Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom.
J Acoust Soc Am. 2009 Dec;126(6):2963-72. doi: 10.1121/1.3243292.
A theoretical model for the dynamics of a bubble in an elastic blood vessel is applied to study numerically the effect of confinement on the free oscillations of a bubble. The vessel wall deformations are described using a lumped-parameter membrane-type model, which is coupled to the Navier-Stokes equations for the fluid motion inside the vessel. It is shown that the bubble oscillations in a finite-length vessel are characterized by a spectrum of frequencies, with distinguishable high-frequency and low-frequency modes. The frequency of the high-frequency mode increases with the vessel elastic modulus and, for a thin-wall vessel, can be higher than the natural frequency of bubble oscillations in an unconfined liquid. In the limiting case of an infinitely stiff vessel wall, the frequency of the low-frequency mode approaches the well-known solution for a bubble confined in a rigid vessel. In order to interpret the results, a simple two-degree-of-freedom model is applied. The results suggest that in order to maximize deposition of acoustic energy, a bubble confined in a long elastic vessel has to be excited at frequencies higher than the natural frequency of the equivalent unconfined bubble.
将一个用于研究弹性血管中气泡动力学的理论模型应用于数值研究限制对气泡自由振动的影响。使用集中参数膜式模型来描述血管壁的变形，该模型与血管内流体运动的纳维-斯托克斯方程耦合。结果表明，有限长容器中的气泡振动具有一系列频率，具有可区分的高频和低频模式。高频模式的频率随着血管弹性模量的增加而增加，对于薄壁容器，其频率可以高于无约束液体中气泡振动的固有频率。在无限刚性血管壁的极限情况下，低频模式的频率接近已知的刚性容器中气泡的限制解。为了解释结果，应用了一个简单的两自由度模型。结果表明，为了使声能的沉积最大化，限制在长弹性容器中的气泡必须在高于等效无约束气泡的固有频率的频率下被激发。
