The effect of acoustic radiation in an ideal fluid on the viscosity of a drop
DOI:
https://doi.org/10.17721/1812-5409.2026/1.16Keywords:
acoustic radiation force, spherical liquid drop, ideal compressible fluid, viscous fluid, plane harmonic wave, sound fieldAbstract
The effect of acoustic radiation force on a spherical drop of viscous liquid, located in turn in an ideal liquid in a plane sound wave field, is investigated. Acoustic radiation force is a measure of the interaction between an incident acoustic wave and a drop of viscous liquid, defined as the time-averaged integral value of the sound pressure over the surface of the viscous drop. A procedure for solving the problem has been developed, which is implemented in two steps. At the first step, an approach was developed to determine the pressure, which involves the use of the velocity field potential obtained as a solution to the linear problem of incident wave scattering at an obstacle. When formulating the boundary conditions, the surface tension pressure of the drop was not taken into account, and its radius was considered constant, i.e., the case of small pulsation oscillations was considered. Satisfying the boundary conditions on the surface of a viscous drop and Sommerfeld's conditions at infinity, together with the use of the orthogonality property of Legendre polynomials, made it possible to obtain an infinite system of algebraic equations with respect to unknown coefficients in the Fourier series expansions of potentials. At the second step of solving the problem, the pressure and hydrodynamic force caused by the acoustic field were calculated using the found potentials. The subsequent averaging of the hydrodynamic force over time allowed us to calculate the acoustic radiation force directly. Numerical calculations were performed for the case where the external fluid is water and the drop is formed from a viscous fluid insoluble in water - glycerin. A series of calculations was performed for a set of values of the radius of the viscous drop. It was found that the acoustic radiation force is not a monotonic function of the incident wave frequency. In the case of a solid spherical particle, the direction of the radiation force, as is known, coincides with the direction of propagation of the acoustic wave. In the case of a viscous spherical drop, the direction of the radiation force can be either coincident with the direction of wave propagation or opposite to it. It has been found that there are frequencies of the incident wave that provide zero radiation force acting on the drop, which in this case is stationary.
Pages of the article in the issue: 126 - 129
Language of the article: Ukrainian
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Copyright (c) 2026 Oleksandr Zhuk, Yaroslav Zhuk, Maria Kashtalyan
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