Landau-Levich Enhanced Cheerios Effect

TL;DR

This study investigates how retraction speed enhances capillary attraction between fibers, revealing a significant increase in force due to dynamical meniscus shape changes, with implications for industrial and biological applications.

Contribution

It introduces an experimental method to measure dynamic capillary forces, demonstrates the inadequacy of classical theory at high speeds, and provides an analytical model for fiber attraction.

Findings

Retraction speed increases capillary force by up to ten times.

Dynamical meniscus shape depends on the capillary number, deviating from classical theory.

An analytical expression accurately predicts the enhanced attraction.

Abstract

We study the capillary attraction force between two fibers dynamically withdrawn from a bath. We propose an experimental method to measure this force and show that its magnitude strongly increases with the retraction speed by up to a factor ten compared to the static case. We show that this remarkable increase stems from the shape of the dynamical meniscus between the two fibers. We first study the dynamical meniscus around one fiber, and obtain experimental and numerical scaling of its size increase with the capillary number, which is not captured by the classical Landau-Levich-Derjaguin theory. We then show that the shape of the deformed air-liquid interface around two fibers can be inferred from the linear superposition of the interface around a single fiber. These results yield an analytical expression for the attraction which compares well with the experimental data. Our study reveals the critical role of the retraction speed to create stronger capillary interactions, with potential applications in industry or biology.