Equations of radial motion of a gas bubble in a compressible viscous liquid have been modified to account for compressibility at the bubble boundary. A new bubble boundary equation has been derived, including a new term resulted from liquid compressibility. The influence of this term has been numerically investigated using isothermal-adiabatic model for the gas inside the bubble. The results clearly indicate that, at the end of the collapse, the new term has a very significant role and its consideration dramatically changes the bubble characteristics. Moreover, the more intense the collapse is, the more significant the effect of the new term is. Also, it has been reasoned out that, the influence of the new term will be established even when the effects of mass (water vapor) exchange, chemical reactions, and gas dynamics inside the bubble are taken into account.
A brief survey is given of the dynamical phenomena accompanying the collapse of cavitation bubbles. The discussion includes shock waves, microjets and the various ways in which collapsing bubbles produce damage.
When an asymmetric bubble collapses it generally produces a well defined high velocity jet. This is remarkable because one might expect such a collapse to produce a complex or chaotic flow rather than an ordered one. I present a dimensional argument for the ubiquity of jets from collapsing bubbles, and model the aspherical collapse of a bubble with pieces of Rayleigh's solution for spherical collapse and its cylindrical analogue. This model explains the ubiquity of jet formation in aspherical collapse, and predicts the shape and velocity profile of the resulting jet. These predictions may be t…
The impact of a collapsing gas bubble above rigid, notched walls is considered. Such surface crevices and imperfections often function as bubble nucleation sites, and thus have a direct relation to cavitation-induced erosion and damage structures. A generic configuration is investigated numerically using a second-order-accurate compressible multi-component flow solver in a two-dimensional axisymmetric coordinate system. Results show that the crevice geometry has a significant effect on the collapse dynamics, jet formation, subsequent wave dynamics, and interactions. The wall-pressure distribut…
The dynamics of rapidly collapsing bubbles are of great interest due to the high degree of energy focusing that occurs withing the bubble. Molecular dynamics provides a way to model the interior of the bubble and couple the gas dynamics with the equations governing the bubble wall. While much theoretical work has been done to understand how a bubble will respond to an external force, the internal dynamics of the gas system are usually simplified greatly in such treatments. This paper shows how the gas system dynamics affect bubble collapse and illustrates what effects various modeling assumpti…
Non-linear equations of radial motion of a gas bubble in a compressible viscous liquid have been modified considering effects of viscosity and compressibility more complete than all previous works. A new set of equations has been derived including new terms resulted from consideration of the viscosity and compressibility not only at the bubble interface, but also in the bulk of liquid. The new equations are two non-linear coupled equations, which can not be merged into one equation unlike all previously derived equations. Numerical calculations have been performed considering effects of heat a…
Cavitation bubbles collapsing and rebounding in a pressure gradient grad(p) form a "micro-jet" enveloped by a "vapor jet". This letter presents unprecedented observations of the vapor jets formed in a uniform gravity-induced grad(p), modulated aboard parabolic flights. The data uncovers that the normalized jet volume is independent of the liquid density and viscosity and proportional to zeta=grad(p)*R0/p, where R0 is the maximal bubble radius and p is the driving pressure. A derivation inspired by "Kelvin-Blake" considerations confirms this law and reveals its negligible dependence of surface …
A vapor bubble collapsing near a solid boundary in a liquid produces a liquid jet that points toward the boundary. The direction of this jet has been studied for boundaries such as flat planes and parallel walls enclosing a channel. Extending these investigations to enclosed polygonal boundaries, we experimentally measure jet direction for collapsing bubbles inside a square and an equilateral triangular channel. Following the method of Tagawa and Peters (Phys. Rev. Fluids 3, 081601, 2018) for predicting the jet direction in corners, we model the bubble as a sink in a potential flow and demonst…
The non-linear bubble dynamics equations in a compressible liquid have been modified considering the effects of compressibility of both the liquid and the gas at the bubble interface. A new bubble boundary equation has been derived, which includes a new term resulted from the liquid bulk viscosity effects. The influence of this term has been numerically investigated considering the effects of water vapor and chemical reactions on the bubble evolution. The results clearly indicate that the new term has an important damping role at the collapse, so that its consideration decreases the amplitude …
We studied spark-generated cavitation bubbles inside water drops produced in microgravity. High-speed visualizations disclosed unique effects of the spherical and nearly isolated liquid volume. In particular, (1) toroidally collapsing bubbles generate two liquid jets escaping from the drop, and the "splash jet" discloses a remarkable broadening. (2) Shockwaves induce a strong form of secondary cavitation due to the particular shockwave confinement. This feature offers a novel way to estimate integral shockwave energies in isolated volumes. (3) Bubble lifetimes in drops are shorter than in exte…
Fast microjets can emerge out of liquid pools from the rebounding of drop-impact craters, or when a bubble bursts at it surface. The fastest jets are the narrowest and are a source of aerosols both from the ocean and a glass of champagne, of importance to climate and the olfactory senses. The most singular jets, which have a maximum velocity of 137$\pm$4 m/s and diameter of 12 $μ$m under reduced ambient pressure, are produced when a small dimple forms at the crater bottom and rebounds without pinching off a small bubble. The rebounding of this dimple is purely inertial but highly sensitive on …
A gas or vapor bubble collapsing in the vicinity of a rigid boundary displaces towards the boundary and produces a high-speed jet directed at the boundary. This behavior has been shown to be a function of the 'anisotropy' of the collapse, measured by a dimensionless representation of the Kelvin impulse known as the anisotropy parameter [Supponen et al., J. Fluid Mech. 802, 263-293 (2016)]. However, characterisation of the anisotropy parameter in different geometries has been limited to simplified analytic solutions. In this work we develop an inexpensive numerical model, based on the Boundary …
In this paper a diffuse-interface model featuring phase change, transition to supercritical conditions, thermal conduction, compressibility effects and shock wave propagation is exploited to deal with the dynamics of a cavitation bubble. At variance with previous descriptions, the model is uniformly valid for all phases (liquid, vapor and supercritical) and phase transitions involved, allowing to describe the non-equilibrium processes ongoing during the collapse. As consequence of this unitary description, rather unexpectedly for pure vapor bubbles, the numerical experiments show that the coll…
The flow driven by a rapidly expanding and collapsing cavitation bubble in a narrow cylindrical gap is studied with the volume of fluid method. The simulations reveal a developing plug flow during the early expansion followed by flow reversal at later stages. An adverse pressure gradient leads to boundary layer separation and flow reversal, causing large shear stress near the boundaries. Analytical solution to a planar pulsating flow shows qualitative agreement with the CFD results. The shear stress close to boundaries has implications to deformable objects located near the bubble: experiments…
Experimental analysis of cavitation bubble dynamics typically uses optical imaging. However, images are often severely affected by distortions and shadows due to refraction and total reflection at the liquid--gas interface. Here it is shown that optical ray-tracing can be a powerful tool for the analysis process by assisting in the comparison of experiments to numerical two-phase flow simulations. To this end, realistic ray-tracing images are generated from numerical simulations that correspond to the experimental setup. We apply the method on the jetting dynamics of single bubbles collapsing …
The nonlinear dynamic behaviour of microscopic bubbles near a wall is investigated. The Keller-Miksis-Parlitz equation is adopted, but modified to account for the presence of the wall. This base model describes the time evolution of the bubble surface, which is assumed to remain spherical, and accounts for the effect of acoustic radiation losses owing to liquid compressibility in the momentum conservation. Two situations are considered: the base case of an isolated bubble in an unbounded medium; and a bubble near a solid wall. In the latter case, the wall influence is modeled by including a sy…
We present a multiscale approach to simulate the impact of a solid object on a liquid surface: upon impact a thin liquid sheet is thrown upwards all around the rim of the impactor while in its wake a large surface cavity forms. Under the influence of hydrostatic pressure the cavity immediately starts to collapse and eventually closes in a single point from which a thin, needle-like jet is ejected. Existing numerical treatments of liquid impact either consider the surrounding air as an incompressible fluid or neglect air effects altogether. In contrast, our approach couples a boundary-integral …
In the present study, a 1-dimensional model is proposed to estimate the pressure drop and heat transfer coefficient for flow boiling in a rectangular microchannel. The present work takes into account the pressure fluctuations caused due to the confined bubble growth and the effect of pressure fluctuations on the heat transfer characteristics. The heat transfer model considers five zones, namely, liquid slug, partially confined bubble, fully confined (elongated) bubble, partial dryout and full dry-out. The model incorporates the thinning of liquid film due to shear stress at liquid-vapour inter…
In the present study, simulations are directed to capture the dynamics of evacuating inner gas of a bubble bursting at the free surface, using Eulerian based volume of fluid (VOF) method. The rate by which surrounding air rushing inside the bubble cavity through the inner gas evacuation is estimated and compared by the collapsing bubble cavity during the sequential stages of the bubble bursting at the free surface. Further, the reachability of inner gas over the free surface is evaluated by establishing the comparison of the same through various horizontal planes, lying at different altitudes …
We numerically investigate the effect of non-condensable gas inside a vapor bubble on bubble dynamics, collapse pressure and pressure impact of spherical and aspherical bubble collapses. Free gas inside a vapor bubble has a damping effect that can weaken the pressure wave and enhance the bubble rebound. To estimate this effect numerically, we derive and validate a multi-component model for vapor bubbles containing gas. For the cavitating liquid and the non-condensable gas, we employ a homogeneous mixture model with a coupled equation of state for all components. The cavitation model for the ca…
Oscillations of gas bubbles in liquids irradiated with acoustic pressure waves may result in an intriguing physical phenomenon called sonoluminescence, where a collapsing bubble emits the light in a broad optical spectral range. However, the intensity of the so-generated light is typically weak for practical purposes. Recently, it has been demonstrated that nanoparticles can be used to increase the efficiency of sonoluminescence, thereby enabling one to generate the light that is intense enough for a number of applications in photonics, biomedicine and material science. In this article, we rev…
The Challenger disaster and purposeful experiments with liquid hydrogen (H2) and oxygen (Ox) tanks demonstrated that cryogenic H2/Ox fluids always self-ignite in the process of their mixing. Here we propose a cavitation-induced self-ignition mechanism that may be realized under these conditions. In one possible scenario, self-ignition is caused by the strong shock waves generated by the collapse of pure Ox vapor bubble near the surface of the Ox liquid that may initiate detonation of the gaseous H2/Ox mixture adjacent to the gas-liquid interface. This effect is further enhanced by H2/Ox combus…
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical prope…
The Gilmore model is combined with the Noble-Abel-stiffened-gas (NASG) equation of state to yield a simple model to predict the expansion and collapse of spherical bubbles based on real gas thermodynamics. The NASG equation of state resolves the temperature inaccuracy associated with the commonly employed Tait equation of state for liquids and, thus, can provide a consistent description of compressible and thermal effects of the bubble content and the surrounding liquid during cavitation. After a detailed derivation of the proposed Gilmore-NASG model, the differences between the classical Gilm…
Spherically collapsing cavitation bubbles produce a shock wave followed by a rebound bubble. Here we present a systematic investigation of the energy partition between the rebound and the shock. Highly spherical cavitation bubbles are produced in microgravity, which suppress the buoyant pressure gradient that otherwise deteriorates the sphericity of the bubbles. We measure the radius of the rebound bubble and estimate the shock energy as a function of the initial bubble radius (2-5.6 mm) and the liquid pressure (10-80 kPa). Those measurements uncover a systematic pressure dependence of the ene…
Numerical simulation of bubble dynamics and cavitation is challenging; even the seemingly simple problem of a collapsing spherical bubble is difficult to compute accurately with a general, three-dimensional, compressible, multicomponent flow solver. Difficulties arise due to both the physical model and the numerical method chosen for its solution. We consider the 5-equation model of Allaire et al. [1], the 5-equation model of Kapila et al. [2], and the 6-equation model of Saurel et al. [3] as candidate approaches for spherical bubble dynamics, and both MUSCL and WENO interface-capturing method…
Ultrasound contrast agents have been recently utilized in therapeutical implementations for targeted delivery of pharmaceutical substances. Radial pulsations of the encapsulated microbubbles under the action of an ultrasound field are complex and high nonlinear, particularly for drug and gene delivery applications with high acoustic pressure amplitudes. The dynamics of a polymer-shelled agent is inspected \textit{in vivo} through applying the method of chaos physics whereas the effects of the outer medium compressibility and the shell were considered. The stability of the ultrasound contrast a…
Sonoluminescence (SL) is the phenomenon in which acoustic energy is (partially) transformed into light. It may occur by means of many or just one bubble of gas inside a liquid medium, giving rise to the terms multi-bubble- and single-bubble sonoluminescence (MBSL and SBSL). In the last years some models have been proposed to explain this phenomenon, but there is still no complete theory for the light emission mechanism (especially in the case of SBSL). In this work, we will not address this more complicated particular issue, but only present a simple model describing the dynamical behaviour of…
Irradiation with UV-C band ultraviolet light is one of the most commonly used ways of disinfecting water contaminated by pathogens such as bacteria and viruses. Sonoluminescence, the emission of light from acoustically-induced collapse of air bubbles in water, is an efficient means of generating UV-C light. However, because a spherical bubble collapsing in the bulk of water creates isotropic radiation, the generated UV-C light fluence is insufficient for disinfection. Here, we show that we can create a UV light beam from aspherical air bubble collapse near a gallium-based liquid-metal micropar…
A simple generalized model (GM) for coated bubbles accounting for the effect of compressibility of the liquid is presented. The GM was then coupled with nonlinear ODEs that account for the thermal effects. Starting with mass and momentum conservation equations for a bubbly liquid and using the GM, nonlinear pressure dependent terms were derived for energy dissipation due to thermal damping (Td), radiation damping (Rd) and dissipation due to the viscosity of liquid (Ld) and coating (Cd). The dissipated energies were solved for uncoated and coated 2- 20 $μm$ bubbles over a frequency range of $0.…
We show that strong electric fields occurring in water near the surface of collapsing gas bubbles because of the flexoelectric effect can provoke dynamic electric breakdown in a micron-size region near the bubble and consider the scenario of the SBSL. The scenario is: (i) at the last stage of incomplete collapse of the bubble the gradient of pressure in water near the bubble surface has such a value and sign that the electric field arising from the flexoelectric effect exceeds the threshold field of the dynamic electrical breakdown of water and is directed to the bubble center; (ii) mobile ele…
We present a computational study of the behaviour of a lipid-coated SonoVue microbubble with initial radius $1 \, μ\text{m} \leq R_0 \leq 2 \, μ\text{m}$, excited at frequencies (200-1500 kHz) significantly below the linear resonance frequency and pressure amplitudes of up to 1500 kPa, an excitation regime used in many focused ultrasound applications. The bubble dynamics are simulated using the Rayleigh-Plesset equation and the Gilmore equation, in conjunction with the Marmottant model for the lipid monolayer coating. Also, a new continuously differentiable variant of the Marmottant model is i…
We report on recent progress in the physical and numerical modeling of compressible two-phase flows that involve phase transition between the liquid and gaseous state of the fluid. The high-speed dynamics of cavitation bubbles is studied in well-resolved simulations (DNS) with a sharp-interface numerical model on a micro scale. The underlying assumption of the employed evaporation/condensation model is that phase change occurs in thermal non-equilibrium and that the associated timescale is larger than that of the wave dynamics. Results for the collapse of a spherical vapor bubble close to a so…
