This is an open access article distributed under the CC BY 4.0
Volume 18 article 745 pages: 681 - 686
The paper investigates the process of pulsation of a spherical cavity (bubble) in a liquid under the influence of a
source of ultrasonic vibrations. The pulsation of a spherical cavity is described by the Kirkwood-Bethe equations,
which are one of the most accurate mathematical models of pulsation processes at an arbitrary velocity of the cavity
boundary. The Kirkwood-Bethe equations are essentially non-linear, therefore, to construct solutions and parametric
analysis of the bubble collapse process under the influence of ultrasound, a numerical algorithm based on the Runge-
Kutta method in the Felberg modification of the 4-5th order with an adaptive selection of the integration step in
time has been developed and implemented. The proposed algorithm makes it possible to fully describe the process
of cavitation pulsations, to carry out comprehensive parametric studies, and to evaluate the influence of various process
parameters on the intensity of cavitation. As an example, the results of calculating the process of pulsation of
the cavitation pocket in water are given and the influence of the amplitude of ultrasonic vibrations and the initial radius
on the process of cavitation of a single bubble is estimated.
This study was supported by the Russian Foundation for
Basic Research (project 19-08-01023 A) also Grants of
the President of the Russian Federation (projects MK-
3869.2019.8 and MD-1798.2019.8).
1. Pirsol, I. (1975). Cavitation. Mir, Moscow.
2. Rozhdestvensky, V.V. (1977). Cavitation. Shipbuilding, Leningrad.
3. Rosenberg, L.D. (1968). Cavitation area. Physics and technique of powerful ultrasound. Nauka, Moscow.
4. Rabinskiy, L.N., Tushavina, O.V. (2019). Investigation of an elastic curvilinear cylindrical shell in the shape of a parabolic cylinder, taking into account thermal effects during laser sintering. Asia Life Sciences, vol. 2, 977-991.
5. Kuznetsova, E.L., Rabinskiy, L.N. (2019). Linearization of radiant heat fluxes in the mathematical modeling of growing bodies by the action of high temperatures in additive manufacturing. Asia Life Sciences, vol. 2, 943-954.
6. Rabinskiy, L.N., Tushavina, O.V., Formalev, V.F. (2019). Mathematical modeling of heat and mass transfer in shock layer on dimmed bodies at aerodynamic heating of aircraft. Asia Life Sciences, vol. 2, 897-911.
7. Rabinskii, L.N., Tushavina, O.V. (2019). Composite heat shields in intense energy fluxes with diffusion. Russian Engineering Research, vol. 39, no. 9, 800- 803.
8. Bulychev, N.A., Kuznetsova, E.L., Rabinskiy, L.N., Tushavina, O.V. (2019). Theoretical investigation of temperature-gradient induced glass cutting. Nanoscience and Technology, vol. 10, no. 2, 123-131.
9. Bulychev, N.A., Bodryshev, V.V., Rabinskiy, L.N. (2019). Analysis of geometric characteristics of twophase polymer-solvent systems during the separation of solutions according to the intensity of the image of micrographs. Periodico Tche Quimica, vol. 16, no. 32, 551-559.
10. Dobryanskiy, V.N., Rabinskiy, L.N. Tushavina, O.V. (2019). Validation of methodology for modeling effects of loss of stability in thin-walled parts manufactured using SLM technology. Periodico Tche Quimica, vol. 16, no. 33, 650-656.
11. Rabinskiy, L.N., Tushavina, O.V. (2019). Problems of land reclamation and heat protection of biological objects against contamination by the aviation and rocket launch site. Journal of Environmental Management and Tourism, vol. 10, no. 5, 967-973.
12. Dinzhos, R., Lysenkov, E., Fialko, N. (2015). Simulation of thermal conductivuty of polymer composites based on poly (methyl methacrylate) with different types of fillers. Eastern-European Journal of Enterprise Technologies, vol. 6, no. 11, 21-24.
13. Dyusembaev, A.E., Grishko, M.V. (2018). On correctness conditions for algebra of recognition algorithms with μ-operators over pattern problems with binary data. Doklady Mathematics, vol. 98, no. 2, 421-424.
14. Ryndin, V.V. (2020). Application of the postulate of nonequilibrium to calculate the nonequilibrium of systems of dissimilar gases and liquids. Periodico Tche Quimica, vol. 17, no. 34, 998-1011.
15. Dobryanskiy, V.N., Rabinskiy, L.N., Tushavina, O.V. (2019). Experimental finding of fracture toughness characteristics and theoretical modeling of crack propagation processes in carbon fiber samples under conditions of additive production. Periodico Tche Quimica, vol. 16, no. 33, 325-336.
16. Antufev, B.A., Egorova, O.V., Medvedskii, A.L., Rabinskiy, L.N. (2019). Dynamics of shell with destructive heat-protective coating under running load. INCAS Bulletin, vol. 11, 7-16.
17. Antufev, B.A., Egorova, O.V., Rabinskiy, L.N. (2019). Dynamics of a cylindrical shell with a collapsing elastic base under the action of a pressure wave. INCAS Bulletin, vol. 11, 17-24.
18. Ksenz, N.V., Yudaev, I.V., Taranov, M.A., Sidorcov, I.G., Semenikhin, A.M., Chernovolov, V.A. (2019). Determination of the efficiency of the operation mode of nonflowing installation for electroactivation of water and aqueous solutions. International Journal of Automation Technology, vol. 13, no. 4, 539-544.
19. Mykhalevskiy, D.M., Kychak, V.M. (2019). Development of information models for increasing the evaluation efficiency of wireless channel parameters of 802.11 standard. Latvian Journal of Physics and Technical Sciences, vol. 56, no. 5, 22-32.
20. Sultanov, K., Khusanov, B., Rikhsieva, B. (2020). Underground pipeline reliability under longitudinal impact load. IOP Conference Series: Materials Science and Engineering, vol. 869, no. 052008.
21. Orlov, A.M., Skvortsov, A.A., Litvinenko, O.V. (2003). Bending vibrations of semiconductor wafers with local heat sources. Technical Physics, vol. 48, no. 6, 736-741.
22. Dinzhos, R.V., Lysenkov, E.A., Fialko, N.M. (2015). Influence of fabrication method and type of the filler on the thermal properties of nanocomposites based on polypropylene. Voprosy Khimii i Khimicheskoi Tekhnologii, vol. 5, no. 103, 56-62.
23. Ryndin, V.V. (2019). Calculation of the nonequilibrium systems consisting of an aggregate of locally- equilibrium subsystems. Periodico Tche Quimica, vol. 16, no. 33, 289-303.
24. Bulychev, N.A., Rabinskiy, L.N. (2019). Ceramic nanostructures obtained by acoustoplasma technique. Nanoscience and Technology: An International Journal, vol. 10, no. 3, 279-286.
25. Pogodin, V.A., Astapov, A.N., Rabinskiy, L.N. (2020). CCCM specific surface estimation in process of low-temperature oxidation. Periodico Tche Quimica, vol. 17, no. 34, 793-802.
26. Skvortsov, A.A., Orlov, A.M., Zuev, S.M. (2012). Diagnostics of degradation processes in the metal- semiconductor system. Russian Microelectronics, vol. 41, no. 1, 31-40.
27. Egorova, O.V., Rabinskiy, L.N., Zhavoronok, S.I. (2020). Use of the higher-order plate theory of I.N. Vekua type in problems of dynamics of heterogeneous plane waveguides. Archives of Mechanics, vol. 72, no. 1, 3-25.
28. Babaytsev, A.V., Kuznetsova, E.L., Rabinskiy, L.N., Tushavina, O.V. (2020). Investigation of permanent strains in nanomodified composites after molding at elevated temperatures. Periodico Tche Quimica, vol. 17, no. 34, 1055-1067.
29. Kurbatov, A.S., Orekhov, A.A., Rabinskiy, L.N., Tushavina, O.V., Kuznetsova, E.L. (2020). Research of the problem of loss of stability of cylindrical thin walled structures under intense local temperature exposure. Periodico Tche Quimica, vol. 17, no. 34, 884-891.