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  • Letter

Stokesian settling from quiescence: Experiments and theory on history effects and unsteady flow structures

Tomek Jaroslawski1,*, Divya Jaganathan2, Rama Govindarajan2, and Beverley J. McKeon1

  • *Contact author: tomek@stanford.edu

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.

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