A simple method to analyze the super-harmonic and ultra-harmonic behavior of the acoustically excited bubble oscillator

Abstract

Acoustically excited bubbles are involved in a wide range of phenomena and applications ranging from oceanography to sonoluminescence; they have applications in chemistry, medical imaging, and therapeutic ultrasound. The complexity of bubble dynamics and the limited understanding of their behavior restricts the exploration of their full potential. The bubble oscillator is a highly nonlinear system, which makes it difficult to generate a comprehensive understanding of its oscillatory behavior. One method used to investigate such complex dynamical systems is the bifurcation analysis. Numerous investigations have employed the method of bifurcation diagrams to study the effect of different control parameters on the bubble behavior. These studies, however, focused mainly on investigating the subharmonic (SH) and chaotic oscillations of the bubbles. Super-harmonic (SuH) and ultra-harmonic (UH) bubble oscillations remain under-investigated. One reason is that the conventional method used for generating bifurcation diagrams cannot reliably identify features that are responsible for the identification of SuH and UH oscillations. Additionally, the conventional method cannot distinguish between the UHs and SHs. We introduce a simple procedure for the generation of bifurcation diagrams to address this shortcoming. This method selects the maxima of the bubble oscillatory response and plots them alongside the traditional bifurcation points for the corresponding control parameter. Through applying this method, the oscillatory behavior of the bubble oscillator is analyzed, and stable SuH and UH bubble oscillations are investigated. Based on this new analysis, the conditions for the generation and amplification of UH and SuH regimes are discussed.

Investigation of the 1/2 order subharmonic emissions of the period-2 oscillations of an ultrasonically excited bubble

“…where D is the thermal diffusivity of the gas which can be calculated using a = L cpρg where L is the gas thermal conductivity and c p is specific heat capacity at constant pressure and ρ g is the gas density. Predictions of the ODE thermal model have been shown to be in good agreement with predictions of the models that incorporate the thermal effects using the PDEs [45] that incorporate the temperature gradients within the bubble. To calculate the radial oscillations of the uncoated bubble while including the thermal effects, Eqs.…”

Nonlinear power loss in the oscillations of coated and uncoated bubbles: Role of thermal, radiation and encapsulating shell damping at various excitation pressures

“…Dissipation effects of Td become weaker for smaller bubbles and when the gas core is C3F8. We showed that scattering to damping ratio (STDR) is pressure dependent; STDR grows with pressure at pressure dependent resonance frequencies (P Df r [24]) and at super harmonic resonances of the system (SuHf r [23]). STDR is generally higher at f > f r .…”

“…Dynamics of the acoustically excited bubbles are nonlinear and chaotic. These dynamics have been the subject of numerous experimental [1,15,[17][18][19][20] and numerical [21][22][23][24][25][26][27][28][29][30] studies . Achieving the full potential of bubbles in applications and understanding their role in the associated phenomena not only requires a detailed knowledge over their complex behavior but also on the effect of bubble oscillations on the propagation of acoustic waves.…”

Nonlinear dynamics and acoustic emissions of interacting cavitation bubbles in viscoelastic tissues

“…It has demonstrated that the qualitative and quantitative changes of the nonlinear dynamics could be investigated effectively over a wide range of control parameters [43] , [45] , [46] , [47] , [48] , [49] . However, the conventional bifurcation analysis may be misleading and cannot reliably identify features that are responsible for the identification of super-harmonic and ultra-harmonic oscillations [43] , [50] , [51] , [52] , [53] . Thus, a more comprehensive bifurcation analysis method was used herein to investigate the nonlinear dynamics of the coupled two-bubble system for a wide range of control parameters as described previously [43] , [50] , [51] , [52] , [53] .…”