School of Chemical Engineering, The University of New South Wales, Sydney, NSW 2052, Australia.
Ultrason Sonochem. 2018 Oct;47:75-98. doi: 10.1016/j.ultsonch.2018.04.014. Epub 2018 Apr 30.
This paper strictly demonstrated a nonlinear Helmholtz equation, with its corresponding new expressions for the wave number of the mixture, for the propagation of sound trough a bubbly liquid. The demonstration was conducted under the assumption of periodicity of volume fluctuations, the acoustic approximation and considering only mono-harmonic pressure oscillations. The model revealed a beautiful symmetry between the average acoustic energy density and the average energy dissipation, as well as between the time average of the first and second derivatives of such fluctuations. The nonlinear model was validated with available experimental data at very low pressure amplitudes yielding the same results as the linear model. However, unlike the linear model, the advantage of the nonlinear model is that the wave number of the mixture is function of the pressure amplitude, which has great implications to model the sound propagation on cavitating bubbly liquids where the linear theory greatly under-predicts.
本文严格证明了非线性亥姆霍兹方程及其相应的混合物波数新表达式，用于研究通过有泡液体的声波传播。该证明是在体积波动的周期性、声学近似和仅考虑单谐波压力振荡的假设下进行的。该模型揭示了平均声能密度与平均能量耗散之间、以及此类波动的一阶和二阶导数的时间平均值之间的美丽对称性。非线性模型通过在非常低的压力振幅下获得的可用实验数据进行了验证，结果与线性模型相同。然而，与线性模型不同的是，混合物的波数是压力振幅的函数，这对于模型化空化有泡液体中的声波传播具有重要意义，因为线性理论对此的预测大大不足。
