Session P21: Bubbles: Acoustics, Growth, and Collapse

Jets from shock wave-induced microbubble collapse

Shock wave-driven microbubble collapse, which sometimes produces high-speed jets, occurs in a wide range of applications involving transient pressure waves and liquid-gas media.

These include, for instance, cavitating flows of fluids containing bubbles and therapeutic shock wave lithotripsy.

Although thoroughly studied through numerical simulations, the small spatial and temporal scales associated with such phenomena make their experimental observation particularly challenging.

Here, shock-induced collapses of micrometric gas bubbles are temporally resolved through ultra-high-speed imaging, which offers unprecedented details on the jetting dynamics.

Such visualizations can be directly compared with a simple model based on Rayleigh-Plesset-type bubble dynamics. 

These results help determine the shock driving conditions required for microbubbles to form jets.   

Application of Koopman LQR to the control of nonlinear bubble dynamics

Koopman operator theory has gained interest in the past decade as a framework for analyzing nonlinear dynamics by embedding in an infinite-dimensional function space. This enables the use of linear control and estimation methods for strongly nonlinear systems. Recently, the linear quadratic regulator (LQR) problem for nonlinear dynamics was formulated in Koopman eigenfunction coordinates and its feasibility demonstrated; however, applications were limited to controlling the Hamiltonian for conservative systems. Here, we extend this framework to use multiple complex eigenfunctions and illustrate its enhanced power by driving several classical nonlinear oscillators to follow arbitrary, prescribed trajectories. We then control nonlinear bubble dynamics, as described by the well-known Rayleigh-Plesset equation, with two novel objectives: 1) stabilization of the bubble at a nonequilibrium radius, and 2) simple harmonic oscillation at amplitudes large enough to incite nonlinearities. Control is implemented through a single-frequency transducer whose amplitude is modulated by the Koopman LQR controller. This work is a step towards controlling nonspherical shape modes of encapsulated microbubbles, which has applications in biomedicine for ultrasound imaging and intravenous drug delivery.   

Gas Motion in a Vertically Vibrated Liquid-Filled Cylinder

When a closed cylinder containing liquid and a small amount of gas is vibrated vertically, stable gas regions can form at the upper and lower ends. Cylinders with diameters of 1-3 cm and heights of 5-10 cm are filled with 20-cSt silicone oil and ambient air and driven by vibrations with frequencies of 50-300 Hz and amplitudes up to 30 G. A model including the vibration-induced Bjerknes force on gas bubbles is developed. This model shows that increasing the amplitude decreases the upper gas region and increases the lower gas region until their sizes become equal. However, it also shows that the lower gas region decreases as the initial gas distribution is biased toward the upper end. Possible causes for this unexpected behavior are discussed. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.   

Towards an effective capillarity in bubble cluster dynamics under ultrasonic excitation

Acoustically driven bubble clouds largely behave as single entities due to the interaction forces between neighbouring oscillating bubbles, known as the secondary Bjerknes forces. Here, we address the cohesion between oscillating bubbles resulting from mutual attraction by examining the analogy between secondary Bjerknes forces and capillary effects. Such an analogy is qualitatively supported by acoustically excited bubble cluster experiments, inspired from the classical wire-frame experiment designed to demonstrate surface tension effects. The results aim to determine whether the resultant of the secondary Bjerknes forces on a movable bar corresponds to a work done per unit surface, as for surface tension. We complement these experiments with theoretical modelling efforts in an attempt to demonstrate that a bubble cloud can be represented as an effective single bubble, which could greatly simplify bubble cluster modelling.   

Linear oscillations of sessile bubbles

The resonant behavior of bubbles in contact with a partially-wetting substrate are important for heat transfer nucleate boiling and solder joint quality in ultrasonic-assisted soldering. A theoretical analysis was carried out to investigate the natural oscillations of a compressible sessile bubble on a planar solid support in an ambient liquid. We consider small disturbances to the spherical-cap interface whose three phase contact line is either (i) pinned or (ii) moves freely with a fixed contact angle. The governing equations for the inviscid incompressible ambient liquid are reduced by a normal-mode expansion to a functional eigenvalue problem on linear operators using a boundary integral approach. We use inverse operators to construct Green’s function for these two contact line conditions, and the Rayleigh-Ritz method to find the characteristic oscillation frequencies and related modal shapes, which are characterized by the mode number pair (l,m). We show how the characteristic oscillation frequencies, modal shape and the flow field depend on the contact angle (α) and dimensionless equilibrium bubble pressure (Π).  Instabilities of the breathing mode (0,0) and the Noether mode (1,1) will be highlighted.   

Propagation and modulation of nonlinear spherical waves emitted by oscillating bubbles

In the numerical simulation of acoustic waves propagating in a liquid as described by the nonlinear Westervelt equation, it is typically assumed that both the wave emitting source and the background medium are at rest. In the present work, the nonlinear acoustic waves emitted at the moving bubble wall of an oscillating bubble are simulated by the means of suitable coordinate transformations of the Westervelt equation under the assumption of spherical symmetry and including the motion of the background medium as a result of the bubble oscillations. It is demonstrated that the motion of the wave emitting bubble wall and the background medium can cause nonlinear modulations of the wave amplitude and the rate of wave steepening. To this end, the finite difference wave solver is coupled to a Rayleigh-Plesset type model to predict the liquid pressure at the wall of a periodically excited gas bubble. Detailed investigations of the liquid pressure spectra at the bubble wall, predicted by the Rayleigh-Plesset type model, and at some distances from the bubble wall, predicted by the wave solver, are presented.   

Gas-Phase Mass Segregation in Acoustic Cavitation at Audible Frequencies

We present an efficient reduced-order model for simulating mass segregation in acoustically collapsing bubbles. The model has been derived by adopting an ansatz for the functional form of the concentration profiles of the species in the gas mixture and accounts for non-equilibrium at the bubble interface. We validate our results against the solution of the advection-diffusion equation and compare them against those obtained by the boundary layer model, extensively used to predict vapor segregation in sonoluminescing bubbles. Obtained in an order of magnitude less computational time, results from our model are very close to those of the advection-diffusion equation in a wide parameter range, well beyond the applicability of the boundary layer method. The better agreement of our model with the advection-diffusion equation is achieved through a more accurate description of both non-equilibrium phase-change dynamics at the bubble wall and the mass transport profiles inside the bubble.   

Listen to your tempura!

From tempura, schnitzel, samosa to french fries, deep-fried foods are gourmet favorites across cultures and times. The perfect delicious crunch is made by cooks who carefully manage the cooking time and oil temperature. A common household technique to estimate the temperature is to insert moisturized chopsticks into the heated oil. The result is dozens of bubbles as well as a crackling sound used to estimate temperature. In this study, we investigate this idea by dipping water-moisturized chopsticks and water-wetted paper into oil at different temperatures. High-speed imagery reveals bubbles of water vapor are formed when the wet objects are submerged. The bubbles' oscillations generates distinct acoustic signatures, which are recorded through a synchronized microphone. The magnitudes of the sound signals are quantified in terms of oil temperature. The visualization also reveals complex bubble dynamics including oil surface deformation, where varying the dimensionless depth H/R of a bubble (bubble depth H and radius R) results in different mechanisms of liquid ligaments expulsions at the oil surface. We use an analogy to cavitation dynamics in the vicinity of the free surface to classify typical expulsion behaviors of the heated liquid.   

The origin of the soap bubble pop

Many familiar events feature a distinctive sound : paper crumpling or tearing, squeaking doors, rain drumming on the ground or the characteristic bubbling sound of boiling water. Though hardly noticeable in our daily environment, these common place sounds carry a profusion of informations about the fleeting physical processes at the root of acoustic emission. In this talk we investigate the popping sound emitted by a bursting soap bubble seen as a paradigm of violently evolving liquid interfaces ; by making use of acoustic antennae and high speed cameras and taking advantage of aeroacoustics conceptual framework, we reveal how the forces due to capillarity, thin film flow and out-of-equilibrium dynamics of surfactants shape the acoustic signature of bursting bubbles. This study provides new informations on the forces exerted by interfaces, paving the way for a complement tool to study violent events.   

Simulations of free bubble growth with a mechanistic interfacial mass transfer model

We report simulations of the growth of stationary and rising vapour bubbles in an extend pool of liquid using an Interface Capturing Computational Fluid Dynamics (CFD) methodology coupled with a method for simulating interfacial mass transfer at the vapour-liquid interface. The model enables mechanistic prediction of the local rate of phase change at the vapour-liquid interface on arbitrary computational meshes and is applicable to realistic cases involving two-phase mixtures with large density ratios. The simulation methodology is based on the Volume Of Fluid (VOF) representation of the flow, whereby an interfacial region in which mass transfer occurs is implicitly identified by a phase indicator, in this case the volume fraction of liquid, which varies from the value pertaining to the 'bulk' liquid to the value of the bulk vapour. Simulations are validated via comparison against experimental observations of bubble growth in water and ethanol, including rising bubble cases in normal gravity. The validation cases represent a severe test for Interface Capturing methodologies due to large density ratios, the presence of strong interfacial evaporation and upward bubble rise motion. Agreement of simulation results with measurements demonstrated that the methodology detailed herein is applicable to modelling phase-change phenomena in real fluids.