Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

Experimental investigation on the effects of the standoff distance and the initial radius on the dynamics of a single bubble near a rigid wall in an ultrasonic field

Bubble behaviors near a boundary in an ultrasonic field are the fundamental forms of acoustic cavitation and of substantial importance in various applications, such as industry cleaning, chemical engineering and food processing. The effects of two important factors that strongly affect the dynamics of a single acoustic cavitation bubble, namely, the initial bubble radius and the standoff distance, were investigated in this work. The temporal evolution of the bubble was recorded using high speed microphotography. Meanwhile, the time of bubble collapse and the characteristics of the liquid jets were analyzed. The results demonstrate that the intensity of the acoustic cavitation, which is characterized by the time of bubble collapse and the liquid jet speed, reaches the optimum level under suitable values of the initial bubble radius and the normalized standoff distance. As the initial bubble radius and the normalized standoff distance increase or decrease from the optimal values, the time of the bubble collapse increases, and the first liquid jet’s speed decreases substantially, whereas the speeds of the second and third liquid jets exhibit no substantial changes. These results on bubble dynamics in an ultrasonic field are important for identifying or correcting the mechanisms of acoustic cavitation and for facilitating its optimization and application.     

Toward efficient interactions of bubbles and coal particles induced by stable cavitation bubbles under 600 kHz ultrasonic standing waves

The interactions of bubbles and coal particles in 600 kHz ultrasonic standing waves (USW) field has been investigated. A high-speed camera was employed to record the phenomena occurred under the USW treatment. The formation and behaviors of cavitation bubbles were analyzed. Under the driving of these cavitation bubbles, whose size is from several microns to dozens of microns, coal particles were aggregated and then attracted by large bubbles due to the acoustic radiation forces. The results of USW-assisted flotation show a significant improvement in recoveries at 600 kHz, which indicates that the interactions of bubbles and particles in the USW field are more efficient than that in the conventional gravitational field. Furthermore, the sound pressure distribution of the USW was measured and predicted by a hydrophone. The analysis of gravity and buoyancy, primary and secondary Bjerknes forces shows that bubble-laden particles can be attracted by the rising bubbles under large acoustic forces. This study highlights the potential for USW technology to achieve efficient bubble-particle interactions in flotation.     

Synergistic effects of the alternating application of low and high frequency ultrasound for particle synthesis in microreactors

Ultrasound (US) is a promising method to address clogging and mixing issues in microreactors (MR). So far, low frequency US (LFUS), pulsed LFUS and high frequency US (HFUS) have been used independently in MR for particle synthesis to achieve narrow particle size distributions (PSD). In this work, we critically assess the advantages and disadvantages of each US application method for the case study of calcium carbonate synthesis in an ultrasonic microreactor (USMR) setup operating at both LFUS (61.7 kHz, 8 W) and HFUS (1.24 MHz, 1.6 W). Furthermore, we have developed a novel approach to switch between LFUS and HFUS in an alternating manner, allowing us to quantify the synergistic effect of performing particle synthesis under two different US conditions. The reactor was fabricated by gluing a piezoelectric plate transducer to a silicon microfluidic chip. The results show that independently applying HFUS and LFUS produces a narrower PSD compared to silent conditions. However, at lower flow rates HFUS leads to agglomerate formation, while the reaction conversion is not enhanced due to weak mixing effects. LFUS on the other hand eliminates particle agglomerates and increases the conversion due to the strong cavitation effect. However, the required larger power input leads to a steep temperature rise in the reactor and the risk of reactor damage for long-term operation. While pulsed LFUS reduces the temperature rise, this application mode leads again to the formation of particle agglomerates, especially at low LFUS percentage. The proposed application mode of switching between LFUS and HFUS is proven to combine the advantages of both LFUS and HFUS, and results in particles with a unimodal narrow PSD (one order of magnitude reduction in the average size and span compared to silent conditions) and negligible rise of the reactor temperature.     

Interplay of local resonances and Bragg band gaps in acoustic waveguides with periodic detuned resonators

This letter is concerned with acoustic wave propagation and transmission in acoustic waveguides with periodically grafted detuned Helmholtz resonators. The interplay of local resonances and Bragg band gaps in such periodic systems is examined. It is shown that, when the resonant frequencies of the resonators are tuned close to a Bragg band gap, the behavior of the Bragg band gap can be affected dramatically. Particularly, by introducing appropriately tuned resonators, the bandwidth of a Bragg band gap can be reduced to zero, leading to a very narrow pass band with great wave attenuation performance near both band edges. The band formation mechanisms of such periodic waveguides are further examined, providing explicit formulae to locate the band edge frequencies of all the band gaps, as well as the conditions to achieve very narrow pass bands in such periodic waveguides.     

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids.The propagation of three longitudinal waves is represented through three scalar potential functions.The lone transverse wave is presented by a vector potential function.The displacements of particles in different phases of the aggregate are defined in terms of these potential functions.It is shown that there exist three longitudinal waves and one transverse wave.The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated.For the presence of viscosity in pore-fluids,the waves refracted to the porous medium attenuate in the direction normal to the interface.The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations.These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave.The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model.The conservation of the energy across the interface is verified.The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.     

Loading rate and confining pressure effect on dilatancy,acoustic emission,and failure characteristics of fissured rock with two pre-existing flaws

Investigating the dilatancy, acoustic emission and failure characteristics of fissured rock are significant to ensure their geotechnical stability. In this paper, the uniaxial and triaxial compression experiments with AE monitoring under different loading rates were carried out on fissured rock specimens with the same geometrical distribution of two pre-existing flaws. The dilatancy and AE activity of these specimens were discussed, and the effects of the confining pressure and loading rate on the mechanical parameters and failure characteristics were analyzed. The results show that the exponential strength criterion is more suitable than the Mohr–Coulomb strength criterion to characterize the strength characteristics of fissured rock. The crack evolution and failure characteristics of fissured rock specimens are more complicated than those of intact rock specimens. The failure characteristics of the fissured rock follow the tensile shear coalescence model, crack branching occurs with increasing the loading rate, and the multi-section coalescence model is verified with increasing the confining pressure. The phenomena of stress drop and yield platform usually occur after the dilatancy onset, the specimen does not fail instantaneously, and the propagation and coalescence of cracks cause a sharp increase in the AE signals, circumferential strain, and volumetric strain.     

横观各向同性液体饱和多孔介质中平面波的传播

基于孔隙介质的Ｂｉｏｔ理论１，研究了横观各向同性液体饱和多孔介质中平面波的传播特性。首先导出了波传播的特征方程并给出了其解析解，结果显示：有４种不同波速的平面体波传播；第一准纵波，第二准纵波，准横波和反平面横波。文中给出了波速和衰减的解析表达式，数值计算了频散曲线和衰减曲线，并讨论了各类准体波位移之间的耦合关系。     

球形钨合金破片终点弹道性能实验研究

实验研究了球形钨合金破片的速度衰减规律、爆轰驱动下的变形和破碎、对半无限钢靶的侵彻以及对薄钢靶的贯穿。结果表明:(1)破片长距离(120m)飞行时的衰减系数为常数,阻力系数与破片初速成线性关系;(2)在爆轰驱动下,直径为6.0和7.5mm的破片破碎率为2%～3%,而直径为8.5mm的破碎率为45%;(3)破片长距离飞行后仍有很强的穿甲能力。     

迭代法分析圆环类微带行波天线的辐射特性

利用圆环类微带行波天线的辐射功率与等效行波磁流衰减常数之间的自洽关系,导出了计算衰减常数的迭代方程;为加快迭代速度,将辐射积分中的格林函数展开成柱面波函数,得到快速收敛的级数和.最后给出了方向图的计算曲线,与实验结果对比吻合良好,表明此方法模拟圆环类微带行波天线辐射特性的有效性.