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Collapse of a Cavitation Bubble in Deuterated Tetradecane
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The influence of the liquid temperature in the range of 273.15–419 K on the vapor compression inside a collapsing cavitation bubble in acetone has been studied. The liquid pressure is 50 bar. The vapor in the bubble is initially in its saturated state, the bubble radius is 500 мm. The fluid flows are governed by the gas dynamic equations with wide-range equations of state, taking into account the heat conductivity and evaporation/condensation on the bubble surface. The numerical technique is based on a TVD-modification of the Godunov method of the second order of accuracy in space and time. Five vapor compression scenarios have been found to sequentially implement with decreasing the liquid temperature. The first scenario is close to homogeneous, the other ones are with the convergence of: one isentropic wave, one shock wave, one isentropic and one shock waves, and two shock waves. At that, the vapor temperature maximum achieved at the boundary of a small central region of the bubble (with a radius less than 2.5 мm) until the first shock wave focusing grows nonmonotonic.
Specific features of the phenomenon of vapor bubble collapse in hot tetradecane (with a temperature of 663 K) are considered for various values of pressures in the liquid in the range from 13 to 100 bar. At the beginning of the collapse, the vapor in the bubble is in the state of saturation with a pressure of 10.3 bar, and with the initial radius of the bubble to equal 500 µm. It is shown that, at a liquid pressure lower than 13 bar, a nearly-uniform vapor compression is realized in the bubble, whereas at higher pressure values, compression is realized by means of radially converging isentropic waves (at 14–18 bar) and shock waves (starting from 19 bar). The degrees of vapor compression, estimated from the vapor pressure, density and temperature at the boundary of a small central region of the bubble of 0.25-µm radius, are compared with the degrees of vapor compression realized when a similar vapor bubble collapses in cold acetone at a temperature of 273 K (as in known experiments on acoustic cavitation of deuterated acetone). It is found that the degrees of compression comparable with those achieved in the case of acetone at a pressure of 15 bar, equal to the amplitude of the acoustic action exercised in the mentioned experiments, are achieved in the case of tetradecane at a pressure of 70 bar. In the latter case, the maximum rate of bubble collapse in tetradecane is 10 times lower than that in acetone (110 m/s versus 1100 m/s).
In this paper, we compare the features of the shock compression of 1-mm vapor bubbles and the nonsphericity growth during their collapse in hydrocarbon (acetone, benzol, and tetradecane) liquids. At the beginning of compression, the vapor is in a saturation state at 1.03 MPa, and the bubble collapse is caused by a liquid pressure of 5 MPa. It has been found that, during the collapse of the bubble in acetone, only weak compression waves occur in its cavity, while intense, radially convergent compression waves that transform into shock waves arise in the bubbles in benzol and tetradecane, which have a significantly greater molecular weight and, consequently, a lower speed of sound in the vapor. This leads to an extreme focusing of energy at the bubble center. A shock wave in tetradecane appears shortly after the onset of collapse, whereas a shock wave in benzol forms only during the reconvergence of the unstressed compression wave to the center of the bubble after its reflections from the center and the interface. As a result, the highest values of thermodynamic parameters are achieved in tetradecane, while the lowest values are attained in acetone. The bubble nonsphericity is shown to increase by two orders of magnitude less in tetradecane than in acetone and benzol by the time it reaches the extreme values of the thermodynamic parameters.
A study was conducted to investigate the formation of convergent shock waves in a bubble upon its collapse. Investigations of these issues were carried out using a dynamic model of a cavitation bubble according to which a number of equations were used to describe motion of the vapor in the bubble and the surrounding fluid. The one-dimensional problem of gas motion in a tube open at one end was considered to conduct the investigations. The investigations revealed that the gases with a high molecular weight and a low adiabatic index were more suitable for the implementation of shock-wave compression mode.
This paper provides the theoretical basis for energetic vapor bubble implosions induced by a standing acoustic wave. Its primary goal is to describe, explain, and demonstrate the plausibility of the experimental observations by Taleyarkhan &etal; [Science 295, 1868 (2002); Phys. Rev. E 69, 036109 (2004)] of thermonuclear fusion for imploding cavitation bubbles in chilled deuterated acetone. A detailed description and analysis of these data, including a resolution of the criticisms that have been raised, together with some preliminary HYDRO code simulations, has been given by Nigmatulin &etal; [Vestnik ANRB (Ufa, Russia) 4, 3 (2002); J. Power Energy 218-A, 345 (2004)] and Lahey &etal; [Adv. Heat Transfer (to be published)]. In this paper a hydrodynamic shock (i.e., 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 (∼108 K and ∼10 g∕cm3, 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 &etal; [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.
Numerical hydrodynamic simulations of the growth and collapse of a 10 [mu]m air bubble in water were performed. Both the air and the water are treated as compressible fluids. The calculations show that the collapse is nearly isentropic until the final 10 ns, after which a strong spherically converging shock wave evolves and creates enormous temperatures and pressures in the inner 0.02 [mu]m of the bubble. The reflection of the shock from the center of the bubble produces a diverging shock wave that quenches the high temperatures ([gt]30 eV) and pressures in less than 10 ps (full width at half maximum). The picosecond pulse widths are due primarily to spherical convergence/divergence and nonlinear stiffening of the air equation of state that occurs at high pressures. The results are consistent with recent measurements of sonoluminescence that had optical pulse widths less than 50 ps and 30 mW peak radiated power in the visible.
A procedure for constructing the analytical equation of state, which is valid within a wide range of pressures and temperatures, is developed for organic liquids such as the usual and deuterated acetone. The development of the equation of state is consistent with the available experimental data for shock compressibility and describes the behavior of the substance in the saturation line at the critical point. The substance at the bubble center is subjected to huge compression during the processes of cavitation vapor-bubble collapse in strong acoustical fields. Superhigh temperatures and compressions in the process of supercompression of microbubbles under collapse in the central zone exists, during the fractions of a picosecond.
A molecular dynamic simulation of a mixture of light and heavy gases in a rapidly imploding sphere exhibits virtually complete segregation. The lighter gas collects at the focus of the sphere and reaches a temperature that is several orders of magnitude higher than when its concentration is 100%. Implosion parameters are chosen via a theoretical fit to an observed sonoluminescing bubble with an extreme expansion ratio (25:1) of maximum to ambient radii.
In cavitation experiments with deuterated acetone, tritium decay activity above background levels was detected. In addition, evidence for neutron emission near 2.5 million electron volts was also observed, as would be expected for deuterium-deuterium fusion. Control experiments with normal acetone did not result in tritium activity or neutron emissions. Hydrodynamic shock code simulations supported the observed data and indicated highly compressed, hot (10(6) to 10(7) kelvin) bubble implosion conditions, as required for nuclear fusion reactions.
We investigate the possibility of medium supercompression in a cavitation bubble during its collapse in tetradecane and make a comparison with its realization in a collapsing bubble in acetone. We show that tetradecane is a more favorable medium than acetone for the possibility of cavitation bubble contents supercompression during its collapse.
The equations of state for benzene, tetradecane, and their deuterated counterparts are derived on the basis of the original method of constructing the wide-range equations of state for hydrocarbon liquids in an analytical form. The equations describe gas and liquid phases at intensive gas-dynamic processes with consideration of evaporation and condensation and include dissociation and ionization processes associated with super-high pressures and temperatures.
A sonoluminescing bubble has been modeled as a thermally conducting, partially ionized, two-component plasma. The model shows that the measured picosecond pulse widths are due to electron conduction and the rapidly changing opacity of the plasma and that these mechanisms are also responsible for the absence of an {open_quotes}afterglow{close_quotes} subsequent to the sonoluminescence flash while the hot bubble expands and cools. The calculated spectra for sonoluminescing nitrogen and argon bubbles suggest that a sonoluminescing air bubble probably contains only argon, in agreement with a recent theoretical analysis. 27 refs., 3 figs.
Ultrasound causes high-energy chemistry. It does so through the process of acoustic cavitation: the formation, growth and
implosive collapse of bubbles in a liquid. During cavitational collapse, intense heating of the bubbles occurs. These localized
hot spots have temperatures of roughly 5000°C, pressures of about 500 atmospheres, and lifetimes of a few microseconds. Shock
waves from cavitation in liquid-solid slurries produce high-velocity interparticle collisions, the impact of which is sufficient
to melt most metals. Applications to chemical reactions exist in both homogeneous liquids and in liquid-solid systems. Of
special synthetic use is the ability of ultrasound to create clean, highly reactive surfaces on metals. Ultrasound has also
found important uses for initiation or enhancement of catalytic reactions, in both homogeneous and heterogeneous cases.
‘Dynamics of a small bubble in a compressible fluid
- A A Aganin