Axisymmetric Bubble Pinch-Off at High Reynolds Numbers

Gordillo, José Manuel; Sevilla, A.; Rodríguez-Rodríguez, Javier; Martı́nez-Bazán, C.

doi:10.1103/physrevlett.95.194501

Cited by 129 publications

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“…Other singularities [1] have been shown to be sensitive to noise [2]. However, experiment and theory up to now have ignored cylindrical asymmetry [21,22,23,24,25,26], or could not show it to be a generic feature of breakup [14]. We have shown that tilting the nozzle by just 0.07 • detectably alters the outcome of breakup.…”

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confidence: 80%

“…2) from a power law α h = 0.50 with logarithmic corrections (dotted lines) that have been derived for Eqn. 2 [14,24] -a limitation also encountered by Bergmann et al at low Froude numbers. However, these corrections are derived by assuming a slender cylinder, which we believe is a poor approximation to our neck shape.…”

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confidence: 93%

“…However, as first pointed out by Longuet-Higgins et al [21] and subsequently elaborated by experiments and simulations [13,14,22,23,24,25,26], the detachment of an air bubble from a nozzle is not a collapse driven by surface tension, but rather is an implosion due to a pressure difference between the hydrostatic pressure in the water and the bubble pressure, ∆P = ∆ρga. Here a is the linear size of the bubble:…”

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confidence: 99%

“…Others have examined the effect of initial conditions on the evolution of the neck in a coflowing air-water jet [24], and for very large bubbles and found that the scaling exponent α h is nonuniversal [14]. Other singularities [1] have been shown to be sensitive to noise [2].…”

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confidence: 99%

“…Burton et al [23] reported the remarkable observation that instead of proceeding smoothly to zero radius, the [14,24]. Data are taken from multiple pinchoffs, and only data for τ ≤ 230 µs are used for fitting.…”

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confidence: 99%

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Breakup of Air Bubbles in Water: Memory and Breakdown of Cylindrical Symmetry

et al. 2006

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Using high-speed video, we have studied air bubbles detaching from an underwater nozzle. As a bubble distorts, it forms a thin neck which develops a singular shape as it pinches off. As in other singularities, the minimum neck radius scales with the time until breakup. However, because the air-water interfacial tension does not drive breakup, even small initial cylindrical asymmetries are preserved throughout the collapse. This novel, non-universal singularity retains a memory of the nozzle shape, size and tilt angle. In the last stages, the air appears to tear instead of pinch.PACS numbers: 47.55.db, 47.55.df, 02.40.Xx The delightful tingling felt when drinking carbonated beverages, the glee of children blowing bubbles in a bathtub, and the importance of deep underwater fissures venting gasses into the oceans hint at the richness and significance of bubble formation in determining the texture and composition of our world. However, the process by which a bubble is formed is still full of surprises. A drop or bubble breaks up by forming a neck that thins to atomic dimensions, a process described as an approach towards a singularity where physical quantities such as stress or pressure grow infinitely large. Singularities often organize the overall dynamical evolution of nonlinear systems. Each symmetry in nature implies an underlying conservation law, so that the symmetries of the singularity associated with pinch-off naturally have important consequences for its dynamics. It was previously believed [1,2,3,4,5,6,7,8,9,10,11,12] that the pinching neck of any drop or bubble would become cylindrically (i.e. azimuthally) symmetric in the course of pinch-off. Recently, pinching necks of air in water were observed to lose cylindrical symmetry in the course of detachment [13,14].Here we show that this loss of symmetry is caused by a new form of memory in singular dynamics: even a small asymmetry in the initial conditions is preserved throughout bubble detachment. This novel singularity retains a memory of the nozzle shape, size and tilt angle. The asymmetry can be made so great that the air appears to tear. This symmetry breaking may be important in numerous applications [15,16,17], and for understanding other physical processes which are modeled as the formation of a singularity, such as star or black hole formation [18] and supernova explosions [19]. Thus our experimental observation of the breakdown of cylindrical symmetry in the air bubble demonstrates a new view of dynamical singularities that may be relevant even on a celestial scale.Singularities govern the dynamics in many familiar break-up events, such as the dispersal of oil drops into * Electronic address: nkeim@uchicago.edu vinegar during the making of a salad dressing, or the dripping of water from a leaky faucet. For many fluid pairs -for example, one viscous fluid breaking in a surrounding fluid of high viscosity [7,8,12] -the shape and dynamics of the pinching neck depend solely on the fluid parameters, as the breakup forgets its initial conditions on ...

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confidence: 80%

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confidence: 93%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Breakup of Air Bubbles in Water: Memory and Breakdown of Cylindrical Symmetry

et al. 2006

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Breakup dynamics of slender bubbles in non‐newtonian fluids in microfluidic flow‐focusing devices

Fünfschilling

Zhu

et al. 2012

AIChE Journal

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International audienceThis study aims to investigate the breakup of slender bubbles in non-Newtonian fluids in microfluidic flow-focusing devices using a high-speed camera and a microparticle image velocimetry (micro-PIV) system. Experiments were conducted in 400- and 600-mu m square microchannels. The variation of the minimum width of gaseous thread with the remaining time before pinch-off could be scaled as a power-law relationship with an exponent less than 1/3, obtained for the pinch-off of bubbles in Newtonian fluids. The velocity field and spatial viscosity distribution in the liquid phase around the gaseous thread were determined by micro-PIV to understand the bubble breakup mechanism. A scaling law was proposed to describe the size of bubbles generated in these non-Newtonian fluids at microscale. The results revealed that the rheological properties of the continuous phase affect significantly the bubble breakup in such microdevice

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Bubble breakup with permanent obstruction in an asymmetric microfluidic T‐junction

Wang

Zhu

2014

AIChE Journal

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Bubble breakup with permanent obstruction in an asymmetric microfluidic T‐junction is investigated experimentally. The breakup process of bubbles can be divided into three stages: squeezing, transition, and pinch‐off stages. In the squeezing stage, the thinning of the bubble neck is mainly controlled by the velocity of the fluid flowing into the T‐junction, and the increase of the liquid viscosity can promote this process. In the transition stage, the minimum width of bubble neck decreases linearly with time. In the pinch‐off stage, the effect of the velocity of the fluid flowing into the T‐junction on the thinning of the bubble neck becomes weaker, and the increase of the liquid viscosity would delay this process. The evolution of the minimum width of the bubble neck with the remaining time before the breakup can be scaled by a power–law relationship. The bubble length has little influence on the whole breakup process of bubbles. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1081–1091, 2015

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Axisymmetric Bubble Pinch-Off at High Reynolds Numbers

Cited by 129 publications

References 11 publications

Breakup of Air Bubbles in Water: Memory and Breakdown of Cylindrical Symmetry

Breakup of Air Bubbles in Water: Memory and Breakdown of Cylindrical Symmetry

Breakup dynamics of slender bubbles in non‐newtonian fluids in microfluidic flow‐focusing devices

Bubble breakup with permanent obstruction in an asymmetric microfluidic T‐junction

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