论文标题
使用谐振微泡的声气水。时间域中的分析
Acoustic Cavitation using Resonating Micro-Bubbles. Analysis in the Time-Domain
论文作者
论文摘要
我们研究了在微泡的存在下时间域的声波传播。这种微泡的特征是质量密度和散装模量，与背景真空相比，它们都非常小。目的是估计产生的压力量非常接近气泡（与气泡半径成正比）。我们表明，在那个较小的距离处，主导场让人联想到由dirac样异质性正式建模的点状障碍物所产生的波浪，并在气泡位置支撑，以及气泡和背景材料作为散射系数之间的对比度。总而言之，我们可以调整气泡材料特性，使其附近的压力达到所需的量。这种设计可能是在声气膜的目的中很有用的，因为人们需要足够但不大的压力来消除不良异常。使用时间域积分方程和渐近分析技术进行数学分析。这里众所周知的特征是，气泡和背景之间的对比度在时间谐波方面产生共振（主要是Minnaert One）。这种临界尺度和产生的共振也反映在声波的时间域估计中。特别是，只有在这种共鸣气泡的情况下，才有可能达到气泡位置附近所需的压力。
We study the time-domain acoustic wave propagation in the presence of a micro-bubble. This micro-bubble is characterized by a mass density and bulk modulus which are both very small as compared to the ones of the background vacuum. The goal is to estimate the amount of pressure that is created very near (at a distance proportional to the radius of the bubble) to the bubble. We show that, at that small distance, the dominating field is reminiscent to the wave created by a point-like obstacle modeled formally by a Dirac-like heterogeneity with support at the location of the bubble and the contrast between the bubble and background material as the scattering coefficient. As a conclusion, we can tune the bubbles material properties so that the pressure near it reaches a desired amount. Such design might be useful in the purpose of acoustic cavitation where one needs enough, but not too much, pressure to eliminate unwanted anomalies. The mathematical analysis is done using time-domain integral equations and asymptotic analysis techniques. A well known feature here is that the contrasting scales between the bubble and the background generate resonances (mainly the Minnaert one) in the time-harmonic regime. Such critical scales, and the generated resonances, are also reflected in the time-domain estimation of the acoustic wave. In particular, reaching the desired amount of pressure near the location of the bubble is possible only with such resonating bubbles.
