Leighton T G
Institute of Sound and Vibration Research, University of Southampton, Highfield, Southampton SO17 1BJ, UK.
Ultrasonics. 2008 Apr;48(2):85-90. doi: 10.1016/j.ultras.2007.10.004. Epub 2007 Nov 4.
The most common nonlinear equation of motion for the damped pulsation of a spherical gas bubble in an infinite body of liquid is the Rayleigh-Plesset equation, expressed in terms of the dependency of the bubble radius on the conditions pertaining in the gas and liquid (the so-called 'radius frame'). However over the past few decades several important analyses have been based on a heuristically derived small-amplitude expansion of the Rayleigh-Plesset equation which considers the bubble volume, instead of the radius, as the parameter of interest, and for which the dissipation term is not derived from first principles. So common is the use of this equation in some fields that the inherent differences between it and the 'radius frame' Rayleigh-Plesset equation are not emphasised, and it is important in comparing the results of the two equations to understand that they differ both in terms of damping, and in the extent to which they neglect higher order terms. This paper highlights these differences. Furthermore, it derives a 'volume frame' version of the Rayleigh-Plesset equation which contains exactly the same basic physics for dissipation, and retains terms to the same high order, as does the 'radius frame' Rayleigh-Plesset equation. Use of this equation will allow like-with-like comparisons between predictions in the two frames.
对于无限大液体介质中球形气泡的阻尼脉动，最常见的非线性运动方程是瑞利 - 普莱斯方程，它以气泡半径与气液相关条件的依赖关系来表示（所谓的“半径框架”）。然而，在过去几十年中，一些重要的分析是基于对瑞利 - 普莱斯方程进行启发式推导的小振幅展开式，该展开式将气泡体积而非半径视为感兴趣的参数，并且其耗散项并非从第一原理推导得出。在某些领域，这个方程的使用非常普遍，以至于它与“半径框架”瑞利 - 普莱斯方程之间的固有差异未得到强调。在比较这两个方程的结果时，重要的是要明白它们在阻尼方面以及忽略高阶项的程度上都存在差异。本文突出了这些差异。此外，本文推导了一个“体积框架”版本的瑞利 - 普莱斯方程，它对于耗散包含与“半径框架”瑞利 - 普莱斯方程完全相同的基本物理原理，并且保留了相同高阶的项。使用这个方程将使得在两个框架中的预测能够进行同类比较。
