N. K. Vakhitova

Collapse and rebound of a laser-induced cavitation bubble

A strong laser pulse that is focused into a liquid produces a vapor cavity, which first expands and then collapses with subsequent rebounds. In this paper a mathematical model of the spherically symmetric motion of a laser-induced bubble is proposed. It describes gas and liquid dynamics including compressibility, heat, and mass transfer effects and nonequilibrium processes of evaporation and condensation on the bubble wall. It accounts also for the occurrence of supercritical conditions at collapse. Numerical investigations of the collapse and first rebound have been carried out for different bubble sizes. The results show a fairly good agreement with experimental measurements of the bubble radius evolution and the intensity of the outgoing shock wave emitted at collapse. Calculations with a small amount of noncondensable gas inside the bubble show its strong influence on the dynamics.

Theory of supercompression of vapor bubbles and nanoscale thermonuclear fusion

HYDRO code model of the spherically symmetric motion for a vapor bubble in an acoustically forced liquid is presented. This model describes cavitation bubble cluster growth during the expansion period, followed by a violent implosion during the compression period of the acoustic cycle. There are two stages of the bubble dynamics process. The first, low Mach number stage, comprises almost all the time of the acoustic cycle. During this stage, the radial velocities are much less than the sound speeds in the vapor and liquid, the vapor pressure is very close to uniform, and the liquid is practically incompressible. This process is characterized by the inertia of the liquid, heat conduction, and the evaporation or condensation of the vapor. The second, very short, high Mach number stage is when the radial velocities are the same order, or higher, than the sound speeds in the vapor and liquid. In this stage high temperatures, pressures, and densities of the vapor and liquid take place. The model presented herein has realistic equations of state for the compressible liquid and vapor phases, and accounts for nonequilibrium evaporation/condensation kinetics at the liquid/ vapor interface. There are interacting shock waves in both phases, which converge toward and reflect from the center of the bubble, causing dissociation, ionization, and other related plasma physics phenomena during the final stage of bubble collapse. For a vapor bubble in a deuterated organic liquid e.g., acetone, during the final stage of collapse there is a nanoscale region diameter 100 nm near the center of the bubble in which, for a fraction of a picosecond, the temperatures and densities are extremely high 10 8 K and 10 g/cm 3 , respectively such that thermonuclear fusion may take place. To quantify this, the kinetics of the local deuterium/deuterium D/D nuclear fusion reactions was used in the HYDRO code to determine the intensity of the fusion reactions. Numerical HYDRO code simulations of the bubble implosion process have been carried out for the experimental conditions used by Taleyarkhan et al. Science 295, 1868 2002; Phys. Rev. E 69, 036109 2004 at Oak Ridge National Laboratory. The results show good agreement with the experimental data on bubble fusion that was measured in chilled deuterated acetone.

On the forced oscillations of a small gas bubble in a spherical liquid-filled flask

A spherically-symmetric problem is considered in which a small gas bubble at the centre of a spherical flask filled with a compressible liquid is excited by small radial displacements of the flask wall. The bubble may be compressed, expanded and made to undergo periodic radial oscillations. Two asymptotic solutions have been found for the low-Mach-number stage. The first one is an asymptotic solution for the field far from the bubble, and it corresponds to the linear wave equation. The second one is an asymptotic solution for the field near the bubble, which corresponds to the Rayleigh-Plesset equation for an incompressible fluid. For the analytical solution of the low-Mach-number regime, matching of these asymptotic solutions is done, yielding a generalization of the Rayleigh-Plesset equation. This generalization takes into account liquid compressibility and includes ordinary differential equations (one of which is similar to the well-known Herring equation) and a difference equation with both lagging and leading time. These asymptotic solutions are used as boundary conditions for bubble implosion using numerical codes which are based on partial differential conservation equations. Both inverse and direct problems are considered

Dynamics of laser-induced cavitation bubbles

Abstract Single cavitation bubble luminescence induced by laser in contrast to single bubble sonoluminescence has no need in a sound field for a strong collapse and for light emission. The cavitation bubbles are produced by focused laser light and make the single strong collapse. As shown experimentally, the number of emitted photons from cavitation luminescence is much greater than it was observed in sonoluminescence due to the large bubble size during the final stage of collapse. To describe the process of laser-induced bubble collapse a mathematical model is used, which is based upon the spherically symmetric motion including compressibility, heat and mass transfer effects. The basic results of the numerical solution are presented for the bubbles with maximum radii of about 1 mm. According to the observed results the minimum bubble radius in collapse is about 15 μm, and the mass decreases up to 5% of the initial value. Calculations with a small amounts of noncondensable gas inside the bubble predict its strong influence on the dynamics. As shown numerically the theoretical model gives a good agreement with experimental measurements.

Weak oscillations of a gas bubble in a spherical volume of compressible liquid

Abstract The following spherically symmetric problem is considered: a single gas bubble at the centre of a spherical flask filled with a compressible liquid is oscillating in response to forced radial excitation of the flask walls. In the long-wave approximation at low Mach numbers, one obtains a system of differential-difference equations generalizing the Rayleigh-Lamb-Plesseth equation. This system takes into account the compressibility of the liquid and is suitable for describing both free and forced oscillations of the bubble. It includes an ordinary differential equation analogous to the Herring-Flinn-Gilmore equation describing the evolution of the bubble radius, and a delay equation relating the pressure at the flask walls to the variation of the bubble radius. The solutions of this system of differential-difference equations are analysed in the linear approximation and numerical analysis is used to study various modes of weak but non-linear oscillations of the bubble, for different laws governing the variation of the pressure or velocity of the liquid at the flask wall. These solutions are compared with numerical solutions of the complete system of partial differential equations for the radial motion of the compressible liquid around the bubble.

Dynamics of bubble clusters

A mathematical model which describes the behavior of a gas bubble cluster in an external acoustic field is presented. According to this model the bubbles of different ambient radii are assumed to be submerged into a spherical liquid volume. The boundary of this volume is considered as a cluster’s boundary. This model includes a set of coupled Rayleigh-type equations for bubble radii and cluster radius. The dynamics of a single bubble cluster excited by external periodic pressure is considered. The problem has been solved numerically under the assumption of spherically-symmetric oscillations of bubbles and the cluster’s boundary. A synchronization phenomenon has been found; namely, the numerical results have shown that bubbles of different initial radii in a cluster collapse in phase. Moreover, it has been noted that at some parameter values such a synchronization may lead to the intensification of bubble collapse.

Hydrodynamics, Acoustics and Transport in Sonoluminescence Phenomena

The spherically-symmetric problem of the oscillations of a gas bubble in the center of a spherical flask filled with a compressible liquid that is excited by pressure oscillations on the flask wall is considered. A generalization of the Rayleigh-Plesset equation for a compressible liquid is given in the form of two ordinary difference-differential equations that take into account the pressure waves which are reflected from the bubble and those that are incident on the bubble from the flask wall. The initial value problem for the initiation of bubble oscillations due to flask wall excitation and for the evolution of these oscillations is considered. Linear and non-linear periodic bubble oscillations are analyzed analytically. Non-linear resonant and near-resonant solutions for the bubble nonharmonic oscillations, which are excited by harmonic pressure oscillations on the flask wall, are obtained. The influence of heat transfer phenomena on the bubble oscillations is analysed.

THE RESONANT SUPERCOMPRESSION AND SONOLUMINESCENCE OF A GAS BUBBLE IN A LIQUID-FILLED FLASK

Abstract The spherically-symmetric problem of the oscillations of a small gas bubble in the center of a spherical flask filled with a compressible liquid that is excited by small radial displacement of the flasks wall is considered. Two asymptotic solutions have been found for the low Mach number stage. The first one is an asymptotic solution for the field far from the bubble, and it corresponds to linear wave theory. The second one is an asymptotic solution for the boundary layer near the bubble and it corresponds to an incompressible fluid. In the analytical solution of the low Mach number step matching of these asymptotic solutions is done. A generalization of the Rayleigh = Plesset equation for a compressible liquid is given in the form of two ordinary difference-differential equations that take into account the pressure waves which are reflecting from the bubble and those that are incident on the bubble from the flask wall. The initial value problem for the initiation of the bubble oscillations due ...

Forced oscillations of a gas bubble in a spherical volume of a compressible liquid

A spherically symmetric problem of oscillations of a single gas bubble at the center of a spherical flask filled with a compressible liquid under the action of pressure oscillations on the flask wall is considered. A system of differential-difference equations is obtained that extends the Rayleigh-Plesset equation to the case of a compressible liquid and takes into account the pressure-wave reflection from the bubble and the flask wall. A linear analysis of solutions of this system of equations is performed for the case of harmonic oscillations of the bubble. Nonlinear resonance oscillations and nearly resonance nonharmonic oscillations of the bubble caused by harmonic pressure oscillations on the flask wall are analyzed.

Dynamics of a bubble in a liquid under laser pulse action

Simulation was performed of the behavior of a vapor bubble in a liquid under laser irradiation in laboratory experiments. A mathematical model was developed to analyze the effect of heat conduction, diffusion, and mass transfer on the bubble dynamics under compression and expansion. It is found that at the stage of collapse, intense condensation occurs on the bubble wall, which results in a significant (more than 15‐fold) decrease in bubble mass and an increase in pressure (to 105 atm) and temperature (to 104 K(. Results of numerical calculations of the radius of the first rebound and the amplitude of the divergent shock wave in water are compared with experimental data. It is shown that small (:about 1%) additives of an incondensable gas lead to a considerable decrease in mass transfer on the bubble wall.