Fast and slow surfactants in turbulence-driven bubble breakup
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Zhan Rui Wu, Tristan Aurégan, Luc Deike
A stormy patch of water can make bubbles in two very different ways: surfactants may leave the larger bubbles untouched while creating up to five times as many tiny ones. The key is not just what the surfactant is, but how fast it arrives.
When a large air cavity breaks in a turbulent flow, it goes through very large deformations and cascading events of new interface formation, including elongated filaments and bubbles over a wide range of scales, with their rate of formation controlled by turbulence and capillary processes. We experimentally investigate the effects of surfactants and salt on the fragmentation of a large air cavity, and observe a fivefold increase of the number of bubbles being produced in some cases. We characterise the bubble size distribution resulting from successive breakups in such a transient configuration. For bubbles larger than the Hinze scale dH (defined as the balance between surface tension and turbulence stresses), we observe that bubble size distributions remain unchanged for all solutions tested. For bubbles below dH, however, we observe an increase of the number of bubbles produced and an associated steepening of the bubble size distribution upon the addition of surfactant or salt. This later effect is only visible for surfactants with an adsorption time scale that is fast enough compared with the rate at which new interfaces are being generated by turbulence.
Transcript
A stormy patch of water can make bubbles in two very different ways: surfactants may leave the larger bubbles untouched while creating up to five times as many tiny ones. The key is not just what the surfactant is, but how fast it arrives. A large air cavity breaks into small bubbles through successive fragmentation events, in a changing process inspired by air entrainment and bubble fragmentation under breaking waves.
This study examines how a surfactant changes bubble breakup in a transient configuration, where a large air cavity fragments into small bubbles. Earlier work had not, to the authors' knowledge, systematically studied how surfactants alter the distribution of bubble sizes in turbulence.
The central idea is a race against time. Imagine trying to coat freshly cut pieces of fruit before they are cut again: the coating can affect the next cut only if it arrives quickly enough. Here, surfactant from the surrounding liquid must reach each newly created bubble surface before the next breakup.
Its arrival time therefore determines whether it can influence the process. A fast surfactant can reach newly formed bubbles and thin strands while the breakup sequence is still under way, although the final rupture can happen faster than the surfactant arrives.
A slow surfactant may not have enough time to reach newly formed bubble surfaces during a single sequence of breakup events. A medium-speed surfactant can behave more like the slow one at low concentration and more like the fast one as concentration rises. The air cavity is released into turbulent flow and goes through a sequence of breakups, producing a broad range of bubble sizes.
The measurements use a wider, large-scale view and a closer, zoomed-in view, improving image resolution through two complementary camera views. The images could suggest that surfactants make one thin air strand produce more child bubbles.
But the actual large bubbles undergo many breakups at the same time. A single large bubble can fragment into many smaller bubbles, with many breakup events taking place between successive images. Without surfactant, the breakup produces some medium-sized bubbles and a similar number of smaller bubbles.
With surfactant, the number of medium-sized bubbles stays similar, but the number of smaller bubbles becomes much larger. A large bubble can break apart without producing many tiny bubbles, but adding a bubble-stabilizing substance makes filament-like pieces shed several small bubbles as breakup unfolds.
This helps explain why contaminated water can contain far more very small bubbles than clean water. Across the experiments, adding surfactants does not change the distribution of the larger bubbles. With increasing amounts of the fast surfactant, however, the total number of smaller bubbles rises while the larger-bubble range stays unchanged.
The slow surfactant leaves both ranges unchanged, while the medium-speed surfactant falls between the two: its smaller-bubble count rises once the concentration is high enough. Salt does not alter these conclusions. The results connect the effect to timing: a surfactant changes breakup only if enough of it reaches a bubble surface between two successive fragmentation events.
Stretching before fragmentation creates much more surface area, so newly formed bubbles start with less surfactant than equilibrium with the bulk would provide. If adsorption is too slow compared with the time between fragmentation events, repeated breakups dilute the surfactant and bubbles essentially behave like clean bubbles.
Surface-active compounds can increase the production of the smallest bubbles by up to a factor of five while leaving the number of larger bubbles unchanged. The small-bubble part of the distribution also becomes steeper as contamination increases.
That shift may matter beyond the laboratory because small bubbles affect air–sea gas exchange and the production of sea-salt particles in the atmosphere. Fast-acting surfactants can sharply increase the number of tiny bubbles without changing the larger ones.
That matters because tiny bubbles help control exchanges between ocean and air, including gases and sea-salt particles.
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