Nonlinear ultrasonic waves in bubbly liquids with nonhomogeneous bubble distribution: Numerical experiments

This paper deals with the nonlinear propagation of ultrasonic waves in mixtures of air bubbles in water, but for which the bubble distribution is nonhomogeneous. The problem is modelled by means of a set of differential equations which describes the coupling of the acoustic field and bubbles vibration, and solved in the time domain via the use and adaptation of the SNOW-BL code. The attenuation and nonlinear effects are assumed to be due to the bubbles exclusively. The nonhomogeneity of the bubble distribution is introduced by the presence of bubble layers (or clouds) which can act as acoustic screens, and alters the behaviour of the ultrasonic waves. The effect of the spatial distribution of bubbles on the nonlinearity of the acoustic field is analyzed. Depending on the bubble density, dimension, shape, and position of the layers, its effects on the acoustic field change. Effects such as shielding and resonance of the bubbly layers are especially studied. The numerical experiments are carried out in two configurations: linear and nonlinear, i.e. for low and high excitation pressure amplitude, respectively, and the features of the phenomenon are compared. The parameters of the medium are chosen such as to reproduce air bubbly water involved in the stable cavitation process.     

Numerical simulations of three-dimensional nonlinear acoustic waves in bubbly liquids

This paper presents three-dimensional simulations of nonlinear propagation of ultrasonic waves through bubbly liquids, which represent the continuity of our previous works included in the numerical tool SNOW-BL. The behavior of three-dimensional nonlinear acoustic waves in bubbly liquids is analyzed by means of numerical predictions. Nonlinearity, attenuation, and dispersion due to the presence of bubbles in the liquid are taken into account. The numerical solution to the differential problem is obtained by means of a finite-difference scheme. The simulations we present here consider a homogeneous distribution of bubbles in the liquid. Results compare high and low-amplitude waves to detect the nonlinear effects of the bubbles. Results are shown for radiation and enclosure problems.     

Leap behavior of ultrasonic standing waves in the liquids

The generation and behavior of ultrasonic standing waves was modeled using the light cut method for transparent fluid. The oscillations of the fluid surface in initial moment of switching on ultrasound and appearance of standing wave channel were observed. The effect of continuous fluid depth decrease and increase on the behavior of ultrasonic standing wave channel was studied. The ultrasonic standing wave channel floated in the liquid between of the crucible bottom and fluid surface and discretely changed its height by half ultrasonic wavelength with the decrease or increase of the liquid level. This channel had the behavior of a “quasi solid state” and damped of convection.     

含气泡液体中的非线性声传播

考虑到分布在液体中的气泡是声波在含气泡液体中传播时引起非线性的一个很重要的因素,本文研究了声波在含气泡液体中的非线性传播.将气体含量的影响引入到声波在液体中传播的方程中,从而得到声波在气液混合物中传播的数学模型.通过对该模型进行数值模拟发现,气体含量、驱动声场声压幅值及驱动声场作用时间均会影响到气液混合物中的声场分布及声压幅值大小.液体中的气泡会"阻滞"液体中声场的传播并将能量"聚集"在声源附近.对于连续大功率的驱动声场来说,液体中的气泡会"阻滞"气液混合物中声场及其能量的传播.     

超声驻波场粒子二维运动控制机理与模型研究*

为了将正交超声驻波技术用于多晶硅陷光结构网格化微加工,以达到均匀加工的目的,本文从理论、模拟和实验等方面研究了粒子由无规则排列到超声作用后形成二维网格状排列的运动过程,网格化控制机理,并建立了二维运动方程。计算机仿真结果与实验结果一致,表明应用超声驻波进行网格化微纳加工设想是可行的。     

On the Kudryashov-Sinelshchikov equation for waves in bubbly liquids

A nonlinear evolution equation for wave propagation in bubbly liquids, taking into account viscosity and heat transfer, has been derived by Kudryashov and Sinelshchikov. In the case of no dissipation the authors have provided analytical solutions representing undistorted waves. These results are cast into a simpler form and studied in more detail. In addition to the wave profiles the corresponding phase curves are presented. Depending on some parameter the solutions represent solitary or periodic waves. Some of the periodic waves exhibit peaks or cusps. From the periodic waves a new type of “meandering” solutions is constructed.     

闭管中大振幅驻波理论

大振幅驻波理论现扩展至计入闭管中附面层损耗时的情况.如前,以质点位移表达非线性波相速应计入质点速度的规律.符合驻波中各参量只在原地随时间作交流变化的现象.所得解完全满足流体动力学方程.把声场参量分解为频率分量时所遇到特殊情况做了讨论和处理.也提出一些新现象.     

Nonlinear standing waves in 2-D acoustic resonators

This paper deals with 2-D simulation of finite-amplitude standing waves behavior in rectangular acoustic resonators. Set of three partial differential equations in third approximation formulated in conservative form is derived from fundamental equations of gas dynamics. These equations form a closed set for two components of acoustic velocity vector and density, the equations account for external driving force, gas dynamic nonlinearities and thermoviscous dissipation. Pressure is obtained from solution of the set by means of an analytical formula. The equations are formulated in the Cartesian coordinate system. The model equations set is solved numerically in time domain using a central semi-discrete difference scheme developed for integration of sets of convection-diffusion equations with two or more spatial coordinates. Numerical results show various patterns of acoustic field in resonators driven using vibrating piston with spatial distribution of velocity. Excitation of lateral shock-wave mode is observed when resonant conditions are fulfilled for longitudinal as well as for transversal direction along the resonator cavity.     

Nonlinear frequency mixing in a resonant cavity: Numerical simulations in a bubbly liquid

The study of nonlinear frequency mixing for acoustic standing waves in a resonator cavity is presented. Two high frequencies are mixed in a highly nonlinear bubbly liquid filled cavity that is resonant at the difference frequency. The analysis is carried out through numerical experiments, and both linear and nonlinear regimes are compared. The results show highly efficient generation of the difference frequency at high excitation amplitude. The large acoustic nonlinearity of the bubbly liquid that is responsible for the strong difference-frequency resonance also induces significant enhancement of the parametric frequency mixing effect to generate second harmonic of the difference frequency.     

The photoelastic visualization of ultrasonic waves in liquids

A technique is presented for the optical display of three-dimensional ultrasonic fields, involving the visualization of thin sections of the field within a layer of suitable photoelastic solid, such as polyurethane rubber. A valid display is produced with a negligible disturbance to the ultrasonic field. The technique has a low sensitivity, but has been successfully applied to the visualization of 200 kHz, continuous-wave fields in water.     

Manipulation of microparticles using phase-controllable ultrasonic standing waves

A method of manipulating microparticles in a liquid using ultrasound is proposed and demonstrated. An ultrasonic standing wave with nodal planes whose positions are controllable by varying the relative phase of two applied sinusoidal signals is generated using a pair of acoustically matched piezoelectric transducers. The resulting acoustic radiation force is used to trap micron scale particles at a series of arbitrary positions (determined by the relative phase) and then move them in a controlled manner. This method is demonstrated experimentally and 5 μm polystyrene particles are trapped and moved in one dimension through 140 μm.     

Effect of ultrasonic standing waves on flotation bubbles

Ultrasonic flotation was an effective method to float fine coal. In this study, the effects of the standing waves with different frequencies on ultrasonic flotation were investigated. The dynamic processes of bubble and coal-bubble were revealed by a high-speed camera. The results showed that under the action of Bjerknes force, bubble aggregates were formed within 450 ms and coal bubble aggregates were formed within 20 ms. The bubble aggregates were statistically analyzed by image processing method. The number of aggregates and small bubbles in the ultrasonic field at 100 kHz was greater than those at 80 and 120 kHz. Besides, 100 kHz ultrasonic flotation achieved the highest yields of clean coal (35.89%) and combustible recovery (45.77%). The cavitation bubbles acted as either a “medium” or an “inclusion”, entrapping and entraining the coal particles in the flotation pulp. It promoted the aggregation of bubbles with coal particles, so the flotation efficiency was effectively improved in the presence of ultrasonic standing waves.     

Nonlinear standing waves in a resonator with feedback control

An experimental study is presented to demonstrate that nonlinear effect on standing waves in a resonator can be reduced by a feedback loop responding to the second harmonic. The resonator was a cylindrical tube sealed at one end and driven by a horn driver unit at another end. The feedback control loop consisted of a pressure sensor, a frequency filter, a phase shifter, and an actuator. The results show that the waveform distortions can be eliminated and large amplitude sinusoidal pressure oscillations are obtained. A simple model is proposed for a qualitative discussion on the control mechanism, which shows that the feedback loop alters the imaginary part of the complex mode frequency so as to suppress (or enhance) the second harmonic.     

Nonlinear evolution of 3D drift-ion-sound standing waves

Temporal evolution of coupled drift-ion-sound standing wave is considered. Perturbation theory based on the multiple-time-scale formalism is built. Nonlinear effects up to the third order in amplitude are discussed.     

Particle separation in microfluidics using different modal ultrasonic standing waves

Microfluidic technology has great advantages in the precise manipulation of micro and nano particles, and the separation of micro and nano particles based on ultrasonic standing waves has attracted much attention for its high efficiency and simplicity of structure. This paper proposes a device that uses three modes of ultrasonic standing waves to continuously separate particles with positive acoustic contrast factor in microfluidics. Three modes of acoustic standing waves are used simultaneously in different parts of the microchannel. According to the different acoustic radiation force received by the particles, the particles are finally separated to the pressure node lines on both sides and the center of the microchannel. In this separation method, initial hydrodynamic focusing and satisfying various equilibrium constraints during the separation process are the key. Through numerical simulation, the resonance frequency of the interdigital transducer, the distribution of sound pressure in the liquid, and the relationship between the interdigital electrode voltage and the output sound pressure are obtained. Finally, the entire separation process in the microchannel was simulated, and the separation of the two particles was successfully achieved. This work has laid a certain theoretical foundation for the rapid diagnosis of diseases in practical applications.     

Practical scale modification of oleogels by ultrasonic standing waves

Lipid-based materials, such as substitutes for saturated fats (oleogels) structurally modified with ultrasonic standing waves (USW), have been developed by our group. To enable their potential application in food products, pharmaceuticals, and cosmetics, practical and economical production methods are needed. Here, we report scale-up of our procedure of structurally modifying oleogels via the use of USW by a factor of 200 compared to our previous microfluidic chamber. To this end, we compared three different USW chamber prototypes through finite element simulations (FEM) and experimental work. Imaging of the internal structure of USW-treated oleogels was used as feedback for successful development of chambers, i.e., the formation of band-like structures was the guiding factor in chamber development. We then studied the bulk mechanical properties by a uniaxial compression test of the sonicated oleogels obtained with the most promising USW chamber, and sampled local mechanical properties using scanning acoustic microscopy. The results were interpreted using a hyperelastic foam model. The stability of the sonicated oleogels was compared to control samples using automated image analysis oil-release tests. This work enabled the effective mechanical-structural manipulation of oleogels in volumes of 10–100 mL, thus paving the way for USW treatments of large-scale lipid-based materials.     

扇形薄板二维驻波的研究

用分离变量法对极坐标下垂直板面方向的金属薄板的小振动方程求解,解出扇形薄板在全部边界均自由的条件下的解析解的简正模式及通解,并计算了不同频率下对应的简正振动模式下薄板上的圆弧形驻波波节线的半径和方程的本征值所满足的规律及薄板的弹性模量,给出了驻波图,与实验上观察到的仅有辐射状波节线或辐射状波节线与圆弧形波节线同时存在这两种简正模式(即克拉尼图形)相比较,发现理论结果与实验符合得很好.     

Two regimes of the parametrically self-exciting ultrasonic standing waves

This paper discusses a nonlinear multi-wave mechanism for the parametrically self-exciting standing waves in a plane-parallel liquid layer driven at one end of the layer. The dependence of this process on the number of parametrically self-exciting waves and the frequency detuning between the frequency "f" of the pump wave and the nearest natural frequency are analyzed. It is found that two regimes with different thresholds are possible. One of them is characterized by self-exciting subharmonic frequencies close to f/2 and the second has a much lower threshold and the presence of a self-exciting subharmonic at a frequency near to the smallest natural frequency. Three dimensionless parameters determining each regime are introduced.     

Calculating shock-wave processes in bubbly liquids

A complete solution is given to the problem of the decay of an arbitrary discontinuity in a onevelocity model for a bubbly liquid and is used to analyze the propagation and interaction of shock waves in liquids with gas bubbles. Zh. Tekh. Fiz. 68, 12–19 (November 1998)