Drag and diffusion coefficients of a spherical particle attached to a fluid interface

TL;DR

This paper derives analytical formulas for the drag and diffusion of spherical particles at fluid interfaces, accounting for contact angle effects, and validates the model with experimental and numerical data.

Contribution

It introduces a perturbation-based analytical model for particle drag and diffusion at fluid interfaces, considering contact angle dependence and extending to higher-order calculations.

Findings

Good agreement with experimental data for contact angles below 90°

Model allows calculation of coefficients up to second order in perturbation

Applicable to other particle shapes with known flow fields

Abstract

Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The model is designed to explicitly account for the dependence on the contact angle between the two fluids and the solid surface. The Lorentz reciprocal theorem is applied in the context of a geometric perturbation approach, which is based on the deviation of the contact angle from a 90{\deg}-value. By testing the model against experimental and numerical data from the literature, good agreement is found within the entire range of contact angles below 90{\deg}. As an advantage of the method reported, the drag and diffusion coefficients can be calculated up to second order in the perturbation parameter, while it is sufficient to know the velocity and pressure fields only up to first order. Extensions to other particle shapes with known velocity and pressure fields are straightforward.