Sliding of a liquid spherical droplet in an external insoluble liquid at low Reynolds numbers

Peter Lebedev-Stepanov

Published 2025-02-05Version 1

The experiment shows that small liquid droplets under the action of gravity and the Archimedes force move in the external viscous liquid practically according to the Stokes drag force equation, and not in accordance with the Hadamard-Rybczynski formula, which was specially developed to describe the motion of a liquid droplet in an external viscous liquid. Various mechanisms are proposed to explain this: increased viscosity at the interface between two liquids and the presence of unaccounted surfactants. However, there is another fundamental mechanism that has not been taken into account. It can be expected that the velocities of such liquids, insoluble in each other, may not equalize at the boundary of the droplet. No slip condition may be may be unnatural at the droplet interface. Instead, one could require the continuity of all components of the viscous stress tensor on the interface without exception. In this paper, it is shown that this approach gives a droplet velocity that coincides with the Stokes drag force formula for a sphere of a given radius.