Positional stability as the light emission limit in sonoluminescence with sulfuric acid

Cross-frequency couplings in non-sinusoidal dynamics of interacting oscillators: Acoustic estimation of the radial position and spatial stability of nonlinear oscillating bubbles

In this work, the analysis of cross-frequency couplings (CFC) is introduced in the context of nonlinear acoustics related to the dynamics of bubble(s)-resonator systems. The results obtained from experiments specifically designed to untangle the causal connection between the CFC patterns observed at the signal level and the underlying physical processes, are discussed. It was found that "causal" amplitude-to-amplitude (AAC) and amplitude-to-phase (APC) couplings emerge in the system dynamics as a consequence of the bubble(s)-resonator mechanistic interaction in the oscillatory steady-state. In these CFC patterns, the amplitude of the fundamental frequency component (f₀) effectively modulates the amplitude and relative phase of the harmonic components (Nf₀). Moreover, these AAC and APC couplings give rise to "epiphenomenal" phase-to-amplitude (PAC) and phase-to-phase (PPC) couplings, in which the link between modulating and modulated parameters represents a correlation rather than a causal connection. It is shown that these CFC patterns can be exploited to determine the presence, spatial stability and radial position of nonlinear oscillating bubble(s) trapped within the acoustic chamber. Potential applications of the proposed techniques are also discussed. Substantial evidence is presented showing that CFC patterns emerging from quasi-periodic non-sinusoidal waveforms are informative on the interaction between underlying oscillators.

Positional stability and radial dynamics of sonoluminescent bubbles under bi-harmonic driving: Effect of the high-frequency component and its relative phase

The use of bi-frequency driving in sonoluminescence has proved to be an effective way to avoid the spatial instability (pseudo-orbits) developed by bubbles in systems with high viscous liquids like sulfuric or phosphoric acids. In this work, we present extensive experimental and numerical evidence in order to assess the effect of the high frequency component (PAc(HF)) of a bi-harmonic acoustic pressure field on the dynamic of sonoluminescent bubbles in an aqueous solution of sulfuric acid. The present study is mainly focused on the role of the harmonic frequency (Nf0) and the relative phase between the two frequency components (φb) of the acoustic field on the spatial, positional and diffusive stability of the bubbles. The results presented in this work were analyzed by means of three different approaches. First, we discussed some qualitative considerations about the changes observed in the radial dynamics, and the stability of similar bubbles under distinct bi-harmonic drivings. Later, we have investigated, through a series of numerical simulations, how the use of high frequency harmonic components of different order N, affects the positional stability of the SL bubbles. Furthermore, the influence of φb in their radius temporal evolution is systematically explored for harmonics ranging from the second to the fifteenth harmonic (N=2-15). Finally, a multivariate analysis based on the covariance method is performed to study the dependences among the parameters characterizing the SL bubble. Both experimental and numerical results indicate that the impact of PAc(HF) on the positional instability and the radial dynamics turns to be progressively negligible as the order of the high frequency harmonic component grows (i.e. N ≫ 1), however its effectiveness on the reduction of the spatial instability remains unaltered or even improved.

Temperature dependence of single-bubble sonoluminescence threshold in sulfuric acid: An experimental study

We experimentally investigated the temperature dependence of intensity of single-bubble sonoluminescence (SBSL) in 85 wt%. sulfuric acid. It was found that the intensity increases as temperature increases from 15 °C and 25 °C, confirming what has been predicted by A. Moshaii et al. [Phys. Rev. E 84, 046301 (2011)] theoretically. This behavior, however, is completely opposite to what has been observed for water. Above 25 °C, the behavior of intensity of SBSL in sulfuric acid is found to be independent of the liquid temperature. Moreover, it was observed that as the temperature increases, contribution to total intensity from the UV portion of the spectrum increases while contribution from the visible portion decreases, indicating higher bubble temperatures at higher liquid temperatures. Results of this experiment further indicate that the intensity threshold at each temperature is not determined by the shape or the positional stability conditions but by the driving pressure at which the transition from SBSL to multibubble sonoluminescence (MBSL) takes place.

Stable tridimensional bubble clusters in multi-bubble sonoluminescence (MBSL)

In the present work, stable clusters made of multiple sonoluminescent bubbles are experimentally and theoretically studied. Argon bubbles were acoustically generated and trapped using bi-frequency driving within a cylindrical chamber filled with a sulfuric acid aqueous solution (SA85w/w). The intensity of the acoustic pressure field was strong enough to sustain, during several minutes, a large number of positionally and spatially fixed (without pseudo-orbits) sonoluminescent bubbles over an ellipsoidally-shaped tridimensional array. The dimensions of the ellipsoids were studied as a function of the amplitude of the applied low-frequency acoustic pressure (PAc(LF)) and the static pressure in the fluid (P0). In order to explain the size and shape of the bubble clusters, we performed a series of numerical simulations of the hydrodynamic forces acting over the bubbles. In both cases the observed experimental behavior was in excellent agreement with the numerical results. The simulations revealed that the positionally stable region, mainly determined by the null primary Bjerknes force (F→Bj), is defined as the outer perimeter of an axisymmetric ellipsoidal cluster centered in the acoustic field antinode. The role of the high-frequency component of the pressure field and the influence of the secondary Bjerknes force are discussed. We also investigate the effect of a change in the concentration of dissolved gas on the positional and spatial instabilities through the cluster dimensions. The experimental and numerical results presented in this paper are potentially useful for further understanding and modeling numerous current research topics regarding multi-bubble phenomena, e.g. forces acting on the bubbles in multi-frequency acoustic fields, transient acoustic cavitation, bubble interactions, structure formation processes, atomic and molecular emissions of equal bubbles and nonlinear or unsteady acoustic pressure fields in bubbly media.

Energy concentration and positional stability of sonoluminescent bubbles in sulfuric acid for different static pressures

In this study we report several experimental and numerical results on the influence of static pressure (P_{0}) over the main parameters in single bubble sonoluminescence (SBSL), using a sulfuric acid aqueous solution (SA) with low concentrations of argon gas dissolved. Bifrequency driving was used in the experiments to enhance spatial stability of the bubbles. The experimental results were compared with simulations provided by a numerical code that models the radial dynamics of the bubbles. The results showed that an increase on the static pressure of the system shifts the Bjerknes instability threshold, allowing the bubble to access higher acoustic pressures (P_{Ac}^{}). Furthermore, a decrease in the measured ambient radius R_{0} and the calculated relative gas concentration c_{∞}/c_{0} were observed. A notorious increment in the bubble collapse violence and energy focusing for P_{0} above 1 bar was achieved. These were mainly indicated by the growth of the bubble expansion ratio (R_{max}/R_{0}), the bubble mechanical energy density, and the maximum bubble wall velocity dR/dt. In agreement with the previous statement, the maximum temperature during the bubble collapse predicted by the model is augmented as well. The use of different harmonics in the ultrasound pressure field regarding energy focusing is also discussed. Finally, we analyzed the stability regions of the R_{0}-P_{Ac}^{} parameter space via numerical predictions for P_{0} above the measured, identifying the shape instabilities as the main limiting agent to obtain further energy concentration in SA systems at high static pressures.

Path suppression of strongly collapsing bubbles at finite and low Reynolds numbers

We study, numerically and experimentally, three different methods to suppress the trajectories of strongly collapsing and sonoluminescent bubbles in a highly viscous sulfuric acid solution. A new numerical scheme based on the window method is proposed to account for the history force acting on a spherical bubble with variable radius. We could quantify the history force, which is not negligible in comparison with the primary Bjerknes force in this type of problem, and results are in agreement with the classical primary Bjerknes force trapping threshold analysis. Moreover, the present numerical implementation reproduces the spatial behavior associated with the positional and path instability of sonoluminescent argon bubbles in strongly gassed and highly degassed sulfuric acid solutions. Finally, the model allows us to demonstrate that spatially stationary bubbles driven by biharmonic excitation could be obtained with a different mode from the one used in previous reported experiments.

Effect of the Rayleigh-Taylor instability on maximum reachable temperatures in laser-induced bubbles

Laser-induced bubbles provide an effective vehicle to achieve high-energy concentrations and maximum temperatures in bubble luminescence phenomena. One limitation to the temperatures that can be achieved is the development of the Rayleigh-Taylor instability (RTI) during the instants previous to the bubble maximum compression. For a given fluid, the control parameters of the experiment are: the bubble maximum radius, the bubble ambient radius, the initial perturbations of the bubble, and the liquid pressure at infinity. In this work, experiments using laser-induced bubbles in a highly viscous phosphoric acid were performed in order to determine the achievable parameters values in the phase space. The effect of R(max), R(0), a(2)(i), a(3)(i), and p(∞) on the maximum temperature achieved by the gas contents inside the bubble were numerically determined. The results show for each static pressure an optimum region for maximum temperatures of the gas contents bounded by the RTI.

Upscaling energy concentration in multifrequency single-bubble sonoluminescence with strongly degassed sulfuric acid

Single-bubble sonoluminescence (SBSL) was explored under a variety of multifrequency excitations. In particular, biharmonic excitation was used to produce SBSL for unprecedented low dissolved noble gas concentrations in a sulfuric acid solution. Reducing the amount of dissolved noble gas makes it possible to reach higher acoustic pressures on the SL bubble, which otherwise are not attainable because of the Bjerknes instability. By using biharmonic excitation, we were able to experimentally trap and to spatially stabilize SL bubbles for xenon pressure overhead as low as 1 mbar. As a result, we have access to regions in phase space where the plasma temperatures are higher than the ones reached before for bubbles driven at ≈30 kHz.

Influence of liquid density on the parametric shape instability of sonoluminescence bubbles in water and sulfuric acid

Parametric shape instability of sonoluminescing argon bubbles in water and aqueous H(2)SO(4) was numerically analyzed considering gas and liquid density variations. The employed model couples Gilmore, Tait (liquid) and van der Waals (gas) equations to simulate radial dynamics and density changes, respectively. Shape stability-instability zones in the P(a)-R(0) space resulted from a linear stability analysis. For the argon-water and argon-water-acid systems, numerical results indicate a rapid rise in both gas and liquid densities during final stages of bubble implosion which result in a stabilizing effect on the parametric instability.

Analytical study of the acoustic field in a spherical resonator for single bubble sonoluminescence

The acoustic field in the liquid within a spherical solid shell is calculated. The proposed model takes into account Stoke's wave equation in the viscous fluid, the membrane theory to describe the solid shell motion and the energy loss through the external couplings of the system. A point source at the resonator center is included to reproduce the acoustic emission of a sonoluminescence bubble. Particular calculations of the resulting acoustic field are performed for viscous liquids of interest in single bubble sonoluminescence. The model reveals that in case of radially symmetric modes of low frequency, the quality factor is mainly determined by the acoustic energy flowing through the mechanical coupling of the resonator. Alternatively, for high frequency modes the quality factor is mainly determined by the viscous dissipation in the liquid. Furthermore, the interaction between the bubble acoustic emission and the resonator modes is analyzed. It was found that the bubble acoustic emission produces local maxima in the resonator response. The calculated amplitudes and relative phases of the harmonics constituting the bubble acoustic environment can be used to improve multi-frequency driving in sonoluminescence.

Dynamics of sonoluminescing bubbles within a liquid hammer device

We studied the dynamics of a single sonoluminescing bubble (SBSL) in a liquid hammer device. In particular, we investigated the phosphoric acid-xenon system, in which pulses up to four orders of magnitude brighter than SBSL in water systems (about 10;{12} photons per pulse) have been previously reported [Chakravarty, Phys. Rev. E 69, 066317 (2004)]. We used stroboscopic photography and a Mie scattering technique in order to measure the radius evolution of the bubbles. Under adequate conditions we may position a bubble at the bottom of the tube (cavity) and a second bubble trapped at the middle of the tube (upper bubble). During its collapse, the cavity produces the compression of the liquid column. This compression drives impulsively the dynamics of the upper bubble. Our measurements reveal that the observed light emissions produced by the upper bubble are generated at its second collapse. We employed a simple numerical model to investigate the conditions that occur during the upper bubble collapse. We found good agreement between numerical and experimental values for the light intensity (fluence) and light pulse widths. Results from the model show that the light emission is increased mainly due to an increase in noble gas ambient radius and not because the maximum temperature increases. Even for the brightest pulses obtained ( 2x10;{13} photons, about 20W of peak power) the maximum temperatures computed for the upper bubble are always lower than 20000K .

Trapping an intensely bright, stable sonoluminescing bubble

Previous works on single bubble sonoluminescence in sulfuric acid solutions have stressed the fact that the sonoluminescence (SL) emissions are the highest ever found, but at the same time the bubble moves in orbits. We have fixed the SL bubble spatially and at the same time we have reached higher SL emissions using another harmonic acoustic signal to produce the acoustic excitation. Multiple harmonic excitation produces up to a fourfold increase in SL emissions, reaching the peak value of about 40 microW for a moving bubble and 15 microW for a nonmoving bubble. The ability to have a bright stationary bubble also opens new research opportunities. In particular, we develop a new method to measure the absolute radius evolution of the bubble that exploits this stability.