This study presents the fundamental equations governing the pressure dependent disipation mechanisms in the oscillations of coated bubbles. A simple generalized model (GM) for coated bubbles accounting for the effect of compressibility of the liquid is presented. The GM was then coupled with nonlinear ODEs that account for the thermal effects. Starting with mass and momentum conservation equations for a bubbly liquid and using the GM, nonlinear pressure dependent terms were derived for power dissipation due to thermal damping (Td), radiation damping (Rd) and dissipation due to the viscosity of liquid (Ld) and coating (Cd). The pressure dependence of the dissipation mechanisms of the coated bubble have been analyzed. The dissipated energies were solved for uncoated and coated 2-20 μm in bubbles over a frequency range of 0.25fr-2.5fr (fr is the bubble resonance) and for various acoustic pressures (1 kPa-300 kPa). Thermal effects were examined for air and C3F8 gas cores. In the case of air bubbles, as pressure increases, the linear thermal model looses accuracy and accurate modeling requires inclusion of the full thermal model. However, for coated C3F8 bubbles of diameter 1-8 μm, which are typically used in medical ultrasound, thermal effects maybe neglected even at higher pressures. For uncoated bubbles, when pressure increases, the contributions of Rd grow faster and become the dominant damping mechanism for pressure dependent resonance frequencies (e.g. fundamental and super harmonic resonances). For coated bubbles, Cd is the strongest damping mechanism. As pressure increases, Rd contributes more to damping compared to Ld and Td. For coated bubbles, the often neglected compressibility of the liquid has a strong effect on the oscillations and should be incorporated in models. We show that the scattering to damping ratio (STDR), a measure of the effectiveness of the bubble as contrast agent, is pressure dependent and can be maximized for specific frequency ranges and pressures.

中文翻译：

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涂层和未涂层​​气泡振荡中的非线性功率损失：在各种激发压力下，热，辐射和封装壳的阻尼作用。

这项研究提出了基本的方程式，这些方程式控制着涂层气泡振荡中与压力有关的耗散机制。提出了一种简单的广义模型（GM），用于考虑气泡可压缩性的涂层气泡。然后，将GM与考虑热效应的非线性ODE耦合。从起泡液体的质量和动量守恒方程开始，并使用GM，推导了非线性压力相关项，这些项是由于热阻尼（Td），辐射阻尼（Rd）和由于液体粘度（Ld）引起的耗散而产生的功率耗散。涂层（Cd）。分析了涂层气泡的耗散机理的压力依赖性。解决了在0.25fr-2的频率范围内气泡中未涂覆和涂覆的2-20μm的耗散能量。5fr（fr为气泡共振），并适用于各种声压（1 kPa-300 kPa）。检查了空气和C3F8气芯的热效应。在气泡的情况下，随着压力增加，线性热模型失去了准确性，而准确的模型则需要包含完整的热模型。但是，对于通常用于医学超声的直径为1-8μm的涂层C3F8气泡，即使在较高压力下也可能忽略热效应。对于未涂层的气泡，当压力增加时，Rd的贡献增长更快，并成为依赖于压力的共振频率（例如基波和超谐波共振）的主要阻尼机制。对于涂层气泡，Cd是最强的阻尼机制。随着压力增加，与Ld和Td相比，Rd对阻尼的贡献更大。对于涂层气泡，通常忽略不计的液体可压缩性会对振荡产生强烈影响，应将其纳入模型中。我们表明，散射与阻尼比（STDR）是衡量气泡作为造影剂有效性的一种方法，与压力有关，可以针对特定的频率范围和压力最大化。