Basset-Boussinesq history force of a fluid sphere

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.