Abstract
The dynamics of a spherical gas bubble induced by a changing pressure field in the radial direction is governed by the Rayleigh-Plesset equation. In this chapter, the model is described and sufficient conditions for the existence and uniqueness of periodic oscillations are given.
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Notes
- 1.
We have to use the formal computation \(\frac{d\dot{R}^2}{d R}=\frac{1}{\dot{R}}\frac{d\dot{R}^2}{d t}=2\ddot{R}\).
- 2.
As a physical constant, the polytropic coefficient can be any real number, but of course it will depend on the specific case under consideration.
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Torres, P.J. (2015). Radial Oscillations of a Bubble in a Time-Periodic Pressure Field. In: Mathematical Models with Singularities. Atlantis Briefs in Differential Equations, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-106-2_9
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DOI: https://doi.org/10.2991/978-94-6239-106-2_9
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