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 work predicting the drainage rate of the thin film between a bubble and the free surface in the presence and absence of surfactants usually makes use of the lubrication theory. On the other hand, in numerous natural situations and experimental works, the bubble approaches the free surface from a certain distance and forms a thin film at a later stage. This article attempts to bridge these two approaches. In particular, in this article, 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 nondeformable 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 nondeformable bubbles (Bo ≪ 1) than for deformable ones (Bo ≫ 1). The presence of surfactants (La > 0) slows 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 is associated with the (Marangoni) elasticity of the interfaces.

Highlights

  • Mezcal is a traditional Mexican spirit, obtained from the distillation of fermented agave juices

  • According to popular accounts and a few formal reports[9], the traditional method employed to determine the alcohol content in Mezcal consists of inspecting the lifetime of bubbles that are formed by splashing a jet of the liquor into a small container (Fig. 1(a) and S1 Video in the Supplementary Information section)

  • A similar technique has been used to determine the alcoholic content in other spirits

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Summary

Introduction

Mezcal is a traditional Mexican spirit, obtained from the distillation of fermented agave juices. The method used to determine the correct alcohol content is of particular interest: a stream of the liquor is poured into a small vessel to induce surface bubbles. These bubbles, known as pearls by the Mezcal artisans, remain stable for tenths of seconds only if the alcohol content is close to 50%. According to popular accounts (informally documented by interviews with artisans) and a few formal reports[9], the traditional method employed to determine the alcohol content in Mezcal consists of inspecting the lifetime of bubbles that are formed by splashing a jet of the liquor into a small container (Fig. 1(a) and S1 Video in the Supplementary Information section). Note that the precise mechanism that determines the film rupture thickness is not known[18]

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