Shape Oscillations of Rising Bubbles

Lunde, Knud; Perkins, Richard J.

doi:10.1007/978-94-011-4986-0_20

Cited by 40 publications

(44 citation statements)

References 11 publications

(22 reference statements)

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“…First, for each value of Mo, the larger the bubble (i.e., Bo and Ga), the larger St, irrespective of the detailed geometry of the corresponding nonvertical regime. This tendency, which is in line with past observations at higher Reynolds number [56], results from the increasing oblateness of the bubble as D increases, which in turn increases the amount of vorticity generated at its surface. Second, the Strouhal number is seen to increase uniformly with Mo: Focusing on the zigzagging regime, St is about 0.045 when Mo = 1.1 × 10 −11 and increases up to 0.136 when Mo = 9.9 × 10 −6 .…”

Section: A Observed Transitionssupporting

confidence: 91%

“…The most likely option left is that they result from the coupling between bubble deformation and wake dynamics, a coupling that has been studied in the past for larger bubbles having Reynolds numbers of O(10 3 ) [51,55,56]. Indeed, every transient change in the bubble shape (especially in the vicinity of the bubble's equator) results in a change in the local curvature of the bubble surface, hence in a variation of the azimuthal surface vorticity.…”

Section: Flattened Spiraling Regimementioning

confidence: 99%

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Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability

et al. 2016

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 16174 (2016)] in which the neutral curve associated with this transition was obtained by considering realistic but frozen bubble shapes. Depending on the dimensionless parameters that characterize the system, various paths geometries are observed by letting an initially spherical bubble starting from rest rise under the effect of buoyancy and adjust its shape to the surrounding flow. These include the well-documented rectilinear axisymmetric, planar zigzagging, and spiraling (or helical) regimes. A flattened spiraling regime that most often eventually turns into either a planar zigzagging or a helical regime is also frequently observed. Finally, a chaotic regime in which the bubble experiences small horizontal displacements (typically one order of magnitude smaller than in the other regimes) is found to take place in a region of the parameter space where no standing eddy exists at the back of the bubble. The discovery of this regime provides evidence that path instability does not always result from a wake instability as previously believed. In each regime, we examine the characteristics of the path, bubble shape, and vortical structure in the wake, as well as their couplings. In particular, we observe that, depending on the fluctuations of the rise velocity, two different vortex shedding modes exist in the zigzagging regime, confirming earlier findings with falling spheres. The simulations also reveal that significant bubble deformations may take place along zigzagging or spiraling paths and that, under certain circumstances, they dramatically alter the wake structure. The instability thresholds that can be inferred from the computations compare favorably with experimental data provided by various sets of recent experiments guaranteeing that the bubble surface is free of surfactants.

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Section: A Observed Transitionssupporting

confidence: 91%

Section: Flattened Spiraling Regimementioning

confidence: 99%

Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability

et al. 2016

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“…Shape oscillations start to occur here. These oscillations, studied before in [5][6][7] and other papers, formed part of the thesis [8] of the junior author. The oscillations can be characterized with the indices n and m, where n is the number of wave lengths in the direction from pole to pole and m the same in azimuthal (equatorial) direction.…”

Section: Introductionmentioning

confidence: 99%

“…An analytical approach would be welcome. In [6] an approximate calculation is given, which will be discussed later in the paper. Here we attempt an exact calculation, for an ellipsoidal shape, in the spirit of the classical calculation of the modes for a spherical shape.…”

Section: Introductionmentioning

confidence: 99%

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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“…One of our objectives is to standardize the initial conditions, a luxury not easily available to experimenters! A curious phenomenon, the path instability, has been the subject of a host of experimental [22][23][24][25] , numerical 26,27 and analytical 28,29 studies. This is the name given to the tendency of the bubble, under certain conditions, to adopt a spiral or zigzagging path rather than a straight one.…”

mentioning

confidence: 99%