Capillary driven fragmentation of large gas bubbles in turbulence

Rivière, Aliénor; Ruth, Daniel; Mostert, Wouter; Deike, Luc; Perrard, Stéphane

doi:10.1103/physrevfluids.7.083602

Cited by 14 publications

(54 citation statements)

References 43 publications

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“…However, the turbulence is only able to deform bubbles that are large enough with respect to the Hinze scale that such ligaments might be created, because surface tension is effective at limiting the severity of deformations to smaller bubbles. These experimental observations parallel a recent interpretation of DNSs of bubble break-up (Rivière et al 2022).…”

Section: Capillary Splitting Of Ligaments Prepared By the Turbulence ...supporting

confidence: 86%

“…Thus, an upper bound and typical scale of the break-up duration is taken to be the eddy turnover time at the parent bubble's scale, T turb (d 0 ) = −1/3 d 2/3 0 , in agreement with experimental and numerical observations of the time over which bubbles are deformed prior to break-up (Risso & Fabre 1998;Martínez-Bazán et al 1999b;Rivière et al 2021). The final timescale we consider is that of the capillary instabilities of gas ligaments that produce a small child bubble of size d, which will occur over the capillary timescale of that child bubble, T cap (d) = (ρ/γ ) 1/2 d 3/2 /(2 √ 3) (Rivière et al 2022). From these three relevant time scales, we define three types of events.…”

Section: Physical Ideassupporting

confidence: 74%

“…We have additionally re-analysed the DNSs of bubbles breaking in homogeneous, isotropic turbulence presented in Rivière et al (2021Rivière et al ( , 2022, tracking the bubble break-up events in a similar way to what has been done on the experimental data in § 4. From these DNSs, we can compute the average number of bubbles formed per event as a function of the parent bubble size, included in figure 17(a) as the red star markers.…”

Section: Statistics On the Number Of Child Bubbles Formedmentioning

confidence: 99%

“…The N(d) ∝ d −3/2 distribution for d < d H has been observed experimentally (Deane & Stokes 2002) and numerically (Wang et al 2016;Mostert et al 2022) for bubbles under breaking waves, though the identification of a sub-Hinze power-law slope is additionally complicated by the transient nature of bubble disintegration (Rivière et al 2021) and breaking wave (Mostert et al 2022) events. Recent work has identified the capillary pinching of gas ligaments created by turbulent deformations as an origin of sub-Hinze bubbles, with theoretical arguments relating to the timescale over which such pinching occurs supporting the N(d) ∝ d −3/2 sub-Hinze scaling (Rivière et al 2022). Relating measured size distributions to theoretical scalings derived from break-up physics is complicated by the fact that bubbles' motions, and hence their residence time in some experimental domain, are dependent on their size and the characteristics of the turbulence they encounter (Garrett et al 2000).…”

Section: Bubble Break-up In Turbulencementioning

confidence: 99%

“…Andersson & Andersson (2006) showed that asymmetries in a deformed bubble shape can become more pronounced as a bubble breaks apart due to the variation in capillary pressure associated with the deformation. More recently, Rivière et al (2022) showed that very small bubbles originate not from turbulent motions at very small scales, but rather from the capillary instabilities of ligaments arising from much larger-scale deformations.…”

Section: Child Size Distribution and Break-up Time Scalesmentioning

confidence: 99%

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

et al. 2022

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We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale $d_{H}$ , the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes $d_0$ much larger than $d_{H}$ (probing up to $d_0/d_{H} = 8.3$ ), the size distribution of bubbles smaller than $d_{H}$ follows $N(d) \propto d^{-3/2}$ , with $d$ the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small bubbles. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of $d_0/d_{H}$ . Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.

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Section: Capillary Splitting Of Ligaments Prepared By the Turbulence ...supporting

confidence: 86%

Section: Physical Ideassupporting

confidence: 74%

Section: Statistics On the Number Of Child Bubbles Formedmentioning

confidence: 99%

Section: Bubble Break-up In Turbulencementioning

confidence: 99%

Section: Child Size Distribution and Break-up Time Scalesmentioning

confidence: 99%

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

et al. 2022

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Breakup prediction of oscillating droplets under turbulent flow

Deberne,

Chéron,

Poux

et al. 2024

International Journal of Multiphase Flow

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Fundamental time scales of bubble fragmentation in homogeneous isotropic turbulence

2023

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We investigate the fundamental time scales that characterise the statistics of fragmentation under homogeneous isotropic turbulence for air–water bubbly flows at moderate to large bubble Weber numbers, $We$ . We elucidate three time scales: $\tau _r$ , the characteristic age of bubbles when their subsequent statistics become stationary; $\tau _\ell$ , the expected lifetime of a bubble before further fragmentation; and $\tau _c$ , the expected time for the air within a bubble to reach the Hinze scale, radius $a_H$ , through the fragmentation cascade. The time scale $\tau _\ell$ is important to the population balance equation (PBE), $\tau _r$ is critical to evaluating the applicability of the PBE no-hysteresis assumption, and $\tau _c$ provides the characteristic time for fragmentation cascades to equilibrate. By identifying a non-dimensionalised average speed $\bar {s}$ at which air moves through the cascade, we derive $\tau _c=C_\tau \varepsilon ^{-1/3} a^{2/3} (1-(a_{max}/a_H)^{-2/3})$ , where $C_\tau =1/\bar {s}$ and $a_{max}$ is the largest bubble radius in the cascade. While $\bar {s}$ is a function of PBE fragmentation statistics, which depend on the measurement interval $T$ , $\bar {s}$ itself is independent of $T$ for $\tau _r \ll T \ll \tau _c$ . We verify the $T$ -independence of $\bar {s}$ and its direct relationship to $\tau _c$ using Monte Carlo simulations. We perform direct numerical simulations (DNS) at moderate to large bubble Weber numbers, $We$ , to measure fragmentation statistics over a range of $T$ . We establish that non-stationary effects decay exponentially with $T$ , independent of $We$ , and provide $\tau _r=C_{r} \varepsilon ^{-1/3} a^{2/3}$ with $C_{r}\approx 0.11$ . This gives $\tau _r\ll \tau _\ell$ , validating the PBE no-hysteresis assumption. From DNS, we measure $\bar {s}$ and find that for large Weber numbers ( $We>30$ ), $C_{\tau }\approx 9$ . In addition to providing $\tau _c$ , this obtains a new constraint on fragmentation models for PBE.

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Capillary driven fragmentation of large gas bubbles in turbulence

Cited by 14 publications

References 43 publications

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

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

Breakup prediction of oscillating droplets under turbulent flow

Fundamental time scales of bubble fragmentation in homogeneous isotropic turbulence

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