Marangoni stress induced by rotation frustration in a liquid foam

TL;DR

This paper investigates how surface tension gradients influence the apparent viscosity of liquid foams by modeling bubble dynamics and shear effects, highlighting the importance of interface rheology and bubble rotation in foam behavior.

Contribution

It introduces a simplified 2D hexagonal bubble model to analyze the impact of surface tension gradients and shear on foam rheology, emphasizing the role of interface rheology in foam dynamics.

Findings

Surface tension continuity determines bubble rotation rate.

Shear induces Marangoni stresses affecting foam viscosity.

Thin film dynamics are crucial at the whole bubble interface scale.

Abstract

The role of surface tension gradients in the apparent viscosity of liquid foams remains largely unexplained. In this article, we develop a toy-model based on a periodic array of 2D hexagonal bubbles, each bubble being separated from its neighbors by a liquid film of uniform thickness. The two interfaces of this thin liquid film are allowed to slide relatively to each other, thus shearing the liquid phase in between. We solve the dynamics under external shear of this minimal system and we show that the continuity of the surface tension around the whole bubble is the relevant condition to determine the bubble rotation rate and the energy dissipation. This result is expected to be robust in more complex situations and illustrates that thin film dynamics should be solve at the scale of the whole bubble interface when interface rheology matters.