Modifications of the equation for gas bubble dynamics in a soft elastic medium

Zabolotskaya, Evgenia A.; Ilinskii, Yurii A.; Meegan, G. Douglas; Hamilton, Mark F.

doi:10.1121/1.2010348

Cited by 29 publications

(33 citation statements)

References 14 publications

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“…͑12͒. 24 Here, eff is an effective viscosity that is assigned the value eff =20 = 20 mPa s, where = 1 mPa s is the viscosity of water. This choice of eff approximates the total damping, due to heat transfer and radiation as well as viscosity, of a 100 m bubble that pulsates at its natural frequency.…”

Section: Simulation Parameters and Lossesmentioning

confidence: 99%

Model of coupled pulsation and translation of a gas bubble and rigid particle

Hay

Hamilton

Ilinskii

et al. 2009

The Journal of the Acoustical Society of America

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A model of the interaction of a spherical gas bubble and a rigid spherical particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model accounts for pulsation and translation of the bubble as well as translation of the particle in an infinite, incompressible liquid. The model derived here is accurate to order R 5 / d 5 , where R is a characteristic radius and d is the separation distance between the bubble and particle. This order is the minimum accuracy required to account for the interaction of the bubble and particle. Dependence on the size and density of the particle is demonstrated through numerical integration of the dynamical equations for both the free and forced response of the system. Numerical results are presented for models accurate to orders higher than R 5 / d 5 to demonstrate the consequences of truncating the equations at order R 5 / d 5 .

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Section: Simulation Parameters and Lossesmentioning

confidence: 99%

Model of coupled pulsation and translation of a gas bubble and rigid particle

Hay

Hamilton

Ilinskii

et al. 2009

The Journal of the Acoustical Society of America

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“…II D. The flow field outside the boundary layer can be considered potential flow, and viscous losses in this region may be included to O e 2 l 2 ð Þ via a dissipation function. 11,30 For the present case the dissipation function is…”

Section: Viscous Dissipationmentioning

confidence: 99%

“…(8) to obtain an expression for the kinetic energy in terms of R ei . Potential energy due to surface tension is given by 30 where r is the surface tension of the liquid and…”

Section: A Kinetic Energymentioning

confidence: 99%

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Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

Kurihara

Hay

Ilinskii

et al. 2011

The Journal of the Acoustical Society of America

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Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability.

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“…This explains why a minute quantity of gas bubbles can dramatically change the effective acoustic properties of a liquid. If the bubble is no longer in a liquid, but in an elastic medium with shear velocity u 0 , its resonance frequency becomes [5,6]:…”

Section: Introductionmentioning

confidence: 99%

Influence of positional correlations on the propagation of waves in a complex medium with polydisperse resonant scatterers

et al. 2011

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We present experimental results on a model system for studying wave propagation in a complex medium exhibiting low frequency resonances. These experiments enable us to investigate a fundamental question that is relevant for many materials, such as metamaterials, where low-frequency scattering resonances strongly influence the effective medium properties. This question concerns the effect of correlations in the positions of the scatterers on the coupling between their resonances, and hence on wave transport through the medium. To examine this question experimentally, we measure the effective medium wave number of acoustic waves in a sample made of bubbles embedded in an elastic matrix over a frequency range that includes the resonance frequency of the bubbles. The effective medium is highly dispersive, showing peaks in the attenuation and the phase velocity as functions of the frequency, which cannot be accurately described using the Independent Scattering Approximation (ISA). This discrepancy may be explained by the effects of the positional correlations of the scatterers, which we show to be dependent on the size of the scatterers. We propose a self-consistent approach for taking this "polydisperse correlation" into account and show that our model better describes the experimental results than the ISA.

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Modifications of the equation for gas bubble dynamics in a soft elastic medium

Cited by 29 publications

References 14 publications

Model of coupled pulsation and translation of a gas bubble and rigid particle

Model of coupled pulsation and translation of a gas bubble and rigid particle

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

Influence of positional correlations on the propagation of waves in a complex medium with polydisperse resonant scatterers

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