Drag and torque coefficients of a translating particle with slip at a gas-liquid interface

TL;DR

This paper analytically investigates how interfacial deformations influence the hydrodynamic forces and torques on a slip-moving spherical particle at a gas-liquid interface, considering physical parameters and particle interactions.

Contribution

It introduces a two-parameter asymptotic model and applies the Lorentz reciprocal theorem to analytically derive drag and torque, accounting for interface deformation effects and particle interactions.

Findings

Interfacial deformations significantly affect particle forces and torques.

Physical parameters like contact angle, Bond number, and slip coefficient influence particle dynamics.

Interaction forces between particles are dipolar and depend on azimuthal angle.

Abstract

The dynamics of colloid-size particles trapped at a liquid interface is an extensively studied problem owing to its relevance to a wide range of engineering applications. Here we investigate the impact of interfacial deformations on the hydrodynamic force and torque exerted on a spherical particle with surface slip moving along a gas-liquid interface. Following a two-parameter asymptotic modeling approach, we perturb the interface from its planar state and apply the Lorentz reciprocal theorem to the zeroth and first-order approximations to analytically calculate the drag and torque on the particle. This allows us to explicitly account for the effect of physical parameters like the three-phase contact angle, the Bond number, and the slip coefficient on the particle motion. In addition, we study the interactions between two translating and rotating particles at a large separation. The interaction forces and torques exerted by the flow-induced deformations are calculated via the linear superposition approximation, where the interaction forces are identified as dipolar in terms of the azimuthal angle.