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Sedimentation of a single soluble particle at low Reynolds and high Péclet numbers

Nan He*, Yutong Cui, David Wai Quan Chin, Thierry Darnige, Philippe Claudin, and Benoît Semin†

  • PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université Paris Cité, F-75005, Paris, France

  • *nan.he@espci.fr
  • †benoit.semin@espci.fr
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Phys. Rev. Fluids 9, 044502 – Published 22 April, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.044502

Abstract

We investigate experimentally the dissolution of an almost spherical butyramide particle during its sedimentation, in the low Reynolds high Péclet regime. The particle sediments in a quiescent aqueous solution, and its shape and position are measured simultaneously by a camera attached to a translation stage. The particle is tracked in real time, and the translation stage moves accordingly to keep the particle in the field of the camera. The measurements from the particle image show that the radius shrinking rate is constant with time, and independent of the initial radius of the particle. We explain this with a simple model, based on the sedimentation law in the Stokes' regime and the mass transfer rate at low Reynolds and high Péclet numbers. The theoretical and experimental results are consistent within 20%. We introduce two correction factors to take into account the nonsphericity of the particle and the inclusions of air bubbles inside the particle, and reach quantitative agreement. With these corrections, the indirect measurement of the radius shrinking rate deduced from the position measurement is also in agreement with the model. We discuss other correction factors, and explain why they are negligible in the present experiment. We also compute the effective Sherwood number as a function of an effective Péclet number.

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Phys. Rev. Fluids 9, 044502– Published 22 April, 2024
  • Received 24 October 2023
  • Accepted 20 March 2024
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