Contactless indentation of a soft boundary by a rigid particle in shear flow

TL;DR

This paper investigates how a rigid particle interacts with a fluid-fluid interface under shear flow, revealing stable contact states and limitations of classical lubrication theory, and proposing a gap renormalization model for better accuracy.

Contribution

It introduces a gap renormalization model that extends classical lubrication theory, accurately describing contactless indentation of a soft boundary by a rigid particle in shear flow.

Findings

Particles can stably contact the interface under sufficient downward force.

Classical lubrication theory fails near equilibrium contact, requiring the new model.

The gap renormalization model aligns well with numerical and experimental data.

Abstract

The dynamics of a rigid particle above a fluid-fluid interface in shear flow is studied here numerically and analytically as a function of the downward force applied on the particle. It is found here that the particle goes below the equilibrium level of the interface for a strong enough downward force. Such states remain stable under flow, with a fluid film of a well-defined thickness separating the particle from the indented interface. This result contradicts the classical lubrication theory, which predicts an infinitely large downward force being necessary for the particle to approach the equilibrium level of the interface. It is found that the classical lubrication approximation is only valid in a narrow range of shear rates, which shrinks to a point when the particle approaches the equilibrium level of the interface. The gap renormalization model, proposed here, cures this limitation of the classical lubrication theory, showing quantitative agreement with the numerical results when the particle touches the equilibrium level of the interface. It is found that the gap renormalization model provides a quantitative interpretation of the recent experimental results, including the range of particle heights above the interface for which the classical lubrication approximation breaks down.