Basset-Boussinesq history force of a fluid sphere

Dominique Legendre, Azeddine Rachih, Claire Souilliez, Sophie Charton, and Eric Climent
Phys. Rev. Fluids 4, 073603 – Published 26 July 2019

Abstract

We consider the Basset-Boussinesq (history) force experienced by a spherical drop. We seek to determine the kernel of the Basset-Boussinesq force when internal circulation of the fluid occurs. We first characterize the slip at a fluid-sphere interface. Under both steady and unsteady conditions, the corresponding slip length is remarkably uniform along the fluid-sphere interface and is directly related to the viscosity ratio. Combining the analytical expression of the Basset-Boussinesq kernel obtained for a solid sphere with the interface slip and the obtained description of the slip at the fluid-fluid interface, we are able to describe the Basset-Boussinesq history force acting on a spherical drop. This expression is valid whatever the viscosity ratio from bubbles to viscous drops.

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  • Received 7 April 2019

DOI:https://doi.org/10.1103/PhysRevFluids.4.073603

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Dominique Legendre1, Azeddine Rachih1,2, Claire Souilliez1, Sophie Charton2, and Eric Climent1

  • 1Institut de Mécanique des Fluides de Toulouse, Université de Toulouse, CNRS, INPT, UPS, 31400 Toulouse, France
  • 2CEA, DEN, MAR, DMRC, SA2I, 30207 Bagnols-sur-Cèze, France

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Vol. 4, Iss. 7 — July 2019

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