Force measurements on rising bubbles

Abstract

The dynamics of millimeter sized air bubbles rising through still water are investigated using precise ultrasound velocity measurements combined with high speed video. From measurements of speed and three dimensional trajectories we deduce the forces on the bubble which give rise to planar zigzag and spiraling motion. I. BACKGROUNDAn understanding of bubble-fluid interactions is important in a broad range of natural, engineering, and medical settings. Air-sea gas transfer, bubble column reactors, oil/natural gas transport, boiling heat transfer, ship hydrodynamics, ink-jet printing and medical ultrasound imaging are just a few examples where the dynamics of bubbles play a role (e.g [6,16,26]).We narrow our focus to a single air bubble rising through still water. The buoyant force which drives the bubble's rise does work resulting in an increase in kinetic energy of the surrounding fluid. This induced flow, in turn, gives rise to hydrodynamic forces on the bubble and hence changes in the bubble trajectory. The measurement of these forces is the aim of the experimental work presented here Our study includes a range of bubble sizes between 0.84 and 1.2 mm in radius. At the small end of this range the bubble's path is rectilinear. As the bubble size is increased, one observes a transition to a planar zigzag path [8,23]. A second instability, often preceded by the zigzag, results in a spiraling path [5,8,15,23]. For even larger bubbles, a third type of oscillating path occurs, which has similarities to the zigzag, sometimes called "rocking". We do not address this state and emphasize that it is different than the zigzag mentioned above. Unlike the zigzag state that we study, the rocking bubble undergoes dramatic shape oscillations and the frequency of path oscillation is several times higher than the zigzag or spiral [5,15]. Our approach is to use well resolved measurements of three-dimensional bubble trajectories to calculate the hydrodynamic forces on the bubbles. Other recent studies have investigated path instabilities with special attention paid to the role of the bubble's wake. Lunde and Perkins [15] used dye to observe the wake of ascending bubbles and solid particles. Brücker [5] used particle image velocimetry to study the wake of large spiraling and rocking bubbles. Mougin and Magnaudet [22,23] These studies have revealed a wake consisting of two long, thin, parallel vortices aligned with the bubble's path. One vortex rotates clockwise and the other counter-clockwise. For a spiraling bubble the wake vortices are continuously generated, while they are interrupted twice per period of path oscillation for the zigzag. Mougin and Magnaudet [22,23] observed a nearly identical wake structure in their numerical simulations (see also [24]). It is believed that the wake vortices play a critical role in generating hydrodynamic forces on the bubble.In the next section we describe the experimental apparatus and measurement techniques, as well a typical bubble trajectory. In section III, we present a method for extracti...

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

“…In cases in which the bubble rather follows a zigzagging or a flattened spiraling path, the decrease of U is succeeded by oscillations whose amplitude depends of course on that of the lateral bubble displacements. Similar oscillations have been reported in experiments [69,70] and DNS [21] at higher Reynolds numbers. The corresponding frequency is twice that of the lateral motion since the drag force is an even function of the bubble inclination with respect to the vertical.…”

A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow

“…Fig. 20 shows the calculated vertical rise velocity as a function of time for various bubbles where one can see that the terminal rise velocity is reached approximately after 0.15 s which is in agreement with the experimental observations reported in [55]. For the final shape of the 1 mm bubble, Fig.…”

Dynamics and morphology of single ellipsoidal bubbles in liquids

“…In Shew et al (2006), a pulsation in the bubble vertical motion at twice the frequency of the bubble horizontal motion was observed for millimetre-sized bubbles rising in water with a zigzag motion. Such a pulsation has not been identified in the helical motion of these bubbles.…”

“…Their dynamics and morphology highly influence the efficiency of these industrial applications because they control the mixing and the mass transfers between the gas and the liquid. Therefore, the dynamics and the morphology of bubbles moving in various liquids have been extensively investigated, theoretically, numerically and experimentally, for many years (Rosenberg (1950), Haberman and Morton (1953), Saffman (1956), Hartunian and Sears (1957), Moore (1958Moore ( , 1963Moore ( , 1965, Aybers and Tapucu (1969a,b), Grace et al (1976), Clift et al (1978), Ryskin and Leal (1984), Dandy and Leal (1986), Blanco and Magnaudet (1995), Duineveld (1995), Lunde and Perkins (1997), Brüker (1999), Ellingsen and Risso (2001), Mougin andMagnaudet (2002), de Vries et al (2002), Haut and Cartage (2005), Shew et al (2006), , , Magnaudet and Mougin (2007), Zenit and Magnaudet (2008), Wylock et al (2011), Legendre et al (2012), Cano-Lozano et al (2012) and Mikaelian et al (2013)). As the continuation of all these studies, three topics on the dynamics and the morphology of single ellipsoidal bubbles rising in liquids are investigated in this paper.…”