Fragmentation in turbulence by small eddies

Abstract

From air-sea gas exchange, oil pollution, to bioreactors, the ubiquitous fragmentation of bubbles/drops in turbulence has been modeled by relying on the classical Kolmogorov-Hinze paradigm since the 1950s. This framework hypothesizes that bubbles/drops are broken solely by eddies of the same size, even though turbulence is well known for its wide spectrum of scales. Here, by designing an experiment that can physically and cleanly disentangle eddies of various sizes, we report the experimental evidence to challenge this hypothesis and show that bubbles are preferentially broken by the sub-bubble-scale eddies. Our work also highlights that fragmentation cannot be quantified solely by the stress criterion or the Weber number; The competition between different time scales is equally important. Instead of being elongated slowly and persistently by flows at their own scales, bubbles are fragmented in turbulence by small eddies via a burst of intense local deformation within a short time.

Experimental observations and modelling of sub-Hinze bubble production by turbulent bubble break-up

“…The most energetic scales capable of deforming a bubble are those at the scale of the bubble, and experiments from which ω was extracted suggested that the break-up frequency initially increases with bubble size as the turbulence becomes more capable of counteracting surface tension, and then decreases for even larger bubbles, as the time required for a turbulent eddy to act across the bubble scale becomes longer (Martínez-Bazán et al 1999b), though this analysis may have missed break-ups in which one child bubble size is close to the parent size (Lehr, Millies & Mewes 2002). Recent experiments from Qi et al (2022) showed that eddies smaller than d 0 can also cause break-up, and other theoretical analyses have considered the action of a range of turbulent scales which may cause break-up. In such models, the product of the rate at which eddies of a given size interact with a bubble and each interaction's likelihood of causing break-up are integrated over a range of eddy sizes (Prince & Blanch 1990;Tsouris & Tavlarides 1994;Luo & Svendsen 1996;Lehr et al 2002;Aiyer et al 2019;Yuan, Li & Carrica 2021), causing the break-up frequency to increase with the bubble size as more turbulent scales contribute to break-up.…”

“…We note that the inertial stresses on a bubble that arise from the velocity slip between the bubble and the surrounding liquid can induce stresses comparable to those associated with the turbulence's inherent velocity gradients at the bubble scale (Masuk, Salibindla & Ni 2021), that eddies smaller than the bubble can also contribute to deformation and break-up (Luo & Svendsen 1996; Qi et al. 2022) and that the turbulent flow can trigger bubble shape oscillations (Risso & Fabre 1998; Ravelet, Colin & Risso 2011). These factors will contribute to bubble deformation and break-up in ways that are not directly parameterised in the definition of .…”

“…Recent experiments from Qi et al. (2022) showed that eddies smaller than can also cause break-up, and other theoretical analyses have considered the action of a range of turbulent scales which may cause break-up. In such models, the product of the rate at which eddies of a given size interact with a bubble and each interaction's likelihood of causing break-up are integrated over a range of eddy sizes (Prince & Blanch 1990; Tsouris & Tavlarides 1994; Luo & Svendsen 1996; Lehr et al.…”

The interaction of droplet dynamics and turbulence cascade

“…The Kolmogorov-Hinze (KH) theory 18,19 is the cornerstone of existing models and applications; this framework is based on the breakup of isolated droplets in turbulence and identifies the scale d H above which a droplet breaks up due to the local environment turbulence and below which surface tension forces are able to resist the action of the turbulent eddies. This picture, based on breakup only, is incomplete and has been recently challenged 20 .…”

“…Empirical evidences, notably in bubbly flows, seem to confirm this distribution 7,9,[23][24][25][26] , although variations may be measured, in particular because of viscous effects in emulsions 27 . Yet, recent experiments on a single bubble contradict this physical picture 20 , and the definition of the critical Weber number We c remains ambiguous and somewhat heuristic, with values in the literature spanning more than one order of magnitude 16,23,28 . Furthermore, the key feature of intermittency, that is the breaking of scale invariance [29][30][31] , has not been considered in the analysis.…”