Institut des NanoSciences de Paris-UMR CNRS 7588, Université Pierre et Marie Curie-Paris 6, 4 place Jussieu, 75252 Paris Cedex 05, France.
J Acoust Soc Am. 2011 Mar;129(3):1209-20. doi: 10.1121/1.3533723.
Experiments are carried out to assess, for the first time, the validity of a generalized Burgers' equation, introduced first by Davidson [J. Acoust. Soc. Am. 54, 1331-1342 (1973)] to compute the nonlinear propagation of finite amplitude acoustical waves in suspensions of "rigid" particles. Silica nanoparticles of two sizes (33 and 69 nm) have been synthesized in a water-ethanol mixture and precisely characterized via electron microscopy. An acoustical beam of high amplitude is generated at 1 MHz inside a water tank, leading to the formation of acoustical shock waves through nonlinear steepening. The signal is then measured after propagation in a cylinder containing either a reference solution or suspensions of nanoparticles. In this way, a "nonlinear attenuation" is obtained and compared to the numerical solution of a generalized Burgers' equation adapted to the case of hydrosols. An excellent agreement (corresponding to an error on the particles size estimation of 3 nm) is achieved in the frequency range from 1 to 40 MHz. Both visco-inertial and thermal scattering are significant in the present case, whereas thermal effects can generally be neglected for most hydrosols. This is due to the value of the specific heat ratio of water-ethanol mixture which significantly differs from unity.
首次进行了实验，以评估广义 Burgers 方程的有效性，该方程最初由 Davidson [J. Acoust. Soc. Am. 54, 1331-1342 (1973)] 引入，用于计算“刚性”颗粒悬浮液中有限振幅声波的非线性传播。已经在水-乙醇混合物中合成了两种尺寸（33nm 和 69nm）的二氧化硅纳米颗粒，并通过电子显微镜进行了精确表征。在水箱内以 1MHz 的高幅度生成声束，通过非线性陡化导致声冲击波的形成。然后在包含参考溶液或纳米颗粒悬浮液的圆柱体内传播后测量信号。这样，可以获得“非线性衰减”，并将其与适用于水溶胶情况的广义 Burgers 方程的数值解进行比较。在 1MHz 至 40MHz 的频率范围内，获得了极好的一致性（对应于对颗粒尺寸估计的误差为 3nm）。在当前情况下，粘滞惯性和热散射都很重要，而对于大多数水溶胶，通常可以忽略热效应。这是由于水-乙醇混合物的比热容值显著不同于 1 所致。
