- Letter
Stokesian settling from quiescence: Experiments and theory on history effects and unsteady flow structures
Phys. Rev. Fluids 10, L062301 – Published 2 June, 2025
DOI: https://doi.org/10.1103/PhysRevFluids.10.L062301
Abstract
Our experiments on a sphere falling from rest under gravity in Stokes flow show the development of unsteady flow structures and significant history effects. Unlike in steady Stokes flow, we observe a vortex ring forming around the sphere and drifting away, which is captured by our unsteady Stokes theory. Consistently, we observe an algebraic, not exponential, relaxation rate of the sphere to its terminal velocity, validating the Basset-Boussinesq-Oseen equation, which is based on unsteady Stokes theory. 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 particle interactions in the Stokes limit.