Nonlinear oscillation and acoustic scattering of bubbles

The scattered acoustic pressure and scattered cross section of bubbles is studied using the scattered theory of bubbles. The nonlinear oscillations of bubbles and the scattering acoustic fields of a spherical bubble cluster are numerically simulated based on the bubble dynamic and fluid dynamic. The influences of the interaction between bubbles on scattering acoustic field of bubbles are researched. The results of numerical simulation show that the oscillation phases of bubbles are delayed to a certain extent at different positions in the bubble cluster, but the radii of bubbles during oscillation do not differ too much at different positions. Furthermore, directivity of the acoustic scattering of bubbles is obvious. The scattered acoustic pressures of bubbles are different at the different positions inside and outside of the bubble cluster. The scattering acoustic fields of a spherical bubble cluster depend on the driving pressure amplitude, driving frequency, the equilibrium radii of bubbles, bubble number and the radius of the spherical bubble cluster. These theoretical predictions provide a further understanding of physics behind ultrasonic technique and should be useful for guiding ultrasonic application.     

On the theory of refractive radio-wave scattering

We consider in detail the frequency correlation of radio-wave fluctuations in one or several thick layers with strong large-scale inhomogeneities of turbulent origin. General expressions are obtained for the space-frequency fluctuation correlation of the radio-waves received. We analyze particular cases of radio wave scattering in turbulent media with inhomogeneities described by power-law spectra with indices p2 and p3. It is shown, in particular, that the coherence band of signals propagated in media with strong large-scale inhomogeneities is critically dependent on the spectral type of thOse inhomogeneities. The occurrence of an additional strongly scattering layer, which has radically different properties compared to the first layer, on the radio-wave path can increase or decrease considerably the frequency correlation of the radio waves received.Radiophysical Research Institute, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 10, pp. 1012–1022, October, 1995.     

Bubble acoustical scattering cross section under multi-frequency acoustic excitation

The acoustical scattering cross section is usually employed to evaluate the scattering ability of the bubbles when they are excited by the incident acoustic waves. This parameter is strongly related to many important applications of performance prediction for search sonar or underwater telemetry, acoustical oceanography, acoustic cavitation, volcanology, and medical and industrial ultrasound. In the present paper, both the analytical and numerical analysis results of the acoustical scattering cross section of a single bubble under multi-frequency excitation are obtained. The nonlinear characteristics(e.g.,harmonics, subharmonics, and ultraharmonics) of the scattering cross section curve under multi-frequency excitation are investigated compared with single-frequency excitation. The influence of several paramount parameters(e.g., bubble equilibrium radius, acoustic pressure amplitude, and acoustic frequencies) in the multi-frequency system on the predictions of scattering cross section is discussed. It is shown that the combination resonances become significant in the multi-frequency system when the acoustic power is big enough, and the acoustical scattering cross section is promoted significantly within a much broader range of bubble sizes and acoustic frequencies due to the generation of more resonances.     

The dependence of ultrasound contrast agents backscatter on acoustic pressure: theory versus experiment

Experimental investigations have not fully explored the interaction between ultrasound beams and microbubble contrast agents. Moreover theoretical investigations have not solved the problem of the microbubble oscillation. A simple in-vitro system based on a commercial scanner (ATL UM9) was used to insonate (3 MHz transmission) diluted contrast suspensions of Definity and Quantison at different acoustic pressures (0.27-1.52 MPa). The experimental data were referred to a blood mimicking fluid in order to extract an estimate of their scattering cross-section. The results were compared with the solutions of the three main bubble oscillatidn models, Rayleigh-Plesset, Herring and Gilmore. Non-linear solutions of the above models were produced numerically using the Mathematica Package Software. The experiments showed that both agents provided a linear increase in scattering cross-section with increasing acoustic pressure. The thick shelled Quantison provided an increasing number of scatterers with increasing acoustic pressure, which proved that free bubbles leaked out of the shell. At high acoustic pressures both Quantison and Definity scattering cross-sections were almost identical, and were probably that of a free bubble. The Rayleigh-Plesset model provided a scattering cross-section almost independent of acoustic pressure. On the contrary the scattering cross-sections calculated by the Herring and Gilmore models solutions displayed a definite dependence on acoustic pressure of an order higher than one, which is slightly higher than the order of dependence exhibited by the experimental data. However, the increase of the experimentally measured scattering cross-section with acoustic pressure was sharper than the calculated one by the above two models. This is most probably due to the fact that the models simulated damped and not free bubble oscillations. In conclusion the Rayleigh-Plesset model was inadequate in describing the bubble oscillations even at small diagnostic acoustic pressures. The Herring and Gilmore models could simulate the dependence of the scattering cross-section of encapsulated microbubbles on acoustic pressure. However the contribution of free bubble oscillations has still to be modelled.     

Interaction between moving bubbles and an acoustic field: Controlling flows and nonlinear acoustic vision

Results from studying the interaction between gas bubbles and the field of a flow-through acoustic resonator, and the Raman scattering of acoustic waves by moving bubbles, are presented. The structure of the distribution of bubble concentration in the resonator is studied. It is shown that nonlinear scattering by moving bubbles can be used to image bubble objects.     

Range-dependent waveguide scattering model calibrated for bottom reverberation in a continental shelf environment

An analytic model is developed for scattering from random inhomogeneities in range-dependent ocean waveguides using the Rayleigh-Born approximation to Green's theorem. The expected scattered intensity depends on statistical moments of fractional changes in compressibility and density, which scatter as monopoles and dipoles, respectively, and the coherence volume of the inhomogeneities. The model is calibrated for ocean bottom scattering using data acquired by instantaneous wide-area ocean acoustic waveguide remote sensing (OAWRS) and geophysical surveys of the ONR Geoclutter Program. The scattering strength of the seafloor on the New Jersey shelf, a typical continental shelf environment, is found to depend on wave number k, medium coherence volume V(c), and seabed depth penetration factor F(p) following a 10 log(10)(F(p)V(c)k(4)) dependence. A computationally efficient numerical approach is developed to rapidly compute bottom reverberation over wide areas using the parabolic equation by exploiting correlation between monopole and dipole scattering terms and introducing seafloor depth penetration factors. An approach is also developed for distinguishing moving clutter from statistically stationary background reverberation by tracking temporal and spatial fluctuations in OAWRS intensity images.     

Nonlinear scattering of acoustic waves by natural and artificially generated subsurface bubble layers in sea

The paper describes nonlinear effects due to a biharmonic acoustic signal scattering from air bubbles in the sea. The results of field experiments in a shallow sea are presented. Two waves radiated at frequencies 30 and 31-37 kHz generated backscattered signals at sum and difference frequencies in a bubble layer. A motorboat propeller was used to generate bubbles with different concentrations at different times, up to the return to the natural subsurface layer. Theoretical consideration is given for these effects. The experimental data are in a reasonably good agreement with theoretical predictions.     

含气泡液体中气泡振动的研究

研究了含气泡液体中单个气泡在驱动声场一定情况下的振动过程. 让每次驱动声场作用的时间特别短, 使气泡半径发生微小变化后再将其变化反馈到气泡群对驱动声场的散射作用中去, 从而可以得到某单个气泡周围受气泡散射影响后的声场, 接着再让气泡在该声场作用下做短时振动, 如此反复. 通过这样的方法, 研究了液体中单个气泡的振动情况并对其半径变化进行了数值模拟, 结果发现, 在液体中含有大量气泡的情况下, 某单个气泡的振动过程明显区别于液体中只有一个气泡的情况. 由于大量气泡和驱动声场的相互作用, 使气泡半径的变化存在多种不同的振动情况, 在不同的气泡大小和含量的情况下, 半径变化过程分别表现为: 在平衡位置附近振荡的过程; 周期性的空化过程; 一次空化过程后保持某一大小振荡的过程; 增长后维持某一大小振荡的过程等. 所以, 对于含气泡液体中气泡振动的研究, 在驱动声场一定的情况下, 必须考虑气泡含量的因素. 关键词： 含气泡液体 超声空化 散射 数值模拟     

Investigation of correlation properties of backscattering by discrete inhomogeneities

Physical modeling of acoustic signal backscattering by discrete random inhomogeneities is performed. The behavior of the transverse correlation radius of the scattered field amplitude is studied. Its experimental dependences on the transducer aperture, on the angle of sounding of an inhomogeneity-containing plane, and on the correlation properties of the scatterer position on this plane are derived. Qualitative theoretical models in the framework of the theory of single scattering are proposed which provide an explanation to the phenomena observed.State University, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 1–2, pp. 106–109, January–February, 1995.     

Scattering measurements from a dissolving bubble

A laboratory-scale study on acoustic scattering from a single bubble undergoing dissolution in undersaturated fresh water is presented. Several experiments are performed with the acoustic source driven with five-cycle tone bursts, center frequency of 120 kHz, to insonify a single bubble located on axis of the combined beam of the set of transducers. The bubble is placed on a fine nylon thread located in the far field of the transducer set, arranged in bistatic configuration, in a tank filled with undersaturated water. Backscattered waveforms from the bubble target are acquired every few seconds for several hours until the bubble has completely dissolved, and detailed dissolution curves are produced from the acoustic data. The rate of bubble dissolution is calculated using the solution developed by Epstein and Plesset [J. Chem. Phys. 18, 1505-1509 (1950)]. The results of the experiments performed are in agreement with the calculations.     

光在水中吸附膜层气泡上的散射特性

光在水中大尺度气泡上散射特性的研究多是基于Davis模型.该模型没有考虑到吸附膜层对光在气泡上散射的影响,而海水中的大多数气泡都有膜层附着,这些膜层会影响到气泡的光散射特性.本文从几何光学的角度出发,建立了吸附膜层气泡的体积散射函数简化公式.在此理论基础上,模拟计算了尺度远大于入射光波长的大气泡散射光强分布曲线,得出光照射下气泡上散射光强的远场特性,讨论了影响气泡散射光强分布的主要因素.并与无膜气泡光散射分布曲线比较,讨论了油膜膜厚、折射率等参量对气泡的光散射特性影响.得出结论:吸附膜层气泡的光强分布曲线与无膜气泡相似,但吸附膜层会削弱前向散射光,增强后向散射光.     

Fluid flow imaging by means of wide-band diffraction tomography.

The problem of reconstructing a two-dimensional distribution of fluid flow from wide-band scattering measurements is considered. Reciprocal scattering measurements are employed, meaning that scattered waves are recorded between a source and receiver, and again with the source and receiver interchanged. As shown, such measurements allow the reconstruction of a fluid flow image separate from that of a distribution of stationary acoustic velocity inhomogeneities.     

Sound scattering from small compact inhomogeneities in a sea waveguide: The inverse problem

An approach based on the redistribution of acoustic energy between waveguide modes is used to state the inverse problem of sound scattering from small compact inhomogeneities in a shallow-water waveguide. Numerical results are presented.     

Theoretical prediction of the scattering of spherical bubble clusters under ultrasonic excitation

Due to the nonlinear vibration of ultrasound contrast agent bubbles, a nonlinear scattered sound field will be generated when bubbles are driven by ultrasound. A bubble cluster consists of numerous bubbles gathering in a spherical space. It has been noted that the forward scattering of a bubble cluster is larger than its backscattering, and some studies have experimentally found the angular dependence of a bubble cluster’s scattering signal. In this paper, a theory is proposed to explain the difference of acoustic scattering at different directions of a bubble cluster when it is driven by ultrasound, and predicts the angular distribution of scattered acoustic pressure under different parameters. The theory is proved to be correct under circumstances of small clusters and weak interactions by comparing theoretical results with numerical simulations. This theory not only sheds light on the physics of bubble cluster scattering, but also may contribute to the improvement of ultrasound imaging technology, including ultrasonic harmonic imaging and contrast-enhanced ultrasonography.     

MODEL COMPARISON FOR ACOUSTIC SCATTERING BY A SPHERICAL AIR BUBBLE IN WATER

The oscillation of a bubble has many vibrational modes, contributing to different portions in acoustic scattering. Without approximations a priori, an hydrodynamic approach is applied to investigate acoustic scattering by a bubble in water, taking into account the heat exchange and viscosity. The scattering function is derived for a wide range of frequencies. Examples are shown to illustrate the thermal and viscous effects on sound scattering. Comparison is made with three existing models. While these models are known not to be applicable for high frequencies, it is shown here that even in the low-frequency region, there are also noticeable discrepancies between the exact solution and the three existing models with regard to the scattering properties such as the scattering cross-section, and the quality factor of resonant peaks. By numerical simulation, we claim that the discrepancies may be due to the incomplete consideration of the thermal exchange process in the previous models. The approach presented here is valid for any other fluid enclosure in liquids.     

Acoustic phase conjugation in a three-phase medium

Acoustic phase conjugation is studied in a sandy marine sediment that contains air bubbles in its fluid fraction. The considered phase conjugation is a four-wave nonlinear parametric sound interaction caused by nonlinear bubble oscillations which are known to be dominant in acoustic nonlinear interactions in three-phase marine sediments. Two various mechanisms of phase conjugation are studied. One of them is based on the stimulated Raman-type sound scattering on resonance bubble oscillations. The other is associated with sound interactions with bubble oscillations whose frequencies are far from resonance bubble frequencies. Nonlinear equations to solve the phase conjugation problem are derived, expressions for acoustic wave amplitudes with a conjugate wave front are obtained and compared for various frequencies of the excited bubble oscillations.     

Measurement of acoustic absorption coefficient with phase-conjugate ultrasonic waves

Experimental results on measurements of the acoustic absorption coefficient in test objects that were obtained with two methods, i.e., a standard insert-substitution method and a modification thereof using phase-conjugate waves, are given. Samples of gelatin and biological tissue in vitro (porcine muscle fibers) were used as test objects. Gelatin objects were manufactured that were both homogeneous and with inhomogeneities in the form of a rough surface or inclusions (air bubbles) distributed over the volume. A rough surface leads mainly to phase distortions of a probe beam, while bubble inclusions cause additional field scattering. For all homogeneous samples, both compared methods produce identical results. In the case of inhomogeneous samples including biological tissues, absorption measurement by a standard method may lead to significant errors. It is demonstrated that the use of properties of phase-conjugate waves provides an opportunity to eliminate almost completely the measurement error connected with phase distortions and reduce the error in the case of a medium with scatterers.     

气泡浓度对海洋激光雷达后向散射特性的影响

对不同浓度气泡幕水下激光雷达的后向散射特性进行了理论分析和实验研究。实验结果表明：由于水中气泡群后向散射的原因,在水下激光雷达整体后向散射信号的回波曲线上,除了水体后向散射导致的信号峰以外,还出现因气泡散射而导致的散射峰,该散射峰叠加在水体的后向散射信号峰上,其位置与水中气泡幕的位置直接相关,而其幅值则受气泡幕的浓度影响。随着气泡幕浓度的增大,其后向散射峰幅值相应增大,这一点与理论分析结果一致,而回波峰值的变化趋势则主要受水体质量的影响。     

Thresholds for cavitation produced in water by pulsed ultrasound

The threshold for transient cavitation produced in water by pulsed ultrasound was measured as a function of pulse duration and pulse repetition frequency at both 0.98 and 2.30 MHz. The cavitation events were detected with a passive acoustic technique which relies upon the scattering of the irradiation field by the bubble clouds associated with the events. The results indicate that the threshold is independent of pulse duration and acoustic frequency for pulses longer than approximately 10 acoustic cycles. The threshold increases for shorter pulses. The cavitation events are likely to be associated with bubble clouds rather than single bubbles.