Mathematical and physical modelling of bubble growth due to ultrasound
Mathematical and physical modelling of bubble growth due to ultrasound
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DOI：
10.1016/j.apm.2003.10.001
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发表时间：
2004-04-01
影响因子：
5
通讯作者：
Hasan, M
中科院分区：
文献类型：
--
作者：
Meidani, ARN;Hasan, M
本文建立了一个数学模型，结合物理模型来模拟液体中单个气泡在精流扩散过程中的生长特性。数学模型建立在动量、能量和质量耦合输运方程的基础上。该模型是一组耦合的、高度非线性的、刚性的微分方程，其特征是气泡边界的快速移动。采用改进的齿轮法对模型方程进行了求解。数值研究了初始气泡半径、液体中溶解气体的初始浓度以及施加超声场的振幅和频率对整流扩散过程的影响。结果表明：当超声压力幅值大于阈值压力时，水中产生气泡；在这种情况下，气泡体积迅速达到其初始值的数倍，并能获得足够的浮力浮到水面。在超声压力场作用下，对水中气泡的生长进行了模拟实验。将气泡生长速率的实验结果与数学模型的结果进行了比较，结果表明实验结果与数学模型的预测结果基本吻合。(C) 2003年Elsevier Inc.出版
A mathematical model, combined with a physical model, has been developed to simulate the growth characteristics of a single bubble in liquid by the process of rectified diffusion. The mathematical model is based on the coupled momentum, energy and mass transport equations. The model forms a set of coupled, highly nonlinear and stiff differential equations and it is characterized by the fast moving boundary of the bubble. The model equations have been solved by the modified Gear method. The effects of initial bubble radius, initial concentration of dissolved gas in liquid and the amplitude and frequency of the imposed ultrasound field on the process of rectified diffusion are numerically studied. The results show that an air bubble in water grows when the ultrasonic pressure amplitude is more than the threshold pressure. In this case, the bubble volume rapidly reaches several times of its initial value and can gain sufficient buoyancy-force to float to the surface. Experiments have been carried out to simulate the growth of an air bubble in water under an ultrasonic pressure field. The experimental results of the bubble growth rate are compared with the results of the mathematical model which show a quite reasonable overall agreement between the experiments and the predictions. (C) 2003 Published by Elsevier Inc.