Towards a theory of self-organization phenomena in bubble-liquid mixtures

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 54, Issue 5, 1996, Pages 4990-5003

  Akhatov, I ^a   Parlitz, U ^b   Lauterborn, W ^b  

^a Birsk Branch of Federal State Budgetary Educational Establishment of Higher Education Bashkir State University   (Russian Federation)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001458887     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.54.4990     Document Type: Article

References (43)

1. RR. Young, Cavitation (McGraw-Hill, London, 1989).
2. T.G. Leighton, The Acoustic Bubble (Academic, London, 1994).
3. Cavitation and Inhomogeneities in Underwater Acoustics, edited by W. Lauterborn (Springer, Berlin, 1980).
4. Mechanics and Physics of Bubbles in Liquids, edited by L. van Wijngaarden (Nijhoff, The Hague, 1982).
5. Bubble Dynamics and Interface Phenomena, edited by J.R. Blake, J.M. Boulton-Stone, and N.H. Tomas (Kluwer Academic, Dordrecht, 1993).
6. G.C. Lichtenberg, in Novi Commentarii Societatis Regiae Scientiarum Gottingensis, edited by J. C. Dieterich (Dieterich, Göttingen, 1778). pp. 168-180.
7. W. Lauterborn, E. Schmilz, and A. Judt, Int. J. Bifurcation Chaos 3, 635 (1993).
8. S.V. Iordanskii, Prikl. Mekh. Tekhn. Fiz. 3, 102 (1960).
9. B.S. Kogarko, Dokl. Akad. Nauk SSSR 137, (1961) [Sov. Phys. Dokl. 6, 305 (1961)].
10. B.S. Kogarko, Dokl. Akad. Nauk SSSR 137, (1961) [Sov. Phys. Dokl. 6, 305 (1961)].
11. G.K. Batchelor, Fluid Dyn. Trans. Warsaw 4, 425 (1967).
12. L. van Wijngaarden, Annu. Rev. Fluid Mech. 4, 369 (1972).
13. R.I. Nigmatulin, Fundamentals of Mechanics of Heterogeneous Media (Nauka, Moscow, 1987).
14. R.I. Nigmatulin, Dynamics of Multiphase Media (Hemisphere, New York, 1991), Vols. 1 and 2.
15. V.E. Nakoryakov, B.G. Pokusaev, and LR. Shreiber, Propagation of Waves in Gas-Liquid and Lapor-Liquid Media (ITF, Novosibirsk, 1983).
16. V.K. Kedrinskii, Prikl. Mekh. Tekh. Fiz. 4, 29 (1968).
17. V.Sh. Shagapov, Prikl. Mekh. Tekhn. Fiz. 18, 90 (1977) [J. Appl. Mech. Tech. Phys. 18, 77 (1977)]
18. V.Sh. Shagapov, Prikl. Mekh. Tekhn. Fiz. 18, 90 (1977) [J. Appl. Mech. Tech. Phys. 18, 77 (1977)]
19. R.F. Ganiev and L.E. Ukrainskii, Prikl. Mekh. (USSR) 11, 3 (1975) [Sov. Appl. Mech. 11, 3 (1975)].
20. R.F. Ganiev and L.E. Ukrainskii, Prikl. Mekh. (USSR) 11, 3 (1975) [Sov. Appl. Mech. 11, 3 (1975)].
21. R.F. Ganiev and V.F. Lapchinskii, Problems of Mechanics in Cosmic Technology (Mashinostroenie, Moscow, 1978).
22. S.L. Gavrilyuk, Prikl. Mekh. Tekh. Fiz. 30, 86 (1989) [J. Appl. Mech. Tech. Phys. 30, 247 (1989)].
23. S.L. Gavrilyuk, Prikl. Mekh. Tekh. Fiz. 30, 86 (1989) [J. Appl. Mech. Tech. Phys. 30, 247 (1989)].
24. N.A. Gumerov, J. Appl. Math. Mech. 56, 50 (1992).
25. L. van Wijngaarden, J. Fluid Mech. 33, 465 (1968).
26. G. Iemetti and M.S. Sagoo, Acustica 41, 32 (1978).
27. P. Ciuti, G. Iemetti, and M.S. Sagoo, Ultrasonics, 18, 111 (1980).
28. I. Akhatov, V. Baikov, and R. Baikov, Izv. Akad, Nauk SSSR, Mekh. Zhidk. Gaza 1, 180 (1986).
29. I. Akhatov and V. Baikov, Inzh. Fiz. Zh. 50, 385 (1986).
30. N.A. Gumerov, in Proceedings of the International Union of Theoretical and Applied Mechanics Symposium on waves in Liquid/Gas and Liquid/Vapor Two-Phase Systems, edited by S. Morioka and L. van Wijngarden (Kluwer Academic, Dordrecht, 1995), pp. 77-86.
31. P. Smereka and S. Banerjee, Phys. Fluids 31, 3519 (1988).
32. L. D'Agostino and C.E. Brennen, J. Fluid Mech. 199, 155 (1989).
33. Y.A. Kobelev and L.A. Ostrovsky, J. Acoust. Soc. Am. 85, 621 (1989).
34. I. Akhatov, U. Parlitz, and W. Lauterborn, J. Acoust. Soc. Am. 96, 3627 (1994). The parameter γ used in that paper corresponds to negative values of γ introduced in the present paper. Physically this means that the case of bubbles larger than the resonance radius was investigated in Ref. [30].
35. U. Parlitz, C. Scheffczyk, I. Alchatov, and W. Lauterborn, Chaos Solitons Fractals 5, 1881 (1995).
36. I. Akhatov, U. Parlitz, and W. Lauterborn, in Self-organization in Cavitation Bubble Fields, Proceedings of the Second International Conference on Multiphase Flow, Kyoto, 1995, edited by A. Serizawa, T. Fukano, and J. Bataille (Japan Society of Multiphase Flow, Kyoto, 1995).
37. V.F.J. Bjerknes, Fields of Force (Columbia University Press, New York, 1906).
38. F.G. Blake, J. Acoust. Soc. Am. 21, 551 (1949).
39. A.J. Walton and G. T. Reynolds, Adv. Phys. 33, 595 (1984).
40. P.S. Epstein and M. S. Plesset, J. Chem. Phys. 18, 1505 (1950).
41. F.G. Blake, Harvard University, Acoustics Research Laboratory Report No. 12, 1949 (unpublished).
42. A. Goldberg, H.M. Schey, and J.L. Schwartz, Am. J. Phys. 35, 177 (1967).
43. W.F. Ames, Numerical Methods for Partial Differential Equations (Academic, New York, 1977).