Lifetime of Surface Bubbles in Surfactant Solutions

Abstract

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.

Bubbles determine the amount of alcohol in Mezcal

“…We have conducted many more simulations and analyses to further understand this effect. These results can be found in Atasi et al 43 .…”

“…It is important to note that this effect has not been discussed in-depth in the literature. Some initial tests and discussions can be found in Atasi et al 43 .…”

The Life of a Surface Bubble

“…Their experiments with silicon oil and quite large bubble (Bo > 1) give a g ∼ 0.21 considering τ = τ B which is consistent even though lower than their analytical model that proposed a g = 1.25 (see [34]). Numerical simulations, based on Stokes equation (no inertia, Re = 0), confirm the exponential decay of the film thickness [28] and show a decay of a with the Bond number Bo B which tends to a g∞ = 0.34, in the limit of large bubbles (large Bo) [17,34]. This result implies that in normalized time, the smaller the bubble, the faster it drains.…”

“…Finally, recent numerical simulations of viscous bubbles (Re = 0.1) have modelled the thinning of the film on top of surface bubbles in presence of surfactants [17], thus the interfaces are not bare anymore. The simulations are able to model Marangoni stress induced by the inhomogeneity of surface tension due to surfactants concentration variation at the interfaces.…”

“…Then, once the bubble is entrapped in a bulk liquid, the density difference fosters a movement that eventually brings the bubble to the surface. A typical distance for a rising bubble to reach its terminal velocity is one centimeter [16,17]. During this process, the shear stresses induced by the flow may accumulate surfactants at the bottom of the bubble and affect the bubble shape and rising velocity.…”