# 声辐射力的热黏性分析

2015年 10月 1日

### 分析声辐射力的不同方法

#### 二阶扰动法

(1)

\mathbf{F}_\textrm{rad} = \oint_{\partial \Omega} [\langle \sigma_2 \rangle -\rho_0\langle\mathbf{u}_1\mathbf{u}_1^\textrm{T}\rangle]\cdot \mathbf{n} \textrm{d}a

#### 无损耗假设

(2)

\langle \sigma_2 \rangle = \langle p_2 \rangle = \frac{1}{2}\kappa_0 \langle p_1^2 \rangle -\frac{1}{2}\rho_0 \langle u_1^2 \rangle

#### 瑞利假设

(3)

\mathbf{F}
_\textrm{rad}= -2\pi a^3 \left[ \frac
{1}{3} \kappa_s \textrm{Re} [f_0^* p_\textrm{in}^* \nabla p_\textrm{in}]-\frac{1} {2}
\rho_0 \textrm{Re}[f_1^* \mathbf{u}_\textrm{in}^* \cdot \nabla \mathbf{u}_\textrm
{in}] \right]

• 对于无黏性和绝热的情况，参考文献3 中由 Gor’kov 给出的结果。
• 参考文献4 中由 Settnes 和 Bruus 给出的包括黏性的结果。
• 参考文献5 中，由 Karlsen 和 Bruus 给出的完整的热黏性理论不仅求解了一个小液滴的散射，还求解了粒子内部的热黏性效应。
• 有关这个领域的许多成果，您可以查看关于悬浮声学的相关研究 (见文献6)。

### COMSOL Multiphysics 中基于方程的建模方法

(4)

\begin{aligned}
\nabla\cdot[\rho_0 \mathbf{u}_2+\langle \rho_1 \mathbf{u}_1 \rangle] = 0 \\
\nabla\cdot [\mathbf{\sigma}_2 – \rho_0\langle\mathbf{u}_1\mathbf{u}_1^\textrm{T}\rangle \mathbf] = \mathbf{0} \\
\nabla\cdot [k \nabla T_2+\langle \mathbf{u}_1\cdot\mathbf{\sigma}_1\rangle + \alpha_0 T_0 \langle p_1 \mathbf{u}_1 \rangle – \rho_0 C_\textrm{p}\langle T_1 \mathbf{u}_1 \rangle] = 0
\end{aligned}

### 扩展阅读

1. Theory and Simulation of the Acoustic Radiation Force on a Single Microparticle in an Ultrasonic Standing Wave Including Thermoviscous Effects”, M. J. H. Jensen, J. T. Karlsen, and H. Bruus.
2. Efficient finite element modeling of radiation forces on elastic particles of arbitrary size and geometry”, P. Glynne-Jones, P. P. Mishra, R. J. Boltryk, and M. Hill.
3. “On the forces acting on a small particle in an acoustical field in an ideal fluid”, L. P. Gor’kov.
4. Forces acting on a small particle in an acoustical field in a viscous fluid”, M. Settnes and H. Bruus.
5. “Forces acting on a small particle in an acoustical field in a thermoviscous fluid”, (accepted) J. T. Karlsen and H. Bruus.
6. Suspension Acoustics: An Introduction to the Physics of Suspensions, S. Temkin.

#### 评论 (2)

2023-05-23

##### Qihang Lin
2023-06-01 COMSOL 员工