Evolution of spherical cavitation bubbles: Parametric and closed-form solutions

Mancas, Stefan C.; Rosu, H. C.

doi:10.1063/1.4942237

Cited by 35 publications

(14 citation statements)

References 12 publications

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“…The leading-order solution R 0 for the collapse stage is then obtained by integrating (14) from t i = −Ψ, at the maximum bubble radius…”

Section: B the Leading-order Solutionmentioning

confidence: 99%

“…The average energy loss rate for a bubble system can be rewritten as follows, using (30), Using (14) and (17), the right-hand side may be expressed entirely as a function of E 0 , p g0…”

Section: A Validationmentioning

confidence: 99%

“…These implicit formulae may be simply solved numerically to obtain the bubble radius. The parametric rational Weierstrass periodic solutions have been found using the connection between the Rayleigh-Plesset equation and Abel's equation 14 .…”

Section: Introductionmentioning

confidence: 99%

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Viscous decay of nonlinear oscillations of a spherical bubble at large Reynolds number

Smith

Wang

2017

Physics of Fluids

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“…The leading-order solution R 0 for the collapse stage is then obtained by integrating (14) from t i = −Ψ, at the maximum bubble radius…”

Section: B the Leading-order Solutionmentioning

confidence: 99%

“…The average energy loss rate for a bubble system can be rewritten as follows, using (30), Using (14) and (17), the right-hand side may be expressed entirely as a function of E 0 , p g0…”

Section: A Validationmentioning

confidence: 99%

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Viscous decay of nonlinear oscillations of a spherical bubble at large Reynolds number

Smith

Wang

2017

Physics of Fluids

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“…Based on the Young-Laplace law 44 , the Laplace pressure from surface tension inversely scales with the bubble size 45, 46 . At the nanometer scale, when a bubble containing fluid is impacted by a traveling wave, the local fluctuation of pressure in the fluid combined with surface tension significantly increases the collapsing possibility of nanobubbles.…”

Section: Introductionmentioning

confidence: 99%

Effect of Shock-Induced Cavitation Bubble Collapse on the damage in the Simulated Perineuronal Net of the Brain

Adnan

2017

Sci Rep

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The purpose of this study is to conduct modeling and simulation to understand the effect of shock-induced mechanical loading, in the form of cavitation bubble collapse, on damage to the brain’s perineuronal nets (PNNs). It is known that high-energy implosion due to cavitation collapse is responsible for corrosion or surface damage in many mechanical devices. In this case, cavitation refers to the bubble created by pressure drop. The presence of a similar damage mechanism in biophysical systems has long being suspected but not well-explored. In this paper, we use reactive molecular dynamics (MD) to simulate the scenario of a shock wave induced cavitation collapse within the perineuronal net (PNN), which is the near-neuron domain of a brain’s extracellular matrix (ECM). Our model is focused on the damage in hyaluronan (HA), which is the main structural component of PNN. We have investigated the roles of cavitation bubble location, shockwave intensity and the size of a cavitation bubble on the structural evolution of PNN. Simulation results show that the localized supersonic water hammer created by an asymmetrical bubble collapse may break the hyaluronan. As such, the current study advances current knowledge and understanding of the connection between PNN damage and neurodegenerative disorders.

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“…Kudryashov & Sinelshchikov (2014) found an implicit analytical solution to the Rayleigh equation for an empty bubble (in terms of the hypergeometric function) and for a gas-filled bubble (in terms of the Weierstrass elliptic function). Mancas & Rosu (2016) obtained the parametric rational Weierstrass periodic solutions using the connection between the Rayleigh-Plesset equation and Abel's equation. Van Gorder (2016) made a theoretical study for N -dimensional bubbles with arbitrary polytropic index of the bubble gas.…”

Section: Introductionmentioning

confidence: 99%

Radiative decay of the nonlinear oscillations of an adiabatic spherical bubble at small Mach number

Smith

Wang

2017

J. Fluid Mech.

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A theoretical study is carried out for bubble oscillation in a compressible liquid with significant acoustic radiation based on the Keller–Miksis equation using a multi-scaled perturbation method. The leading-order analytical solution of the bubble radius history is obtained to the Keller–Miksis equation in a closed form including both compressible and surface tension effects. Some important formulae are derived including: the average energy loss rate of the bubble system for each cycle of oscillation, an explicit formula for the dependence of the oscillation frequency on the energy, and an implicit formula for the amplitude envelope of the bubble radius as a function of the energy. Our theory shows that the frequency of oscillation does not change on the inertial time scale at leading order, the energy loss rate on the long compressible time scale being proportional to the Mach number. These asymptotic predictions have excellent agreement with experimental results and the numerical solutions of the Keller–Miksis equation over very long times. A parametric analysis is undertaken using the above formula for the energy of the bubble system, frequency of oscillation and minimum/maximum bubble radii in terms of the dimensionless initial pressure of the bubble gases (or, equivalently, the dimensionless equilibrium radius), Weber number and polytropic index of the bubble gas.

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Evolution of spherical cavitation bubbles: Parametric and closed-form solutions

Cited by 35 publications

References 12 publications

Viscous decay of nonlinear oscillations of a spherical bubble at large Reynolds number

Viscous decay of nonlinear oscillations of a spherical bubble at large Reynolds number

Effect of Shock-Induced Cavitation Bubble Collapse on the damage in the Simulated Perineuronal Net of the Brain

Radiative decay of the nonlinear oscillations of an adiabatic spherical bubble at small Mach number

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