Dynamics of inviscid capillary breakup: 

collapse and pinchoff of a film bridge

Chen, Y.-J.; Steen, Paul H.

doi:10.1017/s002211209700548x

Cited by 194 publications

(176 citation statements)

References 18 publications

(23 reference statements)

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“…This therefore sets bubble detachment apart from all other breakup situations studied so far where one or both fluids are viscous, or where two inviscid fluids differ little in density, as well as from the inverse case of water in air. In those cases, the breakup is driven by surface tension and α h ≥ 2/3 [3,4,5,6,7,8,9,10,11,12,20]. Here we observe the consequences of a different driving mechanism on the breakup dynamics.…”

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confidence: 73%

“…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.…”

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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: 73%

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confidence: 99%

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

et al. 2006

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“…Of these examples, liquid droplet formation is particularly notable because it exhibits many of the exotic features of a topological transition, such as singularities and scaling, while being accessible enough to warrant thorough experimental examination (12)(13)(14)(15)(16)(17)(18). The result has been a powerful framework that characterizes the final moments of pure liquid droplet detachments using only the relative strengths of surface tension, viscous dissipation, and inertial stress (1,2).…”

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confidence: 99%

Droplet formation and scaling in dense suspensions

Miskin

Jaeger

2012

Proc. Natl. Acad. Sci. U.S.A.

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When a dense suspension is squeezed from a nozzle, droplet detachment can occur similar to that of pure liquids. While in pure liquids the process of droplet detachment is well characterized through self-similar profiles and known scaling laws, we show here the simple presence of particles causes suspensions to break up in a new fashion. Using high-speed imaging, we find that detachment of a suspension drop is described by a power law; specifically we find the neck minimum radius, r m , scales like τ 2 3 near breakup at time τ ¼ 0. We demonstrate data collapse in a variety of particle/ liquid combinations, packing fractions, solvent viscosities, and initial conditions. We argue that this scaling is a consequence of particles deforming the neck surface, thereby creating a pressure that is balanced by inertia, and show how it emerges from topological constraints that relate particle configurations with macroscopic Gaussian curvature. This new type of scaling, uniquely enforced by geometry and regulated by the particles, displays memory of its initial conditions, fails to be self-similar, and has implications for the pressure given at generic suspension interfaces.particle packing | contact angle | irrotational flow | jamming T he rupture of a single volume filled with matter to produce two unconnected volumes, a transition between two distinct topologies, plays a fundamental role in a wide range of phenomena from dripping liquids (1, 2), to breakup of nano-jets (3-5), to metal rods pinching off (6), to black-string instabilities in general relativity (7,8). In biological systems, topological transitions are equally fundamental because they govern processes like cell division (9), endocytosis (10), and collapsing bacterial colonies (11).Of these examples, liquid droplet formation is particularly notable because it exhibits many of the exotic features of a topological transition, such as singularities and scaling, while being accessible enough to warrant thorough experimental examination (12-18). The result has been a powerful framework that characterizes the final moments of pure liquid droplet detachments using only the relative strengths of surface tension, viscous dissipation, and inertial stress (1, 2). For these liquids, the initial conditions become irrelevant as the system nears the singular point of snap off. Instead, the material parameters alone assign both a self-similar profile defining the shape of the drop and a power law governing how this shape scales close to the final moments of breaking.The success of self-similarity and scaling approaches has prompted attempts to extend pure liquid analysis to other instances of free surface flows. In many cases, when the boundary stresses originate from surface tension, the framework of pure liquid detachment can be modified successfully and self-similar structures govern the breakup (19-21). However, in some cases the driving force comes from an alternative source, as in the case of bubble pinch-off (22-24), and self-similarity breaks down: To describe detachm...

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“…With few exceptions, such as a study of the transition between the helicoid and the catenoid (12), little attention has been paid to transitions that take one surface to another. On the other hand, topological transitions have been studied extensively in fluid dynamics, with an emphasis on interface collapse in viscous flows (2,4), and on the more inviscid problems of fluid and soap-film motion (13)(14)(15)(16)(17)(18) and networks of film junctions (19). Yet one elementary question remains unanswered: What is the process that takes a one-sided film to a two-sided one?…”

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confidence: 99%

Soap-film Möbius strip changes topology with a twist singularity

Goldstein

Moffatt

Pesci

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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It is well-known that a soap film spanning a looped wire can have the topology of a Möbius strip and that deformations of the wire can induce a transformation to a two-sided film, but the process by which this transformation is achieved has remained unknown. Experimental studies presented here show that this process consists of a collapse of the film toward the boundary that produces a previously unrecognized finite-time twist singularity that changes the linking number of the film's Plateau border and the centerline of the wire. We conjecture that it is a general feature of this type of transition that the singularity always occurs at the surface boundary. The change in linking number is shown to be a consequence of a viscous reconnection of the Plateau border at the moment of the singularity. High-speed imaging of the collapse dynamics of the film's throat, similar to that of the central opening of a catenoid, reveals a crossover between two power laws. Far from the singularity, it is suggested that the collapse is controlled by dissipation within the fluid film surrounding the wire, whereas closer to the transition the power law has the classical form arising from a balance between air inertia and surface tension. Analytical and numerical studies of minimal surfaces and ruled surfaces are used to gain insight into the energetics underlying the transition and the twisted geometry in the neighborhood of the singularity. A number of challenging mathematical questions arising from these observations are posed.topological transition | contact line

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Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge

Cited by 194 publications

References 18 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

Droplet formation and scaling in dense suspensions

Soap-film Möbius strip changes topology with a twist singularity

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