Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics

Andrew Pickering¹  Pilar Ruiz Gordoa¹ 

[1] Área de Matemática Aplicada, ESCET, Universidad Rey Juan Carlos, C/Tulipán s/n, Móstoles, 28933 Madrid, Spain;

关键词: ultrasonic waves;    bubble layer;    exact solutions;    traveling wave;   

DOI  :  10.3390/math9111309

来源: DOAJ

【 摘 要 】

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

【 授权许可】

Unknown