Induced bubble shape oscillations and their impact on the rise velocity

Vries, J. de; Luther, Stefan; Lohse, Detlef

doi:10.1140/epjb/e2002-00332-5

Cited by 51 publications

(29 citation statements)

References 22 publications

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“…M is for a body of arbitrary shape a tensor, but in our case, where the body is axisymmetric and moves along the symmetry axis, a scalar quantity. Without surface oscillations, the velocity is U T and the added mass M 0 , say, Then, during an oscillation the velocity changes, which has been observed earlier and been brought in connection with added mass changes in [14] . Figure 2 clearly shows that the frequency of the vertical velocity fluctuation coincides with that of the (2,0) mode.…”

Section: The (20) Mode Frequencymentioning

confidence: 69%

On hydrodynamical properties of ellipsoidal bubbles

Wijngaarden

Veldhuis

2008

Acta Mech

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A major part of this paper is taken up by the calculation of the first axisymmetric surface oscillation frequency and the (2, 0) mode of an ellipsoidal bubble, in order to compare with experimentally obtained values of bubbles rising in water. First, an energy method is used for an ellipsoid oscillating in stagnant water. Interestingly, with help of a paper by Bjerknes [12] at 1873!. The results compare poorly with experiments. Agreement improves when the oscillation of the rise velocity is taken into account. The remaining difference between the results of theory and experimental values is ascribed to deviation of the bubble shape from an ellipsoid. Finally, volume oscillations of ellipsoidal bubbles are calculated with the energy method and the results compare well with those of an earlier work, based on an electrical analogon. IntroductionWith pleasure we contribute to this Festschrift for Professor Wilhelm Schneider at the occasion of his 70th birthday. Wilhelm Schneider and one of us (L.v.W) worked together many years in the Scientific Council of CISM in Udine, Italy.We share an interest in classical hydrodynamics and I hope that this contribution will please him. We wish him many years to come in good health. This paper is on gas bubbles rising in clean water, so clean that there are no surfactants. Then, the boundary condition on the interface between gas and liquid is that the tangential shear stress must vanish. Rising in water under buoyancy, very small bubbles (diameter of order of 0.1 mm) remain spherical, but with diameters of 1 mm and larger they assume a shape which is approximately an oblate ellipsoid [1] with the short axis pointing in vertical direction. The ratio of the larger axis to the minor one, indicated here with χ , depends on the speed of rising which in turn depends on the size and on liquid properties. The terminal speed of rise, U T , is often expressed in terms of the Reynolds number Re , defined aswhere D eq is the equivalent bubble diameter and ν the kinematic viscosity of the liquid. The axes ratio depends on the Weber number We defined aswhere ρ and σ are the water density and air-water surface tension, respectively. Below D eq = 1.8 mm (Re ∼ 600), bubbles rise rectilinearly, above that value they describe a spiraling or zigzagging path [2,3], but

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Section: The (20) Mode Frequencymentioning

confidence: 69%

On hydrodynamical properties of ellipsoidal bubbles

Wijngaarden

Veldhuis

2008

Acta Mech

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“…For smaller bubbles, surface tension dominates over stress from the rise, and they are nearly spherical. With increasing size, the surface tension force decreases, while the drag forces increase and as a result, larger bubbles are deformed from spherical to ellipsoidal (Clift et al 1978;De Vries et al 2002;Luther et al 2004). To assess the deformation of rising bubbles in relation to their size, we consider an allometric relationship (i.e., the differential growth of the bubble dimensions) between bubble volume and backscattering cross-section measured with the down-looking echosounder.…”

Section: Assessmentmentioning

confidence: 99%

Quantifying gas ebullition with echosounder: the role of methane transport by bubbles in a medium‐sized lake

Ostrovsky

Mcginnis

Lapidus

et al. 2008

Limnology & Ocean Methods

160

165

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In lakes and reservoirs with variable water level, gas ebullition can play a substantial role in methane transport in the water column and to the atmosphere. However, measuring methane ebullition from sediment is difficult as releases are highly heterogeneous and intermittent on macro- and micro-scales. In contrast to conventional gas traps and optical methods, hydroacoustic technology allows rapid scanning over large volumes of the water column synoptically to quantify gas bubble abundance. A 120-kHz dual beam downward-looking echosounder was used to measure the size distributions of bubbles that do not resonate at the sonar frequency. Data obtained with this sonar permit accurate calculation and evaluation of ebullition flux from the bottom. A robust relationship was established between gas volumes and backscattering cross-section of individual bubbles in experimental conditions, and rise velocities of bubbles were precisely measured. The volume backscattering coefficient was shown to be a good gauge of the total volume of bubbles per cubic meter of water, allowing the use of a single-beam sonar for measuring volumetric bubble concentrations. Data obtained from hydroacoustic surveys on Lake Kinneret, where gaseous methane is emitted from randomly dispersed sediment sources, indicated that ~90% of bubbles escaping from soft sediments ranged from 1.3 mm to 4.5 mm and ~50% ranged from 2.0 mm to 3.2 mm in equivalent radius. In summer-fall 2001, the gaseous methane fluxes from hypolimnetic sediments was ~10 mmol m-2 d-1, accounting for one-third of the observed methane accumulation in the hypolimnion. This relatively high ebullition rate could be attributed to the gradual decreasing of the mean water level in preceding years

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“…Experiments by Wu and Gharib [18] with rising bubbles of equivalent diameter range d = 1 -2 mm in still water have been interpreted as an oscillating bubble being twice as fast as the unperturbed bubble of the same volume. These results were considered surprising by other authors, and refuted, for example by [19] -who, however, in their detailed force balance came with another surprising idea: a claim that the velocity decrease is due to added mass rather than the hydrodynamic drag.…”

Section: Drag Increased By Oscillationmentioning

confidence: 81%

Unexpected behaviour of microbubbles immediately at the aerator exit

Tesař¹

2013

Computational Methods in Multiphase Flow VII

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Microbubbles (of diameter less than 1 mm) are desirable for many engineering applications. Until quite recently, generating them efficiently was a problem. A solution was found in excitation of gas supply by inexpensive and reliable nomoving-part fluidic oscillators. Strangely, generated microbubbles are larger than expected. The author studied their formation using a high-speed camera with a long distance macro-lens. The images revealed the cause being a conjunction of bubbles, mostly taking place within the very proximity of the aerator exit. Small bubbles move slowly and do not vacate fast enough from the position in which they were generated. They thus get into contact with the next generated bubble. Another cause of slow departure is the increased drag caused by shape oscillation driven by energy released in the conjunction. The conjunctions may also occur due to lateral bubble motion if the Reynolds number exceeds the vortex shedding threshold.

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Induced bubble shape oscillations and their impact on the rise velocity

Abstract: When a 2-4 mm diameter bubble rising with constant velocity hits a thin wire, bubble shape oscillations can be induced. As a consequence also the bubble rise velocity strongly oscillates. With the help of a force balance we show that these velocity oscillations are an added-mass effect.

Cited by 51 publications

References 22 publications

On hydrodynamical properties of ellipsoidal bubbles

On hydrodynamical properties of ellipsoidal bubbles

Quantifying gas ebullition with echosounder: the role of methane transport by bubbles in a medium‐sized lake

Unexpected behaviour of microbubbles immediately at the aerator exit

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