Abstract
In this paper, a modified Rayleigh–Plesset equation is derived, which takes into account the radial oscillations of a gas bubble covered with a viscoelastic shell and located in a viscoelastic liquid. For the case of small oscillations of the inclusion with a small amplitude, a comparison is made of the dependence of the damping parameter on the disturbance frequency according to the rheological model of Kelvin–Voigt and Maxwell.
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REFERENCES
L. D. Goldberg, J. S. Raichlen, and F. F. Forsberg, Ultrasound Contrast Agents. Basic Principles and Clinical Applications (Martin Dunitz, London, 2001).
V. Sboros, ‘‘Response of contrast agents to ultrasound,’’ Adv. Drug Deliv. Rev. 60, 1117–1136 (2008).
X. Ma, X. Wang, K. Hahn, and S. Sanchez, ‘‘Motion control of urea-powered biocompatible hollow microcapsules,’’ ACS Nano 10, 3597–3605 (2016).
D. A. Gubaidullin and Yu. V. Fedorov, ‘‘Acoustic waves in a liquid with gas bubbles covered by a viscoelastic shell,’’ Fluid Dyn. 54, 270–278 (2019).
C. Hua and E. Johnsen, ‘‘Nonlinear oscillations following the Rayleigh collapse of a gas bubble in a linear viscoelastic (tissue-like) medium,’’ Phys. Fluids 25, 083101 (2013).
D. A. Gubaidullin and Yu. V. Fedorov, ‘‘Wave dynamics of coated inclusions in a viscoelastic medium,’’ J. Appl. Mech. Tech. Phys. 61, 517–524 (2020).
A. Katiyar and K. Sarkar, ‘‘Effects of encapsulation damping on the excitation threshold for subharmonic generation from contrast microbubbles,’’ J. Acoust. Soc. Am. 132, 3576–3585 (2012).
D. A. Gubaidullin, D. D. Gubaidullina, and Yu. V. Fedorov, ‘‘The influence of heat transfer on the acoustics of a liquid with encapsulated bubbles,’’ Lobachevskii J. Math. 41 (7), 1202–1205 (2020).
V. Sh. Shagapov, M. N. Galimzyanov, and I. I. Vdovenko, ‘‘Characteristics of the reflection and refraction of acoustic waves at normal incidence on the interface between ’pure’ and bubbly liquids,’’ High Temp. 57, 256–262 (2019).
D. A. Gubaidullin and Yu. V. Fedorov, ‘‘Sound waves in a liquid with polydisperse vapor-gas bubbles,’’ Acoust. Phys. 62, 179–186 (2016).
V. Sh. Shagapov, M. N. Galimzyanov, and I. I. Vdovenko, ‘‘Characteristics of the reflection and refraction of acoustic waves at an ’oblique’ incidence on the interface between ’pure’ and bubbly liquids,’’ High Temp. 57, 425–429 (2019).
D. A. Gubaidullin and Yu. V. Fedorov, ‘‘Effect of phase transitions on the reflection of acoustic waves from the boundary of a vapor-gas-liquid mixture,’’ High Temp. 56, 306–308 (2018).
I. K. Gimaltdinov and S. A. Lepikhin, ‘‘Characteristics of the influence of phase sliding and initial pressure on the dynamics of detonation waves in bubbly liquid,’’ High Temp. 57, 420–424 (2019).
D. A. Gubaidullin and Yu. V. Fedorov, ‘‘Peculiarities of acoustic wave reflection from a boundary or layer of a two-phase medium,’’ Acoust. Phys. 64, 164–174 (2018).
Yu. Zhang, Zi. Jiang, J. Yuan, T. Chen, Yu. Zhang, N. Tang, and Xi. Du, ‘‘Ifluences of bubble size distribution on propagation of acoustic waves in dilute polydisperse bubbly liquids,’’ J. Hydrodyn. 31, 50–57 (2019).
D. A. Gubaidullin, D. D. Gubaidullina, and Yu. V. Fedorov, ‘‘Acoustics of a two-fractional polydisperse bubbly liquid with phase transitions,’’ Lobachevskii J. Math. 40 (6), 740–744 (2019).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 7: Theory and Elasticity (Pergamon, New York, 1959).
A. A. Doinikov and P. A. Dayton, ‘‘Maxwell rheological model for lipid-shelled ultrasound microbubble contrast agents,’’ J. Acoust. Soc. Am. 121, 3331–3340 (2007).
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Gubaidullin, D.A., Gubaidullina, D.D. & Fedorov, Y.V. Radial Oscillations of a Shell-Covered Gas Bubble in a Viscoelastic Liquid. Lobachevskii J Math 42, 2124–2128 (2021). https://doi.org/10.1134/S1995080221090109
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DOI: https://doi.org/10.1134/S1995080221090109