Capillary lubrication of a spherical particle near a fluid interface

TL;DR

This paper investigates how a sphere moving near a fluid interface experiences modified hydrodynamic forces and torques due to capillary-induced interface deformation, combining lubrication theory and perturbation analysis.

Contribution

It provides a detailed characterization of the hydrodynamic forces and torques on a sphere near a deformable fluid interface, highlighting the effects of capillary compliance.

Findings

Capillary deformation causes long-range interface effects.

Hydrodynamic forces are significantly altered by surface tension.

Numerical and scaling analyses quantify force modifications.

Abstract

The lubricated motion of an object near a deformable boundary presents striking subtleties arising from the coupling between the elasticity of the boundary and lubricated flow, including but not limited to the emergence of a lift force acting on the object despite the zero Reynolds number. In this study, we characterize the hydrodynamic forces and torques felt by a sphere translating in close proximity to a fluid interface, separating the viscous medium of the sphere's motion from an infinitely-more-viscous medium. We employ lubrication theory and perform a perturbation analysis in capillary compliance. The dominant response of the interface owing to surface tension results in a long-ranged interface deformation, which leads to a modification of the forces and torques with respect to the rigid reference case, that we characterise in details with scaling arguments and numerical integrations.