Self-Similar Capillary Pinchoff of an Inviscid Fluid

Day, Richard F.; Hinch, E. J.; Lister, Joseph

doi:10.1103/physrevlett.80.704

Cited by 271 publications

(293 citation statements)

References 8 publications

Supporting

Mentioning

262

Contrasting

Order By: Relevance

“…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.…”

mentioning

confidence: 75%

“…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.…”

mentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2006

View full text Add to dashboard Cite

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 ...

show abstract

mentioning

confidence: 75%

mentioning

confidence: 99%

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

et al. 2006

View full text Add to dashboard Cite

show abstract

“…In particular, for inviscid irrotational flows it has been shown that the simplified one-dimensional Euler equations exhibit a singularity before the point of breakup is reached 48 . Numerical simulations 49,50 show that in fact the free-surface of the droplet close to the singularity overturns.…”

Section: A Model For Inertio-elastic Pinchingmentioning

confidence: 99%

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

2006

View full text Add to dashboard Cite

The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical “pinch time” tp, an inertial-capillary balance leads to the expected 2∕3-power scaling of the minimum radius with time: Rmin∼(tp−t)2∕3. However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>tp. In this region, the filament radius decreases exponentially with time Rmin∼exp[(tp−t)∕λ1], where λ1 is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions.

show abstract

“…If this cannot occur quickly enough, then the surface tension forces will act to breakup elongated structures through the Rayleigh-Plateau instability. At the final moments of progeny drop pinch-off, the charge density remains finite and the dynamics are governed by the known universal solution for inviscid capillary pinchoff [26]. Fig.…”

mentioning

confidence: 99%

Simulations of Coulombic Fission of Charged Inviscid Drops

Burton

Taborek

2011

Phys. Rev. Lett.

View full text Add to dashboard Cite

We present boundary-integral simulations of the evolution of critically charged droplets. For such droplets, small ellipsoidal perturbations are unstable and eventually lead to the formation of a "lemon"-shaped drop with very sharp tips. For perfectly conducting drops, the tip forms a selfsimilar cone shape with a subtended angle identical to that of a Taylor cone. At the tip, quantities such and pressure and fluid velocity diverge in time with power-law scaling. In contrast, when charge transport is described by a finite conductivity, we find that small progeny drops are formed at the tips whose size decreases as the conductivity is increased. These small progeny drops are of nearly critical charge, and are precursors to the emission of a sustained flow of liquid from the tips as observed in experiments of isolated charged drops.PACS numbers: 47.15.km, 47.11.Hj An isolated droplet of liquid will naturally take the form of a sphere in order to minimize its surface area. If we now place a net amount of electrical charge on the sphere, there is a pressure opposing the effects of surface tension due to the repulsion of mutual charges. As first described by Lord Rayleigh [1], there is a critical amount of charge Q c that can be placed on the drop before the sphere will become unstable to small perturbations from equilibrium:where R is the radius of the drop, σ is the surface tension, and ǫ is the electrical permittivity. The simplest case, and the one first directly observed in experiment [2,3], is that of an ellipsoidal perturbation where the droplet evolves into a "lemon" shape, and high-speed jets of liquid carrying a significant fraction of the total charge are emitted from the tips.The disintegration of such isolated charged drops occurs in natural settings such as thunderstorm clouds and bursting bubbles at the ocean surface [4], industrial applications ranging from ink-jet printing to electrospraying [5], and is especially important in mass spectrometry [6,7]. Charged liquid drops were also used as an early model for the mechanism of nuclear fission [8]. Nearly all previous studies have looked solely at the oscillations around equilibrium and the limits of stability [9-11], or operated under the assumption of infinite conductivity [12][13][14]. This latter assumption is especially important; recent numerical simulations show that bulk conductivity controls the fine fluid jets formed in applied electric fields [15]. Indeed, the specific mode of charge conduction will affect the dynamics of the jet [16]. The most popular models of charge transport suppose bulk conduction [15,17], although recent evidence suggests that conduction along the surface of the drop is significant [18,19].In this letter, we simulate the initial instability and eventual cone-jet formation for charged inviscid drops with total charge Q c . We consider two separate cases:(1) The drop is a perfect conductor. In this regime the "lemon"-shaped drop forms extremely sharp tips, where quantities such as charge density, curvature, and veloci...

show abstract

Self-Similar Capillary Pinchoff of an Inviscid Fluid

Cited by 271 publications

References 8 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

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

Simulations of Coulombic Fission of Charged Inviscid Drops

Contact Info

Product

Resources

About