Research On The Nonlinearity Parameter Of Bubbly Liquids

When the liquid mixed with air bubbles， due to the differences of the acoustic impedanceand sound compression characteristics between air and liquid，acoustics properties of themixed medium changed significantly. Especially, sound velocity and absorption coefficientare quite different from pure liquids near the resonant frequency. In addition, when soundwaves propagating in bubbly liquid, the forced vibration of bubbles can cause strongscattering, and reflect strong nonlinearity, thus the nonlinearity parameter B/A vary greatlyfrom pure liquids.In the medium, ratio of the second-order coefficient and the linear coefficient of theTaylor series of state equation is named as nonlinear parameter B/A. It is used to measure thenonlinear effect of medium. Nonlinearity parameter determines the second-order harmonicamplitude, and reflects the dynamic characteristic of medium. Similarly, the third-ordernonlinearity parameter C/A is the ratio of the third-order coefficient and the linear coefficientof the Taylor series of state equation. It also reflects some nonlinear characteristics of medium.When sound waves propagating in water, due to the exists of bubbles, energy of fundamentalwave will transfer to harmonic waves within a short distance. So the mixed medium reflectsstrong nonlinearity. The resulting of the second-order and third-order harmonic is veryapparent, and can not be ignored.This article established a water electrolysis system. Bubbles with uniform distributionand stable size were obtained by the electrolysis of water in a glass tank. Secondly, opticalmeasurement and acoustic inverse method on the size of bubbles were studied. In the opticalmeasurement method, the contrast results show that, mathematical morphology edge detectionmethod is the most effective in this experiment. The air bubbles can be thought to follow aPoisson distribution. In response to the defects of the previous acoustic method for measuringbubble distribution, a new acoustic inverse method is researched. By measuring bubblesscattering intensity with different acoustic frequencies, diameter and density of bubbles can beinversed.Using the obtained distribution parameters of the electrolytic bubbles, acousticcharacteristics of the bubble curtain are studied. Because of the strong scattering and thebubbles interactions, the sound velocity and acoustic absorption coefficient will change withthe incident wave frequencies in bubbly water. Especially near the resonant frequency,acoustic wave phase velocity reaches a minimum value, and the sound absorption coefficient reaches a maximum value. Studying on the acoustic property of bubble curtain has importantsignificance for the practical application of liquid containing bubbles. It also is a importantfoundation to carry out the next step experiment and research.Then the third-order Rayleigh-Plesset equation of volume form is introduced. Combiningwith the nonlinear wave equation in bubbly water, the breeding mechanism of the high orderharmonics are researched by using the perturbation method. A sound propagation of thesecond-order and the third-order nonlinear physical models is established. Formulas aboutcalculating nonlinear parameter B/A and C/A of bubbly water are given. Researches show thatwave propagation in bubbly water is a very complex process. Especially the third-orderharmonic is caused not only by the fundamental wave, but also by the combined effect offundamental wave and second-order harmonic. Thus bubbly water can be seen as a kind ofliquid medium with special nonlinearity parameter. In addition, the equivalent third-ordernonlinearity parameter is not a constant. It is based on experimental distance and soundfrequency. In particular, C/A varies with the distance increasing, and reached a maximumvalue in resonance frequency. At the same time it is also associated with the bubbledistribution parameters.Finally measurements about the nonlinearity parameter B/A and the third-ordernonlinearity parameter C/A of bubbly water are introduced. Nonlinearity parameterexperiment of pure water and bubbly water were designed. Then the experimental data wereprocessed and analyzed. Firstly, experimental nonlinearity parameter B/A were comparedwith previous theories, so the validation and feasibility of the system can be confirmed. Byestablishing a nonlinear bubbly experimental environment, finite amplitude insert substitutionmethod was applied for researching nonlinearity parameter B/A. According to the experimentresults, various factors were analyzed for the impact of nonlinearity parameter. By measuringthe third-order harmonic and fundamental amplitude, the third-order nonlinearity parameterC/A of the medium was gained.