Liquid meniscus friction on a wet plate: Bubbles, lamellae and foams

TL;DR

This paper reviews the viscous forces acting on a liquid meniscus on wet surfaces, analyzing theoretical models and experimental data, especially for rigid interfaces, and predicts stress on foams in such conditions.

Contribution

It provides a comprehensive review of viscous force models for menisci with simple interfacial properties and offers new predictions for foam stress on wet solids.

Findings

Viscous force scales as Ca^{1/3} and Ca^{2/3} for rigid interfaces.

Theoretical predictions align with experimental data for incompressible interfaces.

The study enhances understanding of meniscus dynamics in microfluidics and coating processes.

Abstract

Many microfluidics devices, coating processes or diphasic flows involve the motion of a liquid meniscus on a wet wall. This motion induces a specific viscous force, that exhibits a non-linear dependency in the meniscus velocity. We propose a review of the theoretical and experimental work made on this viscous force, for simple interfacial properties. The interface is indeed assumed either perfectly compressible (mobile interface) or perfectly incompressible (rigid interface). We show that, in the second case, the viscous force exerted by the wall on the meniscus is a combination of two power laws, scaling like $Ca^{1/3}$ and $Ca^{2/3}$, with $Ca$ the capillary number. We provide a prediction for the stress exerted on a foam sliding on a wet solid and compare it with experimental data, for the incompressible case.