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2021
DOI: 10.1007/s11071-020-06163-8
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Nonlinear dynamics of acoustic bubbles excited by their pressure-dependent subharmonic resonance frequency: influence of the pressure amplitude, frequency, encapsulation and multiple bubble interactions on oversaturation and enhancement of the subharmonic signal

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Cited by 53 publications
(64 citation statements)
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“…The acoustic pressure p a = − p A sin(2πft), where p A and f are the ultrasound amplitude and frequency, respectively. Note that the time delay while the pressure radiated by one bubble propagating to the other bubble was neglected in Eq (1) , it is reasonable because the initial bubble−bubble distances are small (d 0 < 100 μm) in this study, in which case the time delays become insignificant [36] , [43] . Sojahrood et al have provided a nice review of the time delays in the interacting bubble simulations [43] .…”
Section: Theory and Methodsmentioning
confidence: 99%
See 3 more Smart Citations
“…The acoustic pressure p a = − p A sin(2πft), where p A and f are the ultrasound amplitude and frequency, respectively. Note that the time delay while the pressure radiated by one bubble propagating to the other bubble was neglected in Eq (1) , it is reasonable because the initial bubble−bubble distances are small (d 0 < 100 μm) in this study, in which case the time delays become insignificant [36] , [43] . Sojahrood et al have provided a nice review of the time delays in the interacting bubble simulations [43] .…”
Section: Theory and Methodsmentioning
confidence: 99%
“…Note that the time delay while the pressure radiated by one bubble propagating to the other bubble was neglected in Eq (1) , it is reasonable because the initial bubble−bubble distances are small (d 0 < 100 μm) in this study, in which case the time delays become insignificant [36] , [43] . Sojahrood et al have provided a nice review of the time delays in the interacting bubble simulations [43] . Moreover, taking the time delay into account would make the numerical simulations more complex and computationally intensive, especially for the time-varying bubble−bubble distance while the translational motions of bubbles were simultaneously considered in this study.…”
Section: Theory and Methodsmentioning
confidence: 99%
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“…(12) , while the red dots in panel B correspond to the lowest required equivalent pressure amplitude to reach relative expansion [75] , [66] . This threshold correlates with the minimum threshold of bubble destruction of [111] The frequencies and pressure amplitudes corresponding to the optimal setup are denoted by green and blue colours, respectively. In panel C, the growth rate values obtained at the optimal parameter set are plotted as the function of the bubble size.…”
Section: Numerical Resultsmentioning
confidence: 95%