Asymmetric Disconnection of an Underwater Air Bubble: Persistent Neck Vibrations Evolve into a Smooth Contact

Turitsyn, Konstantin; Lai, Lipeng; Zhang, Wendy W.

doi:10.1103/physrevlett.103.124501

Cited by 22 publications

(47 citation statements)

References 27 publications

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“…We find that the singularity (i) occurs at the film boundary, (ii) lacks the cylindrical symmetry found in the collapse of a catenoid (13), or even the bilateral symmetry recently observed in bubble pinch off (20), and changes the linking number between the Plateau border and the centerline of the wire frame, (iii) displays an intriguing crossover from a nonclassical behavior in the collapse of the film to the more familiar one arising from a balance of capillary forces and air inertia (15,21), and (iv) has energetics and geometry that may be understood through analysis of minimal surfaces and ruled surfaces spanning a family of parametrized frames (22).…”

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confidence: 92%

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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confidence: 92%

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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“…Instead, a variety of closure types arise (cf. Turitsyn et al 2009); for example: pointy and angular structures, finger-like forms, jets in the radial direction, and sub-cavities. Combinations of two or more of these events might take place.…”

Section: Effect Of Large-amplitude Disturbancesmentioning

confidence: 99%

“…If axial symmetry is broken by a small azimuthal perturbation, a truly universal system would be expected to converge to the same solution . However, through experiments and simulations of an air bubble disconnecting from an underwater nozzle, Keim, Møller, Zhang & Nagel (2006); Schmidt, Keim, Zhang & Nagel (2009) ;Turitsyn, Lai & Zhang (2009);and Keim (2011) recently showed that a slight azimuthal asymmetry can trigger vibrations that persist in time. The fact that a small perturbation is not smoothed out indicates that the system possesses memory of its initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Collapse and pinch-off of a non-axisymmetric impact-created air cavity in water

et al. 2012

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The axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially-quiescent water surface and observe their subsequent gravity-induced collapse. The cavities are characterized by azimuthal harmonic disturbances with a single mode number m and amplitude a m . For small initial distortion amplitude (1 or 2 % of the mean disc radius), the cavity walls oscillate linearly during collapse, with nearly constant amplitude and increasing frequency. As the amplitude is increased, higher harmonics are triggered in the oscillations and we observe more complex pinch-off modes. For small amplitude disturbances we compare our experimental results with the model for the amplitude of the oscillations by Schmidt et al. (2009) and the model for the collapse of an axisymmetric impact-created cavity previously proposed by Bergmann et al. (2009b). By combining these two models we can reconstruct the three-dimensional shape of the cavity at any time before pinch-off. IntroductionThe pinch-off of an axisymmetric air cavity in water is characterized by a finite-time singularity. The kinetic energy of the flow is focused into a vanishing small volume with a velocity whose magnitude diverges as the pinch-off moment is approached. Several experimental and theoretical scenarios have been recently considered in the study of this problem: a bubble rising from a capillary . Depending on the case, the collapse might be initiated by surface tension, external flow, or hydrostatic pressure. However, irrespective of the cause, towards the end it is the inertia of the fluid that takes over in every case, and the collapse is accelerated as the radius of the cavity shrinks.The time it takes each of these systems to reach the inertial collapse regime varies by orders of magnitude . Hence, it was not an easy task to determine whether there was indeed a universal behaviour underlying this phenomenon. The first proposed model was a power law where the radius decreased proportionally to the arXiv:1109.5823v2 [physics.flu-dyn]

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“…This idea successfully describes several breakup scenarios, such as water drops break up in air [8][9][10][11][12] . However, recent studies reported that there are breakups which remember their initial states [13][14][15][16][17][18][19][20][21] .…”

Section: Introductionmentioning

confidence: 99%

Curvature singularity in the asymmetric breakup of an underwater air bubble

Lai

2012

Physics of Fluids

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The presence of slight azimuthal asymmetry in the initial shape of an underwater bubble entirely alters the final breakup dynamics. Here I examine the influence of initial asymmetry on the final breakup by simulating the bubble surface evolution as a Hamiltonian evolution corresponding to an inviscid, two-dimensional, planar implosion. I find two types of breakups: a previously reported coalescence mode in which distant regions along the air-water surface curve inwards and eventually collide with finite speed, and a hitherto unknown cusp-like mode in which the surface develops sharp tips whose radii of curvature are much smaller than the average neck radius.I present three sets of results that characterize the nature of this cusp mode. First, I show that the cusp mode corresponds to a saddle-node. In other words, an evolution towards a cross-section shape with sharp tips invariably later evolves away from it. In phase space, this saddle-node separates coalescence modes whose coalescence planes lie along different spatial orientations. Second, I show that the formation of the sharp tips can be interpreted as a weakly first-order transition which becomes second-order, corresponding to the formation of a finite-time curvature singularity, in the limit that the initial perturbation amplitude approaches zero. Third I show that, as the curvature singularity is approached, the maximum surface curvature diverges approximately as (t c − t) −0.8 , where t c is the onset time of the singularity and the maximum velocity diverges approximately as (t c − t) −0.4 . In practice, these divergences imply that viscous drag and compressibility of the gas flow, two effects not included in my analysis, become significant as the interface evolves towards the curvature singularity.PACS numbers: 47.55.df, 47.20.Cq, 47.20.Ma

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Asymmetric Disconnection of an Underwater Air Bubble: Persistent Neck Vibrations Evolve into a Smooth Contact

Cited by 22 publications

References 27 publications

Soap-film Möbius strip changes topology with a twist singularity

Soap-film Möbius strip changes topology with a twist singularity

Collapse and pinch-off of a non-axisymmetric impact-created air cavity in water

Curvature singularity in the asymmetric breakup of an underwater air bubble

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