Session D14: Bubbles I

Inertial collapse and oscillations of a bubble in a compressible viscoelastic medium

The inertial collapse and subsequent oscillations of a bubble in a compressible viscoelastic medium are studied theoretically and numerically in the context of therapeutic ultrasound. The focus of the present work is on the response of a bubble subjected to a step increase in pressure, i.e., Rayleigh collapse. Linear constitutive relations that include stress relaxation, elasticity, viscosity and strain rate relaxation are considered. A perturbation analysis is followed to estimate the damping, frequency and relaxation of the oscillations. The results are compared to numerical solutions of the Keller equation, showing good agreement over a wide range of parameters. The nonlinear coupling between viscosity, compressibility, elasticity and relaxation leads to unexpected bubble behavior, e.g., sustained oscillations when damping is expected. Direct simulations of the full three-dimensional equations of motion will be discussed, including viscous and viscoelastic effects, non-spherical behavior and nonlinear constitutive models.   

Modeling of a single clean bubble bouncing on a free surface

Bouncing of a rectilinearly rising bubble on a free surface is modeled with the use of a simple mass-spring system. We use an equation of motion of the system that consists of two springs connected in series, which allows us to account for the restoring forces of both the bubble and free surfaces, and a conservation equation of energy, which allows us to describe an exchange between the surface energy due to deformations of both the bubble and free surfaces and the kinetic energy of the bubble. We can determine that the contact time, i.e. the time duration of a bubble contacting a free surface, should be a half of the characteristic period of the oscillator. We also observe a single clean bubble bouncing on a flat free surface in ultrapure water in order to verify the present model. Analytical and experimental results agree quite well, even in the cases with significant surface deformations. When bubbles are smaller than 0.6 mm in radius, the deformations of both the bubble and free surfaces play important roles in bouncing. In the case of larger bubbles, bouncing is dominated by the free surface deformation since the bubble has already been highly deformed before collision.   

Bubble Motion in a Vibrating Liquid

Gas bubbles can be forced to move downward, overcoming the buoyancy force, by vertical vibration of the liquid containing the bubble. Bubble motion is controlled by interactions of the oscillating pressure field, and the corresponding bubble volume, with the drag force acting on the bubble. The bubble-drag asymmetry and the oscillating pressure gradient can combine to produce net bubble motion. This is analogous to the Bjerknes force in high-frequency vibrations. Experiments have been conducted demonstrating downward bubble motion over a range of vibration conditions (all less than 300 Hz), liquid properties, and pressure in the air above the free surface. Bubble size and velocity were measured using automated image-processing routines. Comparisons with theory and simulations will be shown. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Orbital revolution of a pair of bubbles in an acoustic field

This experimental study aims to clarify the mechanism of orbital motion of two oscillating bubbles in an acoustic field. Trajectory of the orbital motion was observed using a high-speed video camera. Because of a good repeatability in volume oscillation of bubbles, we were also able to observe the radial motion driven at 24 kHz by stroboscopic like imaging; the cyclic bubble oscillation was appeared to slow down by capturing images at the framing rate close to the forcing frequency. The orbital motions of bubbles raging from 0.13 to 0.18 mm were examined with different forcing amplitude and in different viscous oils. As a result, we found that pairs of bubbles revolve along a circular orbit around the center of mass of the orbiting two bubbles. We also found that the two bubbles perform anti-phase radial oscillation. Although this radial oscillation should result in a repulsive secondary Bjerknes force, the bubbles kept a constant separate distance of about 1 mm, which indicates the existence of centripetal primary Bjerknes force. The angular velocity of orbital revolution increases linearly with the increase in Bjerknes force.   

On the influence of nanobubbles on the evaporation inception in liquids

We present a new approach for the calculation of the evaporation inception point in liquids. Using the derivative of the system's energy with respect to the void fraction as a stability criterion for the whole system, we consider that sudden evaporation only occurs when the bubble expansion is energetically favourable. The results obtained are shown to be equivalent to the Blake radius for a single spherical bubbles under tension. This method is proven to provide reasonable results also for superheated water. The method also allows gaining new insight into complex systems where nanobubbles stick to the walls. We provide new clues about future experimental measurements that should shed light into the process of bubble nucleation.   

Bubble motion and size variation during thermal migration with phase change

An analysis of the motion of a spherical bubble in a two-phase, single component system with a vertical linear temperature gradient is presented. The model for the migration of an immiscible bubble considered by Young, Goldstein and Block is modified to allow for phase change at the bubble surface, including the possibility of both bubble translation and the change of bubble radius with time. Depending of the material parameters, the thermocapillary effects that normally lead to migration of an immiscible bubble can be overwhelmed by the effects of latent heat generation, resulting in a change in the mechanism driving the motion. For a water-steam system conditions are determined for a stationary bubble in which the the effects of buoyancy and thermal migration are balanced. The stability of the bubble is also considered.   

Film drainage of viscous liquids on top of bare bubble: Influence of the Bond number

We present experimental result of film drainage on top of gas bubbles pushed by gravity forces toward the upper surface of a liquid bath for Newtonian liquids with mobile interface (UCON, castor oil and soda-lime-silica melt). The temporal evolution of the thickness of the film between a single bubble and the air/liquid interface is investigated \textit{via} interference method under various physical conditions, range of viscosities and surface tension of the liquids, and bubble sizes. These experiments evidence the influence of the deformation of the thin film on the thinning rate and confirm the slow down of film drainage with Bond number as previously reported by numerical work. A simple model that considered the liquid flow in the cap squeezed by buoyancy forces of the bubble is in good agreement with experimental and numerical data. Qualitatively, the smaller is the area of the thin film compare to the surface of the bubble, the faster is the drainage.   

Antibubble dynamics: slipping or viscous interfaces?

An antibubble is a spherical thin air shell that is immersed in a surfactant mixture and drains under the action of hydrostatic pressure. Two lubrication models are proposed that account for either slipping or shear viscosity at the shell interfaces. Numerical solutions show that the antibubble lifetime decreases with increasing slip length or decreasing surface shear viscosity. Comparison with available experimental data is provided and gives some hints to discriminate between the slip and the surface viscous models, though a correspondence between these models is also established.   

Interaction and coalescence of two bubbles rising in a Hele-Shaw cell at high Reynolds numbers

We investigated the relative motion and deformation of two large bubbles released consecutively in a quiescent liquid confined in a thin-gap cell using a high-speed camera and image processing. Though the second bubble injected is smaller, we observed that in all cases it accelerates and catches up with the leading bubble. This acceleration is related to the wake of the leading bubble which also induces important changes in width and curvature of the trailing bubble. On the contrary, the velocity of the leading bubble is unaltered during the interaction. Shape adaptation of the two bubbles is observed prior to coalescence: the shape of the two bubbles together closely resembles a single large bubble. After the interfaces touch, the liquid film is drained at a constant velocity.   

An effect of zigzag and surface motions of a CO2 bubble on the mass transfer from the bubble to the surrounding liquid

A bubbly flow is very useful for aeration, agitation and an enhancement of chemical reaction, etc. in industrial processes. In order to improve the efficiency of the industrial plants, we should acquire the knowledge of a bubbly flow: e.g. bubble motion, mass transfer and surrounding liquid motion. Using a single CO2 bubble well-controlled in its zigzag motion and surface oscillation, we discuss a relation between the bubble motions and the mass transfer. For this particular purpose, we precisely measured the bubble volume and the surface area, using two high-speed cameras and mirrors. By image processing, a 3D-bubble shape was reconstructed based on the projected bubble images. We regarded the volume/surface area of 3D-model as the volume/surface area of the examined bubble. In addition, instantaneous mass-transfer coefficients were calculated from these results. The mass transfer of the bubble was enhanced when the bubble trajectory shifted from the linear mode to the zigzag mode.