Basset-Boussinesq history force and inertia are relevant for unsteady particle settling dynamics

TL;DR

This study experimentally demonstrates the importance of history forces and vortex dynamics in unsteady particle settling, challenging traditional steady-state assumptions and highlighting the algebraic relaxation behavior near Reynolds number unity.

Contribution

It provides experimental validation of the Basset-Boussinesq-Oseen equation and reveals vortex ring formation and lagging effects in unsteady settling near Re=1.

Findings

Algebraic relaxation to terminal velocity observed

Vortex ring forms and drifts around the sphere

Lagging vortex ring appears near Re=1

Abstract

Our experiments on a sphere falling under gravity in Stokes flow show significant history effects. We observe an algebraic, not exponential, relaxation rate to the terminal velocity, validating the solution to the Basset-Boussinesq-Oseen equation. Unlike in steady Stokes theory, our experiments and theory reveal a vortex ring forming around the sphere and drifting away. As the Reynolds number nears unity, the vortex ring lags behind the sphere, departing from Stokesian theory, though the sphere's algebraic response persists. These findings are critical for interactions in the Stokes limit.