Shape oscillations on bubbles rising in clean and in tap water

Abstract

This paper deals with air bubbles rising in purified water in the range of equivalent diameters where surface oscillations appear on the interface. The shape of the bubbles including these capillary distortions is recorded by taking a large number of high speed pictures for each spiraling or zigzagging bubble trajectory. In analogy with surface harmonics, the oscillations are indicated as (2,0) axisymmetric and with wavelength equal to the distance from pole to pole and (2,2) nonaxisymmetric and with wavelength equal to one-half of the length of the equator. In the second series of experiments, the phenomena in the wakes of rising bubbles are made visible by using Schlieren optics, which are applicable because a temperature gradient is applied to the water. The frequencies of vortex shedding correspond to the (2,0) mode of surface oscillation, whereas in other works reported in the literature, they correspond to twice the frequency of the spiraling or zigzagging bubble paths. By measurements and by analysis, it is shown here that the latter is due to contamination of surfactants.

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

“…Qualitatively similar behaviors have been noticed in several experiments, especially those performed in ultrapure water in Ref. [51]. However, it must be stressed that these experiments were performed at significantly higher Reynolds number (Re T 10 3 ), so the observed flattened spiraling paths succeed the planar zigzagging or helical paths when the bubble diameter is increased and announce the transition to the high-Reynolds-number chaotic (rocking) motion, whereas here they precede the occurrence of the well-defined planar zigzagging and spiraling regimes.…”

“…For instance, it has been observed with light rising spheres [59] that increasing the Galilei number (the body-to-fluid density ratio being kept fixed) yields successively rectilinear, steady oblique, oscillating oblique, planar zigzagging, and chaotic paths. Similar observations have been reported with rising bubbles, i.e., in a given fluid, chaotic (frequently referred to as rocking) motions are observed for bubble diameters larger than those giving rise to zigzagging and spiraling paths [2,51,62].…”

“…9. Observations showing the existence of secondary vortex structures have repeatedly been reported in experiments performed in low-Mo fluids [4,26,[51][52][53]. Here the wavelength associated with the secondary loops is somewhat larger than the spacing s v between the two vortex threads, which might suggest that they result from Crow instability [54].…”

“…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.…”

Dynamics of an initially spherical bubble rising in quiescent liquid

“…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.…”