This model was also used to carry

This model was also used to carry out some aspects of the numerical simulations presented in this work (e.g. hydrodynamic force fields and phase parameter spaces). The physical properties of the liquid used in the simulations are summarized in Table 1.
The position, stability and relative intensity of the studied SL bubbles, were evaluated through photographs captured by two cameras (Nikkon D40x and Hitachi KP-F120) set to take pictures from two orthogonal perspectives. Particularly, the observed bubble position was corrected taking into account the curvature of the spherical resonator wall and the changes in the refractive index of the propagation media. Furthermore, the tridimensional position was determined by means of a iterative triangulation algorithm.
The collapse time of the bubbles (), defined as the time interval between the low frequency acoustic pressure zero crossing with negative slope and the SL flash emission, was measured with a timer Stanford Research Systems SR620. This apparatus was operated at its maximum sampling rate (1500samples/s) with a precision of 100ns (determined by the jitter in the MIC signal).

Results and discussion
This section describes and discuss a series of experiments and simulations designed to answer two main questions: Is there an optimum value of N and the relative phase in order to enhance the bubble stability and ras pathway concentration? Is there any limit frequency in which the HF component of bi-harmonic driving cease to have a significant effect on the bubble dynamics? Unless otherwise specified, all the ras pathway data presented in this study (both experimental measurements and numerical simulations) correspond to the case of single bubble sonoluminescence (SBSL). This part of the work is organized as follows: In Section 3.1, the central hypothesis is outlined by means of simulations of the radial dynamics of typical bubbles for different driving frequencies. Subsequently, we compare experimental traces of the measured for bubbles subjected to different bi-harmonics pressure fields. Furthermore, the effect of on the bubble’s stability is demonstrated through photographs. These findings motivated the realization of a series of numerical simulations in order to complement and also support the experimental observations. The numerical simulations, described in Sections 3.2 and 3.3, let us investigate many aspects of SBSL phenomenon under controlled and stable situations which are extremely difficult to achieve in the experiments. In Section 3.2, we discuss how the use of harmonics of different order N affects the positional stability of the sonoluminescent bubbles. On the other hand, the influence of in the of a fixed bubble is explored in Section 3.3. Finally, in Section 3.4 we perform a multivariate analysis based on the covariance method to study the dependences among the experimental bubble parameters obtained from the numerical fits of the . In addition, we tracked the bubbles position on the acoustic chamber () in order to analyze their positional stability. The parametric analysis was complemented with extensive measurements of the collapse time of xenon bubbles carried out for different bi-harmonic drivings (N) and distinct relative phases set in the driving signal.

Conclusions
In this work, we performed an extensive parametric study in order to achieve a deeper understanding about the role of the high frequency component of the acoustic field in the dynamics of sonoluminescent bubbles driven with bi-harmonic signals in H2SO4, specifically in a Ar–SA85 or Xe–SA85 systems.
The diversity of data gathered during this research, consisting of both experimental results and numerical simulations, let us analyze the phenomenon under discussion from a general perspective. This kind of study allowed us to further understand not only the many advantages of the use of multi-harmonic driving in Sonoluminescence, but also some unexplored corners of the bubble dynamics itself like the absence of sharp resonances peaks in the expansion ratio (observed in Fig. 1(b)), for typical acoustic pressures used in Sonoluminescence in the case of SA85, in contrast to that reported in water based systems.