reynolds number. When the sizes of the spheres are exactly equal then fluid inertia causes the dumbbell to settle in a horizontal orientation.