Three-dimensional dynamics of falling films in the presence of insoluble surfactants

TL;DR

This study investigates how insoluble surfactants affect the three-dimensional wave behavior of falling liquid films using numerical simulations validated by experiments, revealing significant impacts on wave shape and interface dynamics.

Contribution

It introduces a hybrid numerical method to simulate surfactant effects on falling films and provides new insights into wave modifications due to Marangoni stresses.

Findings

Surfactants significantly alter wave topology and dynamics.

Marangoni stresses suppress wave peaks and capillary structures.

High Marangoni numbers cause near rigidification of the interface.

Abstract

We study the effect of insoluble surfactants on the wave dynamics of vertically-falling liquid films. We use three-dimensional numerical simulations and employ a hybrid interface-tracking/level-set method, taking into account Marangoni stresses induced by gradients of interfacial surfactant concentration. Our numerical predictions for the evolution of the surfactant-free, three-dimensional wave topology are validated against the experimental work of Park & Nosoko (2003). The addition of surfactants is found to influence significantly the development of horseshoe-shaped waves. At low Marangoni numbers, we show that the wave fronts exhibit spanwise oscillations before eventually acquiring a quasi two-dimensional shape. In addition, the presence of Marangoni stresses are found to suppress the peaks of the travelling waves and preceding capillary wave structures. At high Marangoni numbers, a near complete rigidification of the interface is observed.