Despite the prevalence of surface bubbles in many natural phenomena and engineering applications, the effect of surfactants on their surface residence time is not clear. Numerous experimental studies and theoretical models exist but a clear understanding of the film drainage phenomena is still lacking. In particular, theoretical works predicting the drainage rate of the thin film between a bubble and the free surface in the presence and absence of surfactants usually make use of the lubrication theory. On the other hand, in numerous natural situation and experimental works, the bubble approaches the free surface from a certain distance and forms a thin film at a later stage. This paper attempts to bridge these two approaches. In particular, in this paper, we review these works, and compare them to our Direct Numerical Simulations where we study the coupled influence of bubble deformation and surfactants on the rising and drainage process of a bubble beneath a free surface. In the present study, the level-set method is used to capture the air-liquid interfaces and the transport equation of surfactants is solved in an Eulerian framework. The axisymmetric simulations capture the bubble acceleration, deformation and rest (or drainage) phases from non-deformable to deformable bubbles, as measured by the Bond number (Bo), and from surfactant-free to surfactant coated bubbles, as measured by the Langmuir number (La). The results show that the distance h between the bubble and the free surface decays exponentially for surfactant-free interfaces (La = 0) and this decay is faster for non-deformable bubbles (Bo 1) than for deformable ones (Bo 1). The presence of surfactants (La > 0) slows down the decay of h, exponentially for large bubbles (Bo 1) and algebraically for small ones (Bo 1). For Bo ∼ 1, the lifetime is the longest and associated to (Marangoni) elasticity of the interfaces.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.