Singular perturbation theory applied to the collective oscillation of gas bubbles in a liquid
Singular perturbation theory applied to the collective oscillation of gas bubbles in a liquid
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奇异摄动理论应用于液体中气泡的集体振荡
DOI：
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发表时间：
1981
影响因子：
3.7
通讯作者：
J. Scott
中科院分区：
文献类型：
--
作者：
J. Scott
通过使用多重标度技术，发展了液体中气泡振荡的理论。考虑在表面张力、浮力和固体表面作用下任意形状的气泡的集合。在气泡中不存在热传导和液体可压缩性的情况下，为每种振荡模式定义了守恒“作用”。通过进行二阶分析，找到了控制作用随时间衰减的方程。发生振荡的气泡的几何结构在对流作用下通过潜在的“基本”流动随时间演变，控制方程是针对该流动导出的。气泡脉动影响基本运动的发展。后来在工作中引入了气泡源并讨论了它对振荡的影响。还简要考虑了脉动气泡与液体表面相互作用的结果。描述了由气泡分裂和由气源产生气泡引起的振荡幅度的确定。最后，给出了该理论在具体问题上的一些应用。
By using the technique of multiple scaling a theory of gas-bubble oscillations in a liquid is developed. Collections of bubbles of arbitrary shape under the action of surface tension, buoyancy and solid surfaces are considered. In the absence of thermal conduction in the bubbles and compressibility of the liquid a conserved ‘action’ is defined for each of the modes of oscillation. The equation governing the decay of the action with time is found by carrying the analysis to second order. The geometrical configuration of the bubbles, in which the oscillations take place, evolves in time under convection by an underlying ‘basic’ flow for which the governing equations are derived. The bubble pulsations influence the development of the basic motion. Later in the work a source of gas bubbles is brought in and its effects on the oscillations discussed. The results of the interaction of pulsating bubbles with the liquid surface are also briefly considered. The determination of the amplitude of oscillations induced by the splitting up of bubbles and by the generation of bubbles from the gas source is described. Finally, several applications of the theory to specific problems are given.