**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.

Propagation of weak disturbances in warm water with air bubbles

Vdovenko I.I., Vdovenko N.N.

Bashkir state university, Ufa

### Abstract

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 α_{g}_{0} for two initial bubble sizes
a_{0}=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.

**Keywords**harmonic wave,

bubbles,

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 α_{g}_{0}=10^{–4}
to α_{g}_{0}=10^{–1} at an equilibrium temperature T_{0}=373 К,
near the low frequencies (ω≤ω_{R}, where ω_{R} 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 a_{0}, there is a small increase in the phase
velocity in the low-frequency region (ω≪ω_{R}), and the damping coefficient can vary by
several orders of magnitude. The role of phase transitions is significantly reduced.