A little chemistry can multiply the number of tiny bubbles produced when turbulence tears apart a large air cavity. But the surprise is that surface tension alone does not explain it: the surfactant's adsorption speed matters. When a large air cavity breaks in a turbulent flow, it undergoes very large deformations and cascading events of new interface formation, including elongated filaments and bubbles over a wide range of scales.

The experiments investigate surfactants and salt during fragmentation and observe a fivefold increase in the number of bubbles in some cases. For bubbles larger than the Hinze scale, bubble size distributions remain unchanged for all solutions tested.

For bubbles below the Hinze scale, surfactant or salt increases bubble numbers and steepens the bubble size distribution, but this effect appears only for surfactants with adsorption fast enough compared with new-interface formation by turbulence. In practical configurations, air-water interfaces are almost always contaminated by surface active agents, or surfactants, related to biological or anthropogenic activities.

Surfactants modulate surface waves dynamics, bubble rise velocity, and bubble bursting, with surface tension gradients leading to Marangoni flows and tip streaming. Beyond Marangoni effects, variations in surface tension and sorption kinetics also play important roles, so adsorption and desorption time scales must be compared with the characteristic time scale of the flow.

A comprehensive understanding of surfactant-mediated bubble behaviour is essential for mitigating environmental impacts of marine pollution and optimising industrial gas-liquid processes. The study considers surfactant effects on bubble breakup in a transient configuration, where a large air cavity breaks into small bubbles through successive fragmentation events.

This configuration is largely inspired by air entrainment and bubble fragmentation under breaking waves. Bubble fragmentation under breaking waves or in turbulent flows has been widely investigated through experiments and numerical approaches. Some numerical studies have probed surfactants in two-phase turbulence, and a few experiments investigated salt in bubbly flows, but no systematic studies on surfactants in turbulent bubble distributions existed to the authors' knowledge.

Bubble breakup in turbulence reflects competition between inertial stresses from turbulence, which promote fragmentation, and surface tension forces, which resist it. The Weber number compares these two effects and is commonly used to characterise bubble breakup conditions.

A critical Weber number provides the balance between inertial and surface tension forces and serves as a loose bubble breakup criterion of order unity. The associated length scale is the Hinze scale, which separates the super-Hinze regime, where bubbles break due to turbulence, from the sub-Hinze regime.

The Hinze scale is a soft threshold because turbulent flows are inherently stochastic. In the super-Hinze regime, the bubble size distribution follows a minus ten-thirds power law explained by a turbulent breakup cascade controlled by the eddy turnover time.

In contrast, the sub-Hinze distribution has a gentler minus three-halves slope, explained by capillary breakup involving large deformation, filament formation, and rupture controlled by capillarity. A broad size distribution from an initial air cavity forms through a sequence controlled by turbulent and capillary time scales, with new interfaces formed along the way.

With surfactants, relevant time scales must be compared with capillary and turbulence times that control breakup and deformation. Marangoni stresses from surfactant-concentration gradients along the interface occur on capillary time scales. The presence and amount of surfactant on a newly formed interface are related to the adsorption time, which controls how fast surfactant in the bulk reaches the interface.

The experiments compare sodium dodecyl sulphate, or SDS, with fast adsorption, Tween 20 with slow adsorption, and cetrimonium bromide, or CTAB, with an intermediate adsorption time scale. Figure one compares bubble-breakup time scales across size, normalised by the turbulence integral length and time scales.

Panel a places turbulent stretching, capillary instability, and adsorption for Tween twenty, CTAB, and SDS on the same map, while panel b sketches how a surfactant-covered bubble forms filaments over the eddy time before those filaments fragment on a capillary time. The figure matters because adsorption timing determines whether newly formed interfaces can respond during turbulent breakup.

For SDS, the adsorption time is of the order of milliseconds to seconds depending on concentration, comparable to the eddy turnover time, allowing SDS molecules to adsorb onto newly formed bubbles or filaments. The capillary instability leading to final breakup occurs faster than adsorption.

Tween 20 has an adsorption time of the order of tens of seconds, while the eddy turnover and capillary times are generally shorter, leaving insufficient time for adsorption during a single breakup event. CTAB has an intermediate adsorption time of order one second, comparable to the integral time scale, so it behaves similarly to Tween 20 at low concentrations and transitions toward SDS-like behaviour as concentration increases.

The setup uses a polycarbonate tank filled with approximately one hundred fifty litres of solution, with a hollow hemispherical metal cup positioned underwater at the tank centre. The cup initially faces downwards and contains a constant volume of twenty millilitres of air.

At the beginning of each experiment, the cup rotates upwards while a Phantom VEO4K-990 fast camera records at five hundred frames per second. In panel b, the curves separate into distinct levels after the initial rise, with the highest trace corresponding to the largest SDS concentration and the lowest to the clean case.

Panel c shows the visual contrast directly: the contaminated image contains many more small, clearly outlined bubbles than the clean image below. The released air cavity undergoes successive breakups, producing a broad distribution of bubble sizes, and the configuration is designed to characterise this transient fragmentation process.

Two camera lenses provide a large-scale view at thirty-five micrometres per pixel and a zoomed-in view at nine micrometres per pixel. Each experimental condition is repeated fifteen times with the two-hundred-millimetre lens and twenty-five times with the K2 lens to ensure statistical convergence.

The two views are combined into one bubble size distribution, and uncertainty is estimated by Monte Carlo bootstrapping with one hundred realisations. The study uses five different sets of solutions, including SDS, CTAB, and Tween 20 mixed with deionised water.

Experiments with SDS and Tween 20 are also repeated with a salt mixture representative of salts present in the ocean, and the SDS case is repeated a second time to ensure robustness. For each case, surface tension is measured at the beginning and end with a Langmuir trough, and the static surface tension before compression is recorded.

The concentrations span clean interfaces to fully contaminated conditions, near the critical micelle concentration or a surface tension close to forty millinewtons per metre. The experiment is transient by design: a large cavity is released and breaks due to turbulence.

Bubbles are generated over a relatively short window of approximately one second, or ten integral time scales, after release. During that window, bubbles rise to the surface and break, so the bubble count initially increases and then plateaus. The analysis compares adsorption time with the time between successive breakups, as new area is constantly created.

The experiments qualitatively examine large bubble breakup with and without surfactant, leading to populations of sub-Hinze-scale bubbles. Figure four shows representative fragmentation with filament formation or shedding behind large bubbles, without surfactant and with four thousand micromoles per litre of SDS.

In the lower surfactant sequences, especially row d, the thin filament breaks into multiple small, distinct circular bubbles by the final frame. In contrast, the corresponding clean-water sequence in row b remains dominated by the parent structure, with only a limited detached fragment visible.

Large bubble breakup in turbulence occurs through two successive stages. First, a turbulent eddy deforms the parent bubble over an eddy turnover time of approximately twenty-five milliseconds, stretching it into two lobes connected by a thinning neck.

The neck then thins under capillary forces, sometimes forms a filament, and breaks through a Rayleigh-Plateau-like instability over a capillary time of approximately zero point one to one millisecond, producing small capillary bubbles. In the clean case, a few intermediate-sized bubbles around the Hinze scale form along with a similar number of sub-Hinze bubbles.

In the contaminated case, a similar number of intermediate-sized bubbles form, but the number of sub-Hinze bubbles is drastically larger. Different mechanisms may account for enhanced production of small bubbles in the surfactant-laden case, including tearing or shedding during large-bubble breakup and rupture of elongated ligaments.

Distinguishing between these mechanisms would require dynamically resolved experiments or simulations focused on the different scenarios. The time resolution and use of a single camera are not sufficient to access the detailed dynamics reliably.

The study therefore focuses on statistical analysis of surfactant influence on fragmentation of a relatively large air cavity in turbulence. Figure five presents bubble size distributions for SDS, SDS with sea salt, CTAB, Tween 20, and Tween 20 with sea salt at increasing surfactant concentrations.

The dashed lines reference minus ten-thirds scaling in the super-Hinze regime and minus three-halves scaling in the sub-Hinze regime. The transition between the two regimes occurs at approximately two point five millimetres, close to the calculated Hinze scale, and this is used as the effective Hinze scale.

In panels (a) and (b), the curves largely overlap for larger bubbles, while their separation becomes visible toward smaller sizes as surfactant concentration increases. Panels (c) through (e) show the same overall structure, with the shaded bands indicating uncertainty around each mean distribution.

For a given experiment set, the super-Hinze distribution does not change when surfactants are added and remains very similar across the solutions tested. As SDS concentration increases, with or without sea salt, the total number of sub-Hinze bubbles increases while the super-Hinze count remains unchanged.

That increase in sub-Hinze bubbles is associated with a steeper distribution. With Tween 20, the distribution remains unchanged in both the super-Hinze and sub-Hinze ranges, and sea salt does not alter that conclusion.

CTAB produces intermediate behaviour: sub-Hinze bubble numbers increase significantly once its concentration is large enough. At the lowest contamination, the sub-Hinze power-law distribution for all conditions is compatible with the minus three-halves distribution due to capillary breakup.

When sub-Hinze bubble counts increase, increasing surfactant concentration makes the distribution steeper, meaning the power-law exponent becomes more negative. The changed distribution shape and unchanged effective Hinze scale rule out explaining the trends merely by increasing the Weber number through reduced static surface tension.

As contamination increases and surface tension is reduced, the super-Hinze bubble count remains unchanged in all cases. Fast surfactants such as SDS increase sub-Hinze counts, reaching a factor of five at very low surface tensions. With the slow surfactant Tween 20, sub-Hinze counts remain unchanged even when surface tension is modified.

Adding salt shows a similar trend: sub-Hinze numbers increase with SDS concentration but remain essentially unchanged with increasing Tween 20 concentration. Figure six compares normalized counts of super-Hinze bubbles, shown as open triangles, with sub-Hinze bubbles, shown as solid squares.

As contamination increases and surface tension falls, the super-Hinze counts remain broadly unchanged, while fast surfactants such as SDS show increased sub-Hinze counts, reaching about five times the reference in the plotted range. Panel b presents the same measurements against bulk surfactant concentration as a fraction of the CMC, clarifying how the response depends on contamination type.

Tween 20 shows no count differences as concentration varies, despite a surface-tension reduction comparable to SDS, so the sub-Hinze increase and power-law change are not simply due to reduced surface tension and increased Weber number. Tween 20 is non-ionic, so interactions between the surfactant and sea salt are very limited.

The influence of surfactant on breakup is tightly linked to adsorption time, and surfactants affect breakup only if a significant amount can adsorb between two successive fragmentation events. Stretching before fragmentation creates a large amount of surface area, so surfactant concentration on a newly formed bubble is below its equilibrium value with the bulk.

If adsorption takes much longer than the time between fragmentation events, bubbles essentially behave as clean bubbles after a few breakups because of successive dilutions. The analysis uses the integral time scale as the representative turbulence time and introduces a Biot number comparing turbulence time with adsorption time.

Figure seven connects the normalized number of sub-Hinze bubbles to the Biot number for SDS, CTAB, and Tween twenty. It shows a near-clean-case regime at low Bi, followed by increasing bubble counts at higher Bi, consistent with faster surfactant adsorption between breakup events.

The inset relates adsorption time to bulk concentration, providing the estimates used to compute Bi and interpret this transition. Surface active compounds can drastically increase sub-Hinze bubble production by up to a factor of five while leaving super-Hinze bubble numbers unchanged.

The sub-Hinze range remains described by a power law, but its exponent becomes increasingly more negative than minus three-halves as contamination increases. This steepening may matter for processes sensitive to small-bubble numbers, including air-sea gas exchange and sea salt aerosol production.

Fast surfactants, especially SDS, increase sub-Hinze bubble production by up to a factor of five while leaving super-Hinze bubbles unchanged. The key control is adsorption time compared with the breakup sequence, not simply reduced surface tension.