Ambient Radius Research Articles

Shape and extinction thresholds in sonoluminescence parameter space

Experimental single bubble sonoluminescence (SBSL) ambient radius, acoustic drive pressure (Ro−Pa) phase diagrams are compared with predictions of the Dissociation Hypothesis (DH) and calculations of the n=2,3,4 shape thresholds, focusing on the location of unstable SBSL and the extinction threshold. A phase diagram for experimental runs with a 20% air saturation is shown to indicate the location of the SBSL extinction threshold. Mixtures with appropriate concentrations of argon and nitrogen are presented to show the location of unstable SBSL. The results are consistent with the DH and show that unstable SBSL and the extinction threshold appear to coincide more closely with the n=4 shape threshold.

Parameter space of single-bubble sonoluminescence for various liquid temperatures

In a previous paper by the authors [Phys. Rev. Lett. 77, 3791 (1996)], the region of parameter space (acoustic pressure, ambient bubble radius) in which stable single-bubble sonoluminescence (SBSL) occurs in an air–water system driven at 20.6 kHz was described as a function of the dissolved gas concentration. In this paper, new data (ambient radius, maximum radius, expansion ratio, as well as the emission and extinction thresholds) will be presented for the SBSL parameter space at various liquid temperatures for different gases and liquids. [Work supported by the Office of Naval Research.]

A one‐dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer: 1. Model description

A one‐dimensional, multicomponent sectional model has been developed to simulate the temporal and vertical variations of the aerosol size distribution and composition in the marine boundary layer (MBL). An important aspect of the model is its ability to handle the transport of aerosols in an atmosphere with humidity gradients with no numerical diffusion caused by the swelling and shrinking of the particles as they move through the humidity gradients. This is achieved by rewriting the aerosol general dynamical equation (GDE) in terms of dry radius thus transferring all variations in radius caused by temporal and spatial humidity variations to the rate coefficients appearing in the equations. The model then solves the new GDE in fixed dry size sections, with the humidity dependence of the processes now included in variable coefficients. This procedure also results in correct gradient transport. A limiting assumption is that the particles equilibrate instantaneously with the ambient water vapor. This assumption limits the maximum particle size which can be treated in the model to ambient (wet) radii less than about 30 μm. All processes currently believed to be important in shaping the MBL size distribution are included in the current version of the model. These include generation of sea‐salt aerosol at the ocean surface, nucleation of new particles, coagulation, growth due to condensation of gas‐phase reaction products, growth due to sulfate formation during cloud processing, precipitation scavenging, surface deposition, turbulent mixing, gravitational settling, and exchange with the free troposphere. Simple gas‐phase chemistry which includes the oxidation of dimethylsulfide and SO2 to sulfate is incorporated in the current version of the model.

Analysis of Rayleigh–Plesset dynamics for sonoluminescing bubbles

Recent work on single bubble sonoluminescence (SBSL) has shown that many features of this phenomenon, especially the dependence of SBSL intensity and stability on experimental parameters, can be explained within a hydrodynamic approach. More specifically, many important properties can already be derived from an analysis of bubble wall dynamics. This dynamics is conveniently described by the Rayleigh-Plesset (RP) equation. In this work we derive analytical approximations for RP dynamics and subsequent analytical laws for parameter dependences. These results include (i) an expression for the onset threshold of SL, (ii) an analytical explanation of the transition from diffusively unstable to stable equilibria for the bubble ambient radius (unstable and stable sonoluminescence), and (iii) a detailed understanding of the resonance structure of the RP equation. It is found that the threshold for SL emission is shifted to larger bubble radii and larger driving pressures if surface tension is enlarged, whereas even a considerable change in liquid viscosity leaves this threshold virtually unaltered. As an enhanced viscosity stabilizes the bubbles against surface oscillations, we conclude that the ideal liquid for violently collapsing, surface stable SL bubbles should have small surface tension and large viscosity, although too large viscosity (>40 times the viscosity of water) will again preclude collapses.

Time-resolved measurements of optical emission from sonoluminescence

The results of detailed measurements of sonoluminescence from a gas bubble that is acoustically driven in deionized water are presented. The pulse width and relative jitter of the optical flash and the minimum and ambient radius of the bubble as a function of the driving pressure, temperature, and gas concentration of the water are measured. The optical flash is collected by an f/1.4 lens, and then optically relayed onto the slit of a Hamamatsu C1587 optical streak camera which records the time evolution of the flash with picosecond resolution. Single event streaks are obtained, showing FWHM pulse widths of 200–400 ps, comparable to recently reported results [Gompf et al., Phys. Rev. Lett. 79, 1405 (1997)]. The jitter of the flash between events has been found to be a minimum of ±200 ps. Mie scattering has been used to measure the maximum and ambient bubble radius at the same time for comparison to the model [Moss et al., Science 276, 1398 (1997)]. The consequences of these results on modeling will also be discussed. [This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.]

Effect of quantum radiation pressure on the bubble dynamics in sonoluminescence

In the theoretical frame of quantum vacuum radiation (QVR), the effect of the QVR on the gas bubble dynamics in the single bubble sonoluminescence is studied. The dominated hydrodynamic equation of the gas bubble trapped in a liquid, Rayleigh–Plesset equation, has been modified by considering the reaction of the radiation force on the bubble surface and therefore causing a loss of energy. In the modified model the collapse and expansion of the bubble, especially near the turnaround at minimum radius, related to photon emission instead of independence on it. The numerical computation shows that the emission energy due to the QVR seems too low to explain the experimental data, if some present values of parameters, such as the ambient radius of the bubble and the sound pressure in liquid, are used. The radiation energy due to the QVR, however, can arise by changing those parameters. Based on this, it is concluded that the QVR may be a possible candidate for mechanisms of the sonoluminescence. [Work supported by NSF of China.]

Sound radiation of 3-MHz driven gas bubbles

The sound radiation of 3-MHz acoustically driven air bubbles in liquid is analyzed with respect to possible applications in second harmonic ultrasound diagnostics devices, which have recently come into clinical use. In the forcing pressure amplitude Pa=1–10 atm and ambient radius R0=0.5–5 μm parameter domain, a narrow regime around the resonance radius R0∼1–1.5 μm and relatively modest Pa∼2–2.5 atm is identified in which optimal sound yield in the second harmonic is achieved while maintaining spherical stability of the bubble. For smaller Pa and larger R0 hardly any sound is radiated; for larger Pa bubbles become unstable toward nonspherical shape oscillations of their surface. The computation of these instabilities is essential for the evaluation of the optimal parameter regime. A region of slightly smaller R0 and Pa∼1–3 atm is best suited to achieve large ratios of the second harmonic to the fundamental intensity. Spherical stability is guaranteed in the suggested regimes for liquids with an enhanced viscosity compared to water, such as blood.

Phase diagrams for sonoluminescing bubbles

Sound driven gas bubbles in water can emit light pulses. This phenomenon is called sonoluminescence (SL). Two different phases of single bubble SL have been proposed: diffusively stable and diffusively unstable SL. We present phase diagrams in the gas concentration versus forcing pressure state space and also in the ambient radius versus gas concentration and versus forcing pressure state spaces. These phase diagrams are based on the thresholds for energy focusing in the bubble and two kinds of instabilities, namely (i) shape instabilities and (ii) diffusive instabilities. Stable SL only occurs in a tiny parameter window of large forcing pressure amplitude Pa∼1.2–1.5 atm and low gas concentration of less than 0.4% of the saturation. The upper concentration threshold becomes smaller with increased forcing. Our results quantitatively agree with experimental results of Putterman’s UCLA group on argon, but not on air. However, air bubbles and other gas mixtures can also successfully be treated in this approach if in addition (iii) chemical instabilities are considered. All statements are based on the Rayleigh–Plesset ODE approximation of the bubble dynamics, extended in an adiabatic approximation to include mass diffusion effects. This approximation is the only way to explore considerable portions of parameter space, as solving the full PDEs is numerically too expensive. Therefore, we checked the adiabatic approximation by comparison with the full numerical solution of the advection diffusion PDE and find good agreement.

Phase diagrams for sonoluminescing bubbles

Sound-driven gas bubbles in water can emit light pulses. This phenomenon is called sonoluminescence (SL). Two different phases of single bubble SL are known: diffusively stable and diffusively unstable SL. Phase diagrams are presented in the gas concentration versus forcing pressure state space and also in the ambient radius versus forcing pressure state space. These phase diagrams are based on the thresholds for energy focusing in the bubble and of (i) shape instabilities and (ii) diffusive instabilities. Stable SL only occurs in a tiny parameter window of a large forcing pressure amplitude Pa∼1.2–1.5 atm and a low gas concentration of less than 0.4% of the saturation. The upper concentration threshold becomes smaller with increasing forcing. The results quantitatively agree with experimental results of Putterman’s UCLA group on argon, but not on air. However, air bubbles and other gas mixtures can also successfully be treated in this approach if, in addition, (iii) chemical instabilities are considered. The essential feature is the removal from the bubble of almost all the nitrogen and oxygen as reaction products (i.e., NOx or NH3). Inert gases are crucial for stable sonoluminescence because they do not react with the fluid.

Sonoluminescing bubbles and mass diffusion.

The transduction of sound into light by a pulsating bubble in water occurs when its maximum radius is about ten times greater than its ambient radius. For such high-amplitude motion, the steady-state balance of mass flow between the bubble and gas dissolved in the surrounding fluid can be maintained by diffusion only at low partial pressures, about 3 Torr. The observation of sonoluminescence (SL) from bubbles in 200 Torr solutions of air in water requires the action of some as yet unknown mass flow mechanism. On the other hand, gas solutions prepared at low partial pressures, in the diffusion-controlled regime, enable one to achieve SL in gases that do not emit light at higher partial pressures. These include hydrogenic gases and gases with a ratio of specific heats close to unity, which hardly heat up upon adiabatic compression. Experiments that probe the role of mass transfer in SL are presented along with the implications of their comparison to a multiple-time-scale analysis of mass diffusion.

Probing the unknowns of sonoluminescence

The mechanism whereby a bubble transduces sound into a clocklike stream of picosecond flashes of ultraviolet light is robust, complex, and unknown. A theoretical understanding of the key bubble parameter, its ambient radius, is lacking. An explanation as to why this phenomenon has so far only been seen in water is elusive. In addition, we do not understand why cooling the water dramatically increases the light output or why sonoluminescence is so sensitive to doping with a noble gas. Experimentally, the spectrum has been unable to be followed past 7 electron volts and so the limits of energy concentration which can be achieved with sonoluminescence from a single bubble are not yet measured. In addition to yielding clues experiments in progress will most likely serve to deepen the mystery! [Work supported by the US DOE Division of Advanced Energy Projects; RL is an AT&T Fellow.]

A model of sonoluminescence

A bubble of air, trapped at the centre of a spherical container of water on the surface of which spherical sound waves are maintained by transducers, may emit light, a phenomenon known as sonoluminescence. The surface of the bubble expands and contracts in obedience to the Rayleigh–Lamb equation, which requires knowledge of the gas pressure on the surface of the bubble. In many investigations of bubble pulsations, it is assumed that the air in the bubble moves adiabatically. To understand sonoluminescence, however, it is necessary to allow for the possibility that shocks are generated within the bubble. We couple the Rayleigh–Lamb equation governing the bubble radius to Euler’s equations governing the motion of air in the bubble, and solve the two equations simultaneously. The air is modelled by a van der Waals gas. Results are presented for a number of slightly different conditions of excitation, but in which the response of the system is widely different. If the frequency of the sound is high, the gas in the bubble moves adiabatically and no light is emitted. As the frequency is reduced (for the same ambient bubble radius and driving pressure), the incoming bubble surface acts as a piston that generates an ingoing shock wave that passes through the centre of the bubble, and then, when it strikes the bubble surface, halts and reverses its inward motion; a sequence of such inwardly and outwardly moving shocks occur. The shock waves generate such high temperatures that the air near the centre of the bubble is almost completely ionized, and emits light, which we attribute to bremmstrahlung. The light created by the second inwardly moving shock exceeds that created by the first but, as the frequency of the sound is further reduced, the energy from the first shock rises, and the overall luminosity of the bubble increases. When the sound frequency is further reduced, two shocks are launched successively by the inward moving bubble surface, the second colliding with the first after it has passed through the centre of symmetry but before it can collide with the bubble surface. Even higher temperatures are reached and the luminosity of the bubble continues to increase with decreasing frequency. Details of these solutions are presented, and estimates are made of the luminosity of the bubble in different conditions of excitation. Two other families of solutions are presented. In one, the frequency and ambient bubble radius are fixed and the driving amplitude is varied. In the other, the frequency and driving amplitude are fixed and the radius is varied. The effects of changing only the molecular weight of the trapped gas is also examined.

Toward a hydrodynamic theory of sonoluminescence

For small Mach numbers the Rayleigh–Plesset equations (modified to include acoustic radiation damping) provide the hydrodynamic description of a bubble’s breathing motion. Measurements are presented for the bubble radius as a function of time. They indicate that in the presence of sonoluminescence the ratio of maximum to minimum bubble radius is about 100. Scaling laws for the maximum bubble radius and the temperature and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audible sound fields these equations yield picosecond hot spots, such as are observed experimentally. However, the analysis indicates that a detailed description of sonoluminescence requires the use of parameters for which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extension of bubble dynamics to include nonlinear effects such as shock waves.

Scaling laws for sonoluminescence

The extremely nonlinear dynamics of bubble motion is described by the Navier–Stokes equations of fluid mechanics, as coupled to the laws of heat conduction and mass diffusion. In order to gain insight into the limitations of the hydrodynamic theory of bubble collapse, scaling laws have been derived for the maximum radius, collapse temperature, hot spot lifetime, collapse pressure, and ambient radius in terms of the applied sound field and the assumption that the bubble is a gas-filled cavity. In order to match the scaling laws to the experimental observations of collapse temperature and flash width requires that the Mach number for bubble motion exceed unity. In conclusion, a description of sonoluminescence must include the properties of imploding shock waves. [Work supported by the US DOE Division of Engineering and Geophysics; R. L. is supported by an A.T.&T. fellowship.]

Limitations of the hydrodynamical theory of cavitation induced sonoluminescence.

The extremely short duration (<50 ps) of the flashes of light emitted by a sound field raises problems for the hydrodynamical description of sonoluminescence. Solutions to the Navier–Stokes equations with such a fast but short-lived adiabatic compression develop shock fronts. Even in the linear approximation a single 20-μ bubble that accelerates at this rate would radiate so much sound that its motion would dominate the Q of a 0.1-liter resonator. The extent to which such a quickly accelerating bubble can be considered to be in local equilibrium is discussed. Nevertheless, fluid mechanics provides valuable scaling laws that can be used to analytically determine the ambient radius, phase of collapse, and maximum and minimum radii of the trapped bubble’s oscillation. [Work supported by the USDOE: Office of Basic Science (theory) and Division of Advanced Energy Projects (experiment) and R. L. is an AT&T fellow.]

Dynamic behavior of a porous char particle burning in an oxygen‐containing environment: Part II: Transient analysis of a shrinking particle

AbstractThe diffusion and reaction model developed in a previous paper is extended allowing for shrinkage of the char particles. It is shown that possible shrinkage, arising from disintegration of the solid structure at a certain conversion level, modifies severely the extinction behavior of the reacting particles. Specifically, the region of ambient temperature and particle radius in which the predictions of the nonisothermal and of the isothermal versions of the model differ significantly becomes smaller. However, the particle shrinkage does not affect the ignition phenomena observed since a particle usually ignites at low conversion levels where the radius change is still negligible.