Nonlinear Oscillations of a Cluster of Bubbles in a Sound Field. Bifurcation Structure.

Takahira, Hiroyuki; Yamane, Soichiro; Akamatsu, Teruaki

doi:10.1299/jsmeb.38.432

Cited by 37 publications

(25 citation statements)

References 15 publications

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“…Therefore, each bubble oscillates in response to two main pressure fields, the primary acoustic ultrasound pressure wave and secondary pressure waves scattered from all the bubbles in proximity. Hence, a MB cluster can be considered as a system of coupled oscillators where the dynamics of each oscillator depends on the rest [51].…”

Section: Introductionmentioning

confidence: 99%

Collective nonlinear behavior of interacting polydisperse microbubble clusters

Haghi

Sojahrood

Kolios

2019

Ultrasonics Sonochemistry

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Exploiting the full potential of MBs for applications requires a good understanding of their complex dynamics. Improved understanding of MB oscillations can lead to further enhancement in optimizing their efficacy in many applications and also invent new ones. Previous studies have predominantly addressed the behavior of a single isolated MB in an infinite liquid domain, whereas most applications employ MBs in clusters. Oscillating MBs have been shown to generate secondary pressure waves that modify the dynamics of the MBs in their proximity. A modified Keller-Miksis equation is used to account for inter-bubble interactions. The oscillatory dynamics of each MB within clusters was computed by numerically solving the resulting system of coupled nonlinear second order differential equations. Frequency response analysis and bifurcation diagrams were employed to track the dynamics of interacting MBs. Here we investigate the dynamics of polydisperse MB clusters over a wide range of acoustic and geometric parameters. An emergent collective behavior within bubble clusters was observed whereby individual dynamics of smaller bubbles were suppressed resulting in a collective behavior dominated by the dynamics of the largest MB within the cluster. The emergent dynamics of smaller MBs within bubble clusters can be characterized by constructive and destructive inter-bubble interactions. In constructive interactions, the radial oscillations of smaller bubbles matched those of the largest MB and their oscillations are amplified. In destructive interactions, the oscillations of smaller bubbles are suppressed so that their oscillations match those of the largest MB. Furthermore, a special case of constructive interactions is presented where dominant MB (largest) can force smaller MBs into period doubling and subharmonic oscillations.

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Section: Introductionmentioning

confidence: 99%

Collective nonlinear behavior of interacting polydisperse microbubble clusters

Haghi

Sojahrood

Kolios

2019

Ultrasonics Sonochemistry

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“…[7,8] and references therein). Later, these models were extended to the coupled Rayleigh-Plesset equations which take into account bubble-bubble interactions via the Bjerknes force (see [9][10][11][12][13] and references therein). From a mathematical point of view, these models are described by a system of coupled nonlinear oscillators, with external periodic force, and, thus, various types of dynamics can be observed in them.…”

Section: Introductionmentioning

confidence: 99%

“…Some bifurcations of two and N coupled bubbles were studied in [9,13,16]. However, in [9] unencapsulated bubbles were considered, while in [13,16] an inappropriate model of the shell was investigated (see discussion in [8]).…”

Section: Introductionmentioning

confidence: 99%

Hyperchaos and multistability in the model of two interacting microbubble contrast agents

Garashchuk

Sinelshchikov

Kazakov

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study nonlinear dynamics of two coupled contrast agents that are micro-meter size gas bubbles encapsulated into a viscoelastic shell. Such bubbles are used for enhancing ultrasound visualization of blood flow and have other promising applications like targeted drug delivery and noninvasive therapy. Here we consider a model of two such bubbles interacting via the Bjerknes force and exposed to an external ultrasound field. We demonstrate that in this five-dimensional nonlinear dynamical system various types of complex dynamics can occur, namely, we observe periodic, quasi-periodic, chaotic and hypechaotic oscillations of bubbles. We study the bifurcation scenarios leading to the onset of both chaotic and hyperchaotic oscillations. We show that chaotic attractors in the considered system can appear via either Feigenbaum's cascade of period doubling bifurcations or Afraimovich-Shilnikov scenario of torus destruction. For the onset of hyperchaotic attractor we propose a new bifurcation scenario, which is based on the appearance of a homoclinic chaotic attractor containing a saddle-focus periodic orbit with its two-dimensional unstable manifold. Finally, we demonstrate that the bubbles' dynamics can be multistable, i.e. various combinations of co-existence of the above mentioned attractors are possible. These cases include co-existence of hyperchaotic regime with any of the other remaining types of dynamics for different parameter values. Thus, the model of two coupled gas bubbles provide a new examples of physically relevant system with multistable hyperchaos.

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“…A pair of single-element 2.25-MHz unfocused transducers (Olympus, Center Valley, PA; bandwidth 1-3.0 MHz) were aligned coaxially in a tank of deionized water and oriented facing each other. Monodisperse MBs were injected into a sample chamber that was made with a plastic frame covered with an acoustically To numerically simulate the attenuation and sound speed, the Marmottant model [16], which accounts for radial-dependent shell properties, was modified to include MB multiple scattering using the approach introduced in [39]. At each frequency and pressure, 63 MBs were selected from the size distribution in Fig.…”

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confidence: 99%

Pressure dependence of the attenuation and sound speed in a bubbly medium: Theory and experiment

Sojahrood

Haghi

et al. 2016

Journal of the Acoustical Society of America

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Results of the measurements of sound speed and attenuation in a bubbly medium are reported. Monodisperse bubble solutions are sonicated with broadband ultrasound pulses with pressure amplitudes ranging between 12.5-100 kPa. Fundamental relationships between the frequency dependent attenuation, sound speed and pressure are established. A new model for the estimation of sound speed and attenuation is derived that incorporates the effect of nonlinear bubble oscillations on the wave propagation in the bubbly media. Model predictions are in good agreement with experimental results. PACS numbers: 43.25.Yw, 43.35.Bf, 43.35.Ei Acoustically excited microbubbles (MBs) are present in a wide range of phenomena; they have applications in sonochemistry [1]; oceanography and underwater acoustics [2, 3]; material science [4], sonoluminescence [5] and in medicine [6][7][8][9][10][11][12]. Due to their broad and exciting biomedical applications, it has been stated that˝The future of medicine is bubbles˝ [12]. MBs are used in ultrasound molecular imaging [6,7] and recently have been used for the non-invasive imaging of the brain microvasculature [7]. MBs are being investigated for site-specific enhanced drug delivery [8][9][10][11] and for the non-invasive treatment of brain pathologies (by transiently opening the impermeable blood-brain barrier (BBB) to deliver macromolecules [9]; with the first in human clinical BBB opening reported in 2016 [8]). However several factors limit our understanding of MB dynamics which consequently hinder our ability to optimally employ MBs in these applications. The MB dynamics are nonlinear and chaotic [13][14][15]; furthermore, the typical lipid shell coatings add to the complexity of the MBs dynamics due to the nonlinear behavior of the shell (e.g., buckling and rupture [16]). Importantly, the presence of MBs changes the sound speed and attenuation of the medium [17][18][19][20][21]. These changes are highly nonlinear and depend on the MB nonlinear oscillations which in turn depend on the ultrasound pressure and frequency, MB size and shell characteristics [17][18][19][20]. The increased attenuation due to the presence of MBs in the beam path may limit the pressure at the target location. This phenomenon is called pre-focal shielding (shadowing) [21,22]. Additionally, changes in the sound speed can change the position and dimensions of the focal region; thus, reducing the accuracy of focal placement (e.g., for targeted drug delivery). In imaging applications, MBs can limit imaging in depth due to the shadowing caused by prefocal MBs [21,22]. In sonochemistry, changes in the attenuation and sound speed impact the pressure distribution inside the reactors and reduces the procedure efficacy [23]. An accurate estimation of the pressure dependent atten-uation and sound speed in bubbly media remains one of the unsolved problems in acoustics [24]. Most current models are based on linear approximations which are only valid for small amplitude MB oscillations [17]. Linear approximations, however, are no...

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Nonlinear Oscillations of a Cluster of Bubbles in a Sound Field. Bifurcation Structure.

Cited by 37 publications

References 15 publications

Collective nonlinear behavior of interacting polydisperse microbubble clusters

Collective nonlinear behavior of interacting polydisperse microbubble clusters

Hyperchaos and multistability in the model of two interacting microbubble contrast agents

Pressure dependence of the attenuation and sound speed in a bubbly medium: Theory and experiment

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