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Труды Института механики им. Р.Р. Мавлютова
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Proceedings of the Mavlyutov Institute of Mechanics

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Vdovenko I.I., Vdovenko N.N. Propagation of weak disturbances in warm water with air bubbles. Proceedings of the Mavlyutov Institute of Mechanics. 2017. 12(1). 135–142.
2017. Vol. 12. Issue 1, Pp. 135–142
DOI: 10.21662/uim2017.1.019
Propagation of weak disturbances in warm water with air bubbles
Vdovenko I.I., Vdovenko N.N.
Bashkir state university, Ufa


The features of reflection and refraction of harmonic waves at the interface between a ”pure“ liquid and a liquid with bubbles with a vapor-gas mixture under direct and oblique incidence are studied. A numerical analysis is made of the effect of the initial volumetric gas content αg0 for two initial bubble sizes a0=10–6 m and 10–3 m. The influence of the disturbance frequencies on the reflection and refraction coefficients of sound in direct incidence and on the dependence of the angle of refraction on the angle of incidence is studied.


harmonic wave,
reflection coefficient,
refractive index,
bubble liquid

Article outline

Problem: To study the dynamics of weak perturbations in a liquid with vapor and gas bubbles.

Methods: The solution of the problem is sought in the form of a damped traveling wave. From the condition for the existence of a solution of this form, taking into account the effects of acoustic discharge of bubbles, a dispersion equation is written out.

In a study was determined:

1. When the initial volumetric gas content varies from αg0=10–4 to αg0=10–1 at an equilibrium temperature T0=373 К, near the low frequencies (ω≤ωR, where ωR is the natural frequency of the bubbles), the damping coefficient varies insignificantly (depending on the frequency of the perturbations).

2. With a decrease in the equilibrium radius of the bubbles a0, there is a small increase in the phase velocity in the low-frequency region (ω≪ωR), and the damping coefficient can vary by several orders of magnitude. The role of phase transitions is significantly reduced.