Lagrangian formalism for computing oscillations of spherically symmetric encapsulated acoustic antibubbles

• Autorzy: Johansen K. , Postema M.
• Języki publikacji: EN

Abstrakty

EN

Antibubbles are gas bubbles containing a liquid droplet core and, typically, a stabilising outer shell. It has been hypothesised that acoustically driven antibubbles can be used for active leakage detection from subsea production facilities. This paper treats the dynamics of spherically symmetric microscopic antibubbles, building on existing models of bubble dynamics. A more complete understanding of microbubble dynamics demands that the effects of the translational dynamics is included into the Rayleigh-Plesset equation, which has been the primary aim of this paper. Moreover, it is a goal of this paper to derive a theory that is not based on ad-hoc parameters due to the presence of a shell, but rather on material properties. To achieve a coupled set of differential equations describing the radial and translational dynamics of an antibubble, in this paper Lagrangian formalism is used, where a Rayleigh-Plesset-like equation allows for the shell to be modelled from first principles. Two shell models are adopted; one for a Newtonian fluid shell, and the other for a Maxwell fluid shell. In addition, a zero-thickness approximation of the encapsulation is presented for both models. The Newtonian fluid shell can be considered as a special case of the Maxwell fluid shell. The equations have been linearised and the natural and damped resonance frequencies have been presented for both shell models.

Słowa kluczowe

EN

microbubbles; spatio–temporal bubble dynamics; Rayleigh-Plesset equation

• Wydawca: Polskie Towarzystwo Akustyczne. Oddział Gdański
• Czasopismo: Hydroacoustics
• Rocznik: 2016
• Tom: Vol. 19
• Strony: 197--207
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Johansen K.

• School of Engineering, James Watt Building, University of Glasgow, Glasgow, G12 8QQ, Scotland

autor

Postema M.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, ulica Adolfa Pawińskiego, 02-106 Warsaw, Poland
• School of Electrical and Information Engineering, Chamber of Mines Building, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2050, South Africa
• Department of Physics and Technology, University of Bergen, Allegaten 55, 5007 Bergen, Norway

Bibliografia

• [1] J. Moreno-Trejo, R. Kumar, T. Markeset, Mapping factors influencing the selection of subsea petroleum production systems: a case study, Int. J. Syst. Assur. Eng. Manag., vol. 3, no. 1, pp. 6–16, 2012.
• [2] J. Blackford, H. Stahl, Preface to the QICS special issue, Int. J. Greenhouse Gas Control, vol. 38, p. 1, 2015.
• [3] T.G. Leighton, P.R. White, Quantification of undersea gas leaks from carbon capture and storage facilities, from pipelines and from methane seeps, by their acoustic emissions, Proc. Roy. Soc. A, vol. 468, pp. 485–510, 2012.
• [4] K. Johansen, S. Kotopoulis, M. Postema, Ultrasonically driven antibubbles encapsulated by Newtonian fluids for active leakage detection, Lect. Notes in Eng. Comp. Sci., vol. 2216, pp. 750–754, 2015.
• [5] A. A. Doinikov, P. A. Dayton, Spatio-temporal dynamics of an encapsulated gas bubble in an ultrasound field, J. Acoust. Soc. Am., vol. 120, no. 2, pp. 661–669, 2006.
• [6] A. A. Doinikov, Translational motion of a spherical bubble in an acoustic standing wave of high intensity, Phys. Fluids, vol. 14, no. 4, pp. 1420–1425, 2002.
• [7] A. A. Doinikov, Equations of coupled radial and translational motions of a bubble in a weakly compressible liquid, Phys. Fluids, vol. 17, no. 12, pp. 128101-1–128101-4, 2005.
• [8] L. Landau, E. Lifshitz, Theory of Elasticity, Pergamon, Oxford, 1986.
• [9] A. A. Doinikov, P. A. Dayton, Maxwell rheological model for lipid-shelled ultrasound microbubble contrast agents., J. Acoust. Soc. Am., vol. 121, no. 6, pp. 3331–3340, 2007.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)