Session BH: Bubbles II

Modeling of a bubble bouncing on a free surface in super purified water

A model for a bouncing of a bubble on free surface in super purified water is proposed. The model is based on mass-spring system and energy conservation system. In order to describing the effect of the bubble and free surface motion in the model, we assume two springs connected in series. We also define that the initial kinetic energy when the bubble contacts with free surface is converted into the increase in surface energy when the rise velocity of the bubble is zero. From the two equations, the contact time which is also the half period of the oscillator is represented by the deformations and the approach velocity. An experiment is also performed to discuss the applicability of the model. Especially, the bubble motion and the free surface deformation are captured. The good agreement is found between the contact time given by images and that derived by the model. However if we consider only the free surface deformation effect, the estimated contact time becomes smaller than that of the model with both of the deformations. We thus conclude that both of the deformation effects are essential for the estimation of the system.   

High-speed jet formation after solid object impact

A circular disc impacting on a water surface creates a remarkably vigorous jet. Upon impact an axisymmetric air cavity forms and eventually pinches off in a single point halfway down the cavity. Immediately after closure two fast sharp-pointed jets are observed shooting up- respectively downwards from the closure location, which by then has turned into a stagnation point surrounded by a locally hyperbolic flow pattern. This flow, however, is not the mechanism feeding the two jets. Using high-speed imaging and numerical simulations we show that jetting occurs as a consequence of the local flow around the base of the jet, which is forced by the colliding cavity walls. Based on this insight, we then show how the analytical description of a collapsing void (using a line of sinks along the axis of symmetry) can be continued beyond the time of pinch-off, namely by turning it into a discontinuous line plus a point sink located near the base of the jet. The model is in quantitative agreement with the numerical and experimental data.   

Jet dynamics after cavity collapse

It has been recently shown -Gekle, Gordillo, van der Meer and Lohse, \textit{Phys. Rev. Lett.}, 2008 (submitted)- that the liquid velocity field after cavity collapse can be analytically described as a superposition of a discontinuous line of sinks plus a concentrated point sink. This theory is able to quantitatively predict the axial and radial positions of the base of the high speed jets ejected. Nevertheless, the flow field within the fast sharp pointed jets shooting up and downwards cannot be predicted using this simplified description. Instead, we will show that downstream of a small region with a size of the order of the jet base, in which the liquid is accelerated upwards, liquid velocity and jet shape can be described by a simple unidirectional model in remarkable agreement with simulations. Up to first order, fluid particles conserve their velocities but we also show that, no matter how large the local Weber number at pinch-off is, capillarity ends up playing a role in the breakup of the ejected liquid jets.   

Impact of solid objects on water: The influence of air

Upon the impact of a disk on a water surface a cavity is created which collapses under the influence of the hydrostatic pressure. This eventually leads to the formation of a neck connecting the entrapped air pocket above the disk with the surroundings. The collapsing cavity walls push out air at an increasing speed as the neck narrows towards the pinch-off point. Using high-speed imaging we investigate the influence of the air flow on the collapse. At high air speeds, we observe a characteristic nose-like deformation of the cavity wall which is also found in numerical boundary integral calculations that include both water and air. The neck radius at which this nose appears can be predicted using a similar kinetic energy argument as was presented in J.M. Gordillo et al., Phys. Rev. Lett. 95, 194501 (2007).   

Impact of a solid object on a foam

Solid foams are commonly used to absorb shocks. We consider here the efficiency of liquid foams as kinetic energy absorbers. We first discuss the possibility of trapping a projectile in the foam. Then we focus on the dynamics of the impacting object, which depends on the foam's rheological properties. By varying the impact velocity, we explore different regimes and observe the foam's response. We finally propose a model capturing these impact features and predicting the amount of foam needed to stop a projectile.   

Liquid motion induced by the collision of a pair of bubbles

Characteristics of the liquid motion through the collision of a pair of bubbles were experimentally investigated. Hypodermic needles and a bubble launcher utilizing pressure oscillation were employed to exactly extract and highly reproduce the interaction between the liquid-phase motion and bubble motion through the collision. We obtained the accurate velocity fields of the liquid motion using recursive cross correlation PIV technique. After the bubbles collide, the vertical velocity of each bubble decreased rapidly. From the PIV results, when the bubble velocity decreased, we found out the bubble wake which kept its own momentum flew into the area between bubbles. That flow continued the upward motion even after bubbles passed. From the time-series PIV data, we calculated the standard deviation of liquid-phase velocity as the parameter of disturbance. The standard deviation of the vertical liquid velocity in the upper area of collision point shows high values. The upward flow generated by the bubble collision (in a strict sense, interaction of the surrounding liquid of the colliding bubbles) results in this intensive disturbance.   

The coefficient of restitution for air bubbles colliding against solid walls in viscous liquids

The motion of air bubbles undergoing collisions with solid walls was studied experimentally. Using a high speed camera, the processes of approach, contact and rebound was recorded for a wide range of fluid properties. The process is characterized considering a modified Stokes number, $St^*=(C_{AM}\rho d_{eq} U_o)/(9\mu)$, which compares the inertia associated with the bubble (added mass) and viscous dissipation. We found that the dependence of the coefficient of restitution, $\epsilon=-U_{reb}/U_o$, with the impact Stokes number can be approximated by $\log\epsilon \sim (St^*)^{-1/2}$, which is different from that found for the case of solid spheres are fluid drops. A discussion of the nature of this dependence is presented.   

Effects of bubble size distributions on acoustics of dilute bubbly liquids

We examine the acoustic properties of dilute bubbly liquids whose equilibrium bubble radius is widely scattered. First, we rigorously derive a continuum model for the mixture using an ensemble averaging technique. In computations of the averaged equations for polydisperse bubbles, there is a need to evaluate moments of the distribution of initial bubble radius, which are computationally prohibitive. For the case of impulsive pressure forcing, it is mathematically shown that inviscid bubble oscillations reach a statistical equilibrium and lead to time-invariant values of the moments due to phase cancellations amongst the different-sized bubbles. At statistical equilibrium, the moments can be computed using the period-averaged radius instead of the instantaneous one. The period-averaged formula enables us to substantially reduce the numerical effort associated with bubble size distributions. Based on the continuum model with the period-averaged formula, we solve linear wave propagation in the mixture and compare the results to the theory of Commander and Prosperetti (1989) to demonstrate the usefulness of the present model. We also show that distributions of bubble sizes effectively smooth out a rapid change of phase velocity and a sharp maximum of attenuation observed around resonance in the case of monodisperse bubbles.   

Dynamics of microbubbles under the effect of ultrasonic pressure waves

Ultrasound contrast agents are small ($1-10~\mu m$) gas-filled bubbles encapsulated by a lipid bilayer to stop dissolution of the gas in the surrounding liquid. They are used in medical clinical practice to improve the signal to noise ratio of human tissue images with poor quality due to low acoustic impedance mismatch between the tissue of interest and its surroundings. The dynamics of these bubbles are poorly understood and they are typically considered as passive flow tracers. This lack of understanding of the hydrodynamic and acoustically-induced forces on the bubbles impairs the development of more sensitive applications such as targeted drug delivery. We have performed experiments with microbubbles immersed in stagnant and pulsatile flows and characterized their trajectories with and without the application of an ultrasound field. We will describe the competition of hydrodynamic forces (viscous drag, added mass, lift, etc.) and Bjerkens force (ultrasound radiation) in determining the trajectories of this microbubbles in simple geometries that mimic the human circulatory system.   

Rapid Evaporation of microbubbles

When a liquid is heated to a temperature far above its boiling point, it evaporates abruptly. Boiling of liquid at high temperatures can be explosive and destructive, and poses a potential hazard for a host of industrial processes. Explosive boiling may occur if a cold and volatile liquid is brought into contact with a hot and non-volatile liquid, or if a liquid is superheated or depressurized rapidly. Such possibilities are realized, for example, in the depressurization of low boiling point liquefied natural gas (LNG) in the pipelines or storage tanks as a result of a leak. While boiling of highly heated liquids can be destructive at \textit{macroscale}, the (nearly) instantaneous pace of the process and the release of large amount of kinetic energy make the phenomena extremely attractive at \textit{microscale} where it is possible to utilize the released energy to derive micromechanical systems. For instance, there is currently a growing interest in micro-explosion of liquid for generation of micro bubbles for actuation purposes. The aim of the current study is to gain a fundamental understanding of the subject using direct numerical simulations. In particular, we seek to investigate the boundary between stable and unstable nucleus growth in terms of the degree of liquid superheat and to compare the dynamics of unstable and stable growth.