Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

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ID: 267864
2021
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Abstract
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.
Reference Key
gordoa2021mathematicsultrasonic Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Pilar Ruiz Gordoa;Andrew Pickering;Gordoa, Pilar Ruiz;Pickering, Andrew;
Journal Mathematics
Year 2021
DOI
10.3390/math9111309
URL
https://www.mdpi.com/2227-7390/9/11/1309
Keywords
ultrasonic waves traveling wave bubble layer exact solutions

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