Minnaert共振频率附近泡状流体中声波的有效介质理论
Effective medium theory for acoustic waves in bubbly fluids near Minnaert resonant frequency
摘要：
本文推导了声波在Minnaert共振频率附近泡状流体中传播的有效介质理论。我们开始与入射波的散射问题的多次散射制定了大量相同的小气泡在均匀的流体。在一定条件下，证明了点相互作用近似的合理性，并建立了当气泡数趋于无穷大时的有效介质理论.并导出了该算法的收敛速度。因此，我们表明，在Minnaert共振频率附近和以下，所获得的有效介质可以具有高折射率，这是在“Subwavelength focusing in bubbly media using broadband time reversal”，Physical Review，B（2015），由M.此外，我们的结果表明，所获得的有效介质可以在Minnaert共振频率以上是耗散的，而在该频率下，有效介质理论不成立。我们的理论揭示了超材料，其中包括气泡流体作为一个例子，在共振频率附近的非凡的波动特性的机制。
英文摘要：
We derive an effective medium theory for acoustic wave propagation in bubbly fluid near Minnaert resonant frequency. We start with a multiple scattering formulation of the scattering problem of an incident wave by a large number of identical small bubbles in a homogeneous fluid. Under certain conditions on the configuration of the bubbles, we justify the point interaction approximation and establish an effective medium theory for the bubbly fluid as the number of bubbles tends to infinity. The convergence rate is also derived. As a consequence, we show that near and below the Minnaert resonant frequency, the obtained effective media can have a high refractive index, which is the reason for the super-focusing experiment observed in "Subwavelength focusing in bubbly media using broadband time reversal", Physical Review, B (2015), by M. Lanoy et al. Moreover, our results indicate that the obtained effective medium can be dissipative above the Minnaert resonant frequency, while at that frequency, effective medium theory does not hold. Our theory sheds light on the mechanism of the extraordinary wave properties of metamaterials, which include bubbly fluid as an example, near resonant frequencies.
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