Session GF: Drops and Bubbles V

Formation of a single micro bubble by controlled acoustic gas pressure wave

We have developed micro bubble generator which can control both bubble size and generation frequency independently and accurately, by using acoustic gas pressure wave. However, though, the mechanism of this generator has not been fully understood. We further investigated the role of the acoustic gas pressure wave and found the optimal pressure wave for a single micro bubble formation. We succeeded in forming a bubble, whose radius was ranging from 0.3 to 0.8 mm, with extremely small standard deviation of less than 1 micro meter. By analyzing images taken by high-speed photography, detachment of a bubble from a nozzle, especially shrinkage of a capillary bridge connecting a bubble and a nozzle, is investigated in detail. Force balance on a growing bubble is evaluated with the help of experimental data of time rate of both bubble radius and position of the center of mass of a bubble, by applying a spherical bubble formation model. As results, we find that with the decrease in gas pressure, the capillary bridge is sucked down into a nozzle and added mass force is exerted in the upward direction, both of which promote detachment of a bubble from a nozzle.   

Translational motion and shape deformation of a pair of bubbles in an acoustic field

Translational motions of bubbles with volume and shape oscillations were studied using high-speed photography. The volume oscillations of bubbles, which cause hydrodynamic interactions between two bubbles, were captured in detail. Bubbles of around resonant sizes were forced to oscillate in acoustic fields having frequency of 18.0 and 34.5 kHz, and amplitude ranging from 20 to 100 kPa. The recording rate of 125,000, 250,000 and 1000,000 frames per second were used in high-speed photography. Experimental results for the translation are compared to the previous theoretical model derived by Takahira (1992). This model takes into account the diffusion of vorticity from bubble surface, and is valid even for the translation of intermediate Reynolds number. The validity of the model is verified experimentally for bubbles having Reynolds number of the order of 10. The effect of shape deformations on the translation was also examined.   

Surface modes of bubbles in an acoustic field

We investigate the nonspherical oscillations, or surface modes, of bubbles of radius between 10 and 60 microns within an ultrasonic field of frequency of 130 kHz. We show experimentally that a threshold in acoustic pressure is required to trigger the surface modes, that they appear only after a few cycles of ultrasons, and that the observed mode number (2 to 6) is linearly related to the resting radius of the bubble and does not depend significantly on the acoustic pressure. We relate the observations to a parametric instability: The amplitude of nonspherical oscillations is modulated by the radial dynamics. Using a simple, linear radial dynamics, we reproduce the dependence of the observed mode number with the radius. A more accurate, nonlinear radial dynamics model determined from a modified Rayleigh-Plesset equation yields excellent agreement, both for the threshold in acoustic pressure and for the mode number, in the whole parameter space. The implications of these results for the coated microbubbles widely used as ultrasound contrast agents in medical acoustics are discussed.   

On the transition frequencies of acoustically coupled gas bubbles

The transition frequencies of acoustically coupled gas bubbles are reexamined to further clarify their physical properties. In recent papers we have pointed out that a fundamental component in multibubble systems had been overlooked. We have shown theoretically that a bubble interacting with a neighboring bubble in a sound field has up to three ``transition frequencies'' which invert the pulsation phase of the bubble [Ida, Phys. Lett. A \textbf{297}, 210 (2002)]. The number is larger than that of resonance frequencies of the system and at least one of the three is thus not a resonance frequency. In the following papers we have suggested that the height relation between the newly derived characteristic frequency and the driving frequency determines the sign of the secondary Bjerknes force [Ida, Phys. Rev. E \textbf{67}, 056617 (2003)] and that the ``avoided crossing'' and accompanying state exchange taking place between bubbles can be detected by observing the transition frequencies [Ida, Phys. Rev. E \textbf{72}, 036306 (2005)]. We here attempt to clarify several similarities and differences among the natural, resonance, and transition frequencies. This effort thoroughly clarifies the roles of the transition frequencies in bubble-bubble interaction [Ida, Phys. Fluids \textbf{17}, 097107 (2005)].   

Shape oscillation and mode transition of bubble(s) under ultrasonic vibration

Behaviors of bubble(s) exhibiting non-linear shape oscillation under ultrasonic vibration are focused. Size of the bubbles interested in the present study is of O(1 mm) in diameter. The bubbles were injected through the micro syringe to the test fluid (water or water/surfactant mixture) filled in the rectangular tank. Ultrasonic vibration were triggered after the detach of the bubble from the tip of the syringe; thus the bubbles were exposed to the periodic oscillation in rising the test fluid. The authors clearly detect radial and shape oscillations under the large-amplitude vibration by use of high-speed camera. Preferable mode number of the shape oscillation, and the transition process from the radial to the shape oscillation are discussed.   

The collapse of a bubble in an electric field

The collapse of a bubble in an electric field at low Mach numbers is examined. A modified Rayleigh-Plesset equation is derived along with another equation for the ellipsoidal shape deformations which are assumed to be small. Numerical integration of these equations indicate that a bubble can be made to collapse by instantaneously switching on an electric field. Non-harmonic volumetric oscillations are also observed for time-dependent electric fields of sufficiently large amplitude. We also show that the rate of bubble collapse driven by external pressure variations due, for instance, to acoustic forcing, can be accelerated.   

Micro-scale heat transfer mechanisms of single-bubble nucleation events

The formation, growth and departure of a single bubble at the surface of a heated wall is a fundamental problem which has applications ranging from bubble micropumps and inkjet printers to cooling applications based on boiling heat transfer. The precise prediction of this phenomenon, however, is made difficult by the strong coupling of mass, momentum and energy in the vicinity of a dynamic liquid/vapor interface. Although several important mechanisms (such as microlayer evaporation, transient conduction via surface rewetting and microconvenction from bubble pumping) have been identified over the last half-century, their exact contribution to the bubble growth and overall wall heat transfer has been subject to much debate even in the current literature. In order to quantitatively answer the above question, a novel multi-layer MEMS sensor array has been constructed to obtain high-resolution measurements of surface temperature and heat flux underneath a single bubble within a perfluorcarbon liquid. The result of these measurements has allowed for the detailed description of all three transient mechanisms, and a quantification of their contributions to the bubble growth and heat transfer associated with the ebullition event. Specifically, it is found that convection near the periphery of the bubble interface typically makes the largest contribution to the wall heat transfer at large superheats, followed by rewetting transient conduction and microlayer evaporation, respectively.   

Break-up of an air bubble in water: Memory of azimuthal asymmetry

Recent experiments showed that the break-up of an air bubble in water retains a detailed memory of asymmetries present in the initial shape [1]. To gain insight into the physical mechanism for this memory, we analyze how non-axisymmetric perturbations change the collapse dynamics of a cylindrical void in water. We also consider the effects of surface tension and viscous dissipation, both of which act to smooth out shape perturbations. \newline \newline [1] N. Keim et al, cond-mat/0605669   

Transition from spherical cap to toroidal bubbles.

A puzzling feature of large buoyancy-driven bubbles is that, given an initial gas volume, the final shape can be either a spherical cap or a torus. We~perform a numerical investigation of the evolution of such bubbles using a Volume of Fluid method that does not explicitly reconstruct interfaces. We first determine the localization of the transition from spherical cap to toroidal bubbles in the parameter space built on the Bond and Archimedes numbers. Two different transition scenarios are identified. In the limit of large Ar (resp. large Bo), the bubble pinch-off is due to an upward jet (resp. downward jet) coming from the rear part (resp. front part) of the bubble. We also examine the influence of the initial conditions on the final bubble topology. More precisely, increasing the initial oblateness for a fixed Bond number is found to broaden the domain of existence of spherical cap bubbles.   

The generation of singular liquid jets in the axisymmetric bubble pinch-off at high Reynolds numbers

In this presentation we review the \emph{symmetric} and \emph{asymmetric} type of bubble pinch-off local geometries described in {\it PRL}, {\bf 95}, 194501, and provide with the different scalings for the minimum radius, $R_0$, as the singularity is approached. Moreover, in the case of gas inertia is not relevant in the description of the latest stages of bubble breakup (\emph{symmetric pinch-off}), local bubble shape is given by $F(z,t)/R_0(t)=1-[1/(6\,log(R_0))]\,(z/R_0)^2$. However, we also discuss that the asymptotic solutions for the \emph{symmetric} case are only reached for times so close to pinch off that they might be difficult to find and, therefore, bubble pinch-off strongly depends on initial conditions. Regarding the \emph{asymmetric} type of breakup, we provide new experimental evidence that support that, close to pinch-off, gas and liquid inertia are balanced. We will show that the velocity of the singular liquid jets formed within air and helium bubbles generated from a needle immersed in a coaxial co-flow strongly depends on gas density. More precisely, the ratio of the liquid jet velocity formed using air ($u_a$) to the liquid jet velocity formed using helium ($u_{h}$) is given, for the same operating conditions, by $u_a/u_h\simeq\,(\rho_{air}/\rho_{helium})^{1/n}$, with $2 [Preview Abstract]