Basset-Boussinesq history force of a fluid sphere.

Dominique Legendre (1) , Azeddine Rachih (2, 1) , Claire Souilliez (3, 1) , Sophie Charton (2) , Éric Climent (1)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)
3 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

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.

Mots clés: Drop; History force

Domaines: Mécanique des fluides [physics.class-ph]; Physique Nucléaire Expérimentale [nucl-ex]

Dominique Legendre, Azeddine Rachih, Claire Souilliez, Sophie Charton, Éric Climent. Basset-Boussinesq history force of a fluid sphere.. Physical Review Fluids, 2019, 4 (7), pp.073603. ⟨10.1103/PhysRevFluids.4.073603⟩. ⟨cea-02535280⟩