The selection of layer thicknesses to control acoustic radiation force profiles in layered resonators

Ultrasonic standing waves can be used to generate radiation forces on particles within a fluid. A number of authors have derived detailed representations of these forces but these are most commonly applied using an approximation to the energy distribution based upon an idealized standing wave within a mode based upon rigid boundaries. An electro-acoustic model of the acoustic energy distribution within a standing wave with arbitrary thickness boundaries has been expanded to model the radiation force on an example particle within the acoustic field. This is used to examine the force profile on a particle at resonances other than those predicted with rigid boundaries, and with pressure nodes at different positions. A simple analytical method for predicting modal conditions for combinations of frequencies and layer thickness characteristics is presented, which predicts that resonances can exist that will produce a pressure node at arbitrary positions in the fluid layer of such a system. This can be used to design resonators that will drive particles to positions other than the center of the fluid layer, including the fluid/solid boundary of the layer, with significant potential applications in sensing systems. Further, the model also predicts conditions for multiple subwavelength resonances within the fluid layer of a single resonator, each resonance having different nodal planes for particle concentration.     

Modelling of particle paths passing through an ultrasonic standing wave

Within an ultrasonic standing wave particles experience acoustic radiation forces causing agglomeration at the nodal planes of the wave. The technique can be used to agglomerate, suspend, or manipulate particles within a flow. To control agglomeration rate it is important to balance forces on the particles and, in the case where a fluid/particle mix flows across the applied acoustic field, it is also necessary to optimise fluid flow rate. To investigate the acoustic and fluid forces in such a system a particle model has been developed, extending an earlier model used to characterise the 1-dimensional field in a layered resonator. In order to simulate fluid drag forces, CFD software has been used to determine the velocity profile of the fluid/particle mix passing through the acoustic device. The profile is then incorporated into a MATLAB model. Based on particle force components, a numerical approach has been used to determine particle paths. Using particle coordinates, both particle concentration across the fluid channel and concentration through multiple outlets are calculated. Such an approach has been used to analyse the operation of a microfluidic flow-through separator, which uses a half wavelength standing wave across the main channel of the device. This causes particles to converge near the axial plane of the channel, delivering high and low particle concentrated flow through two outlets, respectively. By extending the model to analyse particle separation over a frequency range, it is possible to identify the resonant frequencies of the device and associated separation performance. This approach will also be used to improve the geometric design of the microengineered fluid channels, where the particle model can determine the limiting fluid flow rate for separation to occur, the value of which is then applied to a CFD model of the device geometry.     

Nonlinear Spherical Standing Waves in an Acoustically Excited Liquid Drop

Nonlinear evolution of a standing acoustic wave in a spherical resonator with a perfectly soft surface is analyzed. Quadratic approximation of nonlinear acoustics is used to analyze oscillations in the resonator by the slowly varying amplitude method for the standing wave harmonics and slowly varying profile method for the standing wave profile. It is demonstrated that nonlinear effects may lead to considerable increase in peak pressure at the center of the resonator. The proposed theoretical model is used to analyze the acoustic field in liquid drops of an acoustic fountain. It is shown that, as a result of nonlinear evolution, the peak negative pressure may exceed the mechanical strength of the liquid, which may account for the explosive instability of drops observed in experiments.     

A broadband asymmetric microwave metamaterial based on LC and standing-wave resonances

Three metamaterial samples were simulated, numerically analyzed, and fabricated with different resonator lengths on similar unit cells. According to the results in addition to conventional LC resonance of the resonator, standing wave resonance was also observed within the resonator-dielectric-grounded back wire waveguide. We observed that the orientation of the sides of this waveguide relative to the polarization of the incident electromagnetic wave has a direct effect on the resonant frequency. The best asymmetric shape of the resonator with the minimum reflection coefficient in a wide frequency range of about 5.5 GHz with only 3% of reflection was introduced. According to the results, metamaterial polarizers and optical filters can be produced based on the standing wave resonances.     

Filamentary coagulation of particles from water-heterogeneous systems in the field of an acoustic resonator

The coagulation of particles from water-heterogeneous systems in the field of a confocal ultrasonic resonator is studied. It is found that, at frequencies of several megahertz, when acoustic power of about 1 W is applied to the resonator, long stable filaments consisting of the material of the heterogeneous system are formed in the vicinity of the resonator axis. The filaments consist of thin disks formed by coalescent particles spaced at intervals strictly equal to half of the sound wavelength. The features of this coagulation are determined for suspensions of various nature (metal and dielectric particles, colloidal solutions, and oil emulsions). It is established that the coagulation in a standing acoustic wave occurs faster than under natural conditions (under the influence of gravity). The possibility of using this effect for cleaning liquids from impurities and separating hyperfine particles without employing filter materials is discussed.     

Investigation of two-dimensional acoustic resonant modes in a particle separator

Within an acoustic standing wave particles experience acoustic radiation forces, a phenomenon which is exploited in particle or cell manipulation devices. When developing such devices, one-dimensional acoustic characteristics corresponding to the transducer(s) are typically of most importance and determine the primary radiation forces acting on the particles. However, radiation forces have also been observed to act in the lateral direction, perpendicular to the primary radiation force, forming striated patterns. These lateral forces are due to lateral variations in the acoustic field influenced by the geometry and materials used in the resonator. The ability to control them would present an advantage where their effect is either detrimental or beneficial to the particle manipulation process. The two-dimensional characteristics of an ultrasonic separator device have been modelled within a finite element analysis (FEA) package. The fluid chamber of the device, within which the standing wave is produced, has a width to height ratio of approximately 30:1 and it is across the height that a half-wavelength standing wave is produced to control particle movement. Two-dimensional modal analyses have calculated resonant frequencies which agree well with both the one-dimensional modelling of the device and experimentally measured frequencies. However, these two-dimensional analyses also reveal that these modes exhibit distinctive periodic variations in the acoustic pressure field across the width of the fluid chamber. Such variations lead to lateral radiation forces forming particle bands (striations) and are indicative of enclosure modes. The striation spacings predicted by the FEA simulations for several modes compare well with those measured experimentally for the ultrasonic particle separator device. It is also shown that device geometry and materials control enclosure modes and therefore the strength and characteristics of lateral radiation forces, suggesting the potential use of FEA in designing for the control of enclosure modes in similar particle manipulator devices.     

环形波导中非传播表面孤波

本文利用多重尺度微扰方法,研究在垂直外加激励下的环形波导中不可压缩流体的无旋运动,计算结果表明,在环的大半径近似下,可以得到流体表面位移满足的非线性Schrodinger方程及其单孤波解,与Wu.Keolian和Rudnick的实验观察符合。 关键词：     

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.     

三腔谐振腔渡越时间效应的小信号分析

 以小信号条件下入射相位为φ0的单个电子在驻波电场中的运动为基础,研究了电子束在三腔谐振腔π模驻波场中的渡越时间效应,导出了三腔谐振腔的电子负载电导的表达式,讨论了三腔谐振腔中束波能量交换情况。     

矩形谐振器中非传播重力-表面张力孤波的理论研究

本文用多重尺度微扰方法研究了外加驱动下,计及表面张力时矩形谐振器中有限深流体重力-表面张力驻波模的弱非线性调制。对吴君汝等人所发现的非传播表面孤波现象进行了较为详细的分析计算,修正和发展了Larraza,Putterman和Miles的非传播孤波理论,得到了正确的二次谐波共振条件。在σ-kd图上对非传播表面孤波的存在区域进行了仔细的理论分析,发现除静态液面深度外,流体的表面张力是产生和控制非传播表面孤波的另一重要参数。最后讨论了矩形谐振器的非线性共振曲线特性,并与实验进行了比较。 关键词：     

Acoustic radiation force on a multilayered sphere in a Gaussian standing field

We develop a model for calculating the radiation force on spherically symmetric multilayered particles based on the acoustic scattering approach. An expression is derived for the radiation force on a multilayered sphere centered on the axis of a Gaussian standing wave propagating in an ideal fluid. The effects of the sound absorption of the materials and sound wave on acoustic radiation force of a multilayered sphere immersed in water are analyzed, with particular emphasis on the shell thickness of every layer, and the width of the Gaussian beam. The results reveal that the existence of particle trapping behavior depends on the choice of the non-dimensional frequency ka, as well as the shell thickness of each layer. This study provides a theoretical basis for the development of acoustical tweezers in a Gaussian standing wave, which may benefit the improvement and development of acoustic control technology, such as trapping, sorting, and assembling a cell, and drug delivery applications.     

Resonant properties of a nonlinear dissipative layer excited by a vibrating boundary: Q-factor and frequency response

Simplified nonlinear evolution equations describing non-steady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach based on a nonlinear functional equation is used. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. The process of development of a standing wave is described analytically on the base of exact nonlinear solutions for different laws of periodic motion of the wall. For harmonic excitation the wave profiles are described by Mathieu functions, and their mean energy characteristics by the corresponding eigenvalues. The sawtooth-shaped motion of the boundary leads to a similar process of evolution of the profile, but the solution has a very simple form. Some possibilities to enhance the Q-factor of a nonlinear system by suppression of nonlinear energy losses are discussed.     

Uniform radio frequency fields in loop-gap resonators for EPR spectroscopy

At high frequencies, e.g., Q- and W-bands, it is advantageous to make the axial length of loop-gap resonators (LGRs) at least as long as a free-space wavelength. The opposite scaling of capacitance and inductance with LGR length suggests that the length of an LGR can be increased without limit, with the axial radio frequency (rf) field profiles and resonance frequency independent of length. This scaling is accurate for resonator dimensions much less than one free-space wavelength. When the resonator length approaches one-tenth of a free-space wavelength, the rf field uniformity degrades. From one-tenth to one free-space wavelength, computer simulations and experimental measurements show that the axial magnetic field energy density profile is peaked in the center of the LGR, gradually decreases from 25 to 50% at a distance one radius from the end, and rapidly there-after. The nonuniformity is of two types. One type, in the vicinity of one radius of the end, is caused by the flaring of the field as it curves from the central loop to the end region, into the larger return loop(s). The other type, in the central part of the resonator, is caused by impedance mismatch at the ends of the LGR. The LGR may be viewed as a strongly reentrant (ridge) waveguide nearly open at both ends and supporting a standing wave. A transmission line model relates the central nonuniformity to the fringing capacitance and inductance at the ends of the resonator. This nonuniformity can be eliminated in several ways including modifying the ends of the LGR by adding a small metal bridge or a dielectric ring. These uniformity trimming elements increase the fringing capacitance and/or decrease the fringing inductance. With trimmed ends, LGRs can be made many free-space wavelengths long. The maximum resonator length is determined by the proximity in frequency of the fundamental LGR mode to the next highest frequency mode as well as the quality factor. Results of this theory are compared and conformed with finite-element simulations. This theory connects the uniform LGR with the uniform field cavity resonators previously introduced by this laboratory.     

Laser-induced condensation in colloid—polymer mixtures

We study a mixture of hard sphere colloidal particles and non-adsorbing polymers exposed to a plane wave external potential which represents a three-dimensional standing laser field. With computer simulations and density functional theory we investigate the structure and phase behaviour using the simple Asakura-Oosawa model. For varying laser wavelength λ we monitor the emergence of structure in response to the external field, as measured by the amplitude of the oscillations in the one-body density distribution. Between the ideal gas limit for small λ and the bulk limit of large λ there is a non-monotonic crossover that is governed by commensurability of λ and the colloid diameter. The theoretical curves are in good agreement with simulation results. Furthermore, the effect of the periodic field on the liquid-vapour transition is studied, a situation that we refer to as laser-induced condensation. Above a threshold value for λ the theoretical phase diagram indicates the stability of a ‘stacked’ fluid phase, which is a periodic succession (in the beam direction) of liquid and vapour slabs. This partially condensed phase causes a splitting of the liquid-vapour binodal leading to two critical and a triple point. All our predictions should be experimentally observable for colloid-polymer mixtures in an optical resonator.     

电子在激光驻波场中运动产生的太赫兹及X射线辐射研究

采用单电子模型和经典辐射理论分别对低能和高能电子在线偏振激光驻波场中的运动和辐射过程进行了研究. 结果表明: 垂直于激光电场方向入射的低速电子在激光驻波场中随着光强的增大, 逐渐从一维近周期运动演变为二维折叠运动, 并产生强的微米量级波长的太赫兹辐射; 高能电子垂直或者平行于激光电场方向入射到激光驻波场中, 都会产生波长在几个纳米的高频辐射; 低能电子与激光驻波场作用中, 激光强度影响着电子的运动形式、辐射频率以及辐射强度; 高能电子入射时, 激光强度影响了电子高频辐射的强度, 电子初始能量影响着辐射的频率; 电子能量越高, 产生的辐射频率越大. 研究表明可以由激光加速电子的方式得到不同能量的电子束, 并利用电子束在激光驻波场的辐射使之成为太赫兹和X射线波段的小型辐射源. 研究结果可以为实验研究和利用激光驻波场中的电子辐射提供依据.     

The effect of static pressure on the inertial cavitation threshold

The amplitude of the acoustic pressure required to nucleate a gas or vapor bubble in a fluid, and to have that bubble undergo an inertial collapse, is termed the inertial cavitation threshold. The magnitude of the inertial cavitation threshold is typically limited by mechanisms other than homogeneous nucleation such that the theoretical maximum is never achieved. However, the onset of inertial cavitation can be suppressed by increasing the static pressure of the fluid. The inertial cavitation threshold was measured in ultrapure water at static pressures up to 30?MPa (300 bars) by exciting a radially symmetric standing wave field in a spherical resonator driven at a resonant frequency of 25.5 kHz. The threshold was found to increase linearly with the static pressure; an exponentially decaying temperature dependence was also found. The nature and properties of the nucleating mechanisms were investigated by comparing the measured thresholds to an independent analysis of the particulate content and available models for nucleation.     

基于介质谐振器原理的左手材料设计

本文通过对高介电常数介质基于介质谐振器理论进行分析,明确了利用高介电常数介质产生负介电常数或负磁导率的途径在于介质中产生具有Lorentz谐振形式的电磁响应的电偶极子或磁偶极子,指出了这种偶极子的产生来源于电磁波在介质中形成的驻波,而左手通带的形成正是由于电偶极子和磁偶极子之间的相互影响,破坏了驻波形成的条件所实现的. 模拟结果表明,通过将尺寸相同,介电常数不同的介质进行组合,使二者电谐振和磁谐振的频率点重合从而实现左手通带,最后利用高介电常数,低损耗的陶瓷进行样品制作并测试,测试结果证实了基于这一原理实 关键词： 全介质左手材料 介质谐振器 磁偶极子 电偶极子     

谐振管内非线性驻波的有限体积数值算法

为了扩展谐振管内非线性驻波在工程中的应用, 以及克服现有数值计算方法仅局限于求解直圆柱形和指数形谐振管内非线性驻波的问题. 根据变截面的非稳态可压缩热黏性流体Navier-Stokes方程和空间守恒方程, 并基于求解压力速度耦合方程的半隐式算法和交错网格技术, 构建一种能够计算任意形状轴对称谐振管受活塞驱动时内部非线性驻波的有限体积算法. 分别对圆柱形、指数形和圆锥形谐振管内的非线性驻波进行仿真计算. 通过与现有试验结果以及数值仿真结果的对比, 验证了该方法的正确性.并获得除驻波声压之外的另外一些新的物理结果, 包括速度、密度、温度的瞬时变化.在直圆柱形谐振管内产生冲击声压波, 速度波形中出现钉状结构.而在指数形和圆锥形谐振管内产生高声压幅值的驻波, 没有出现冲击波, 速度波形中均未发现钉状结构. 计算结果表明谐振管内非线性驻波的物理属性与谐振管形状之间有密切关系.     

Theoretical and numerical calculations for the time-averaged acoustic force and torque acting on a rigid cylinder of arbitrary size in a low viscosity fluid

In this paper, theoretical calculations as well as numerical simulations are performed for the time-averaged acoustic force and torque on a rigid cylinder of arbitrary size in a fluid with low viscosity, i.e., the acoustic boundary layer is thin compared to the cylinder radius. An exact analytical solution and its approximation are proposed in the form of an infinite series including Bessel functions. These solutions can be evaluated easily by a mathematical software package such as mathematica and matlab. Three types of incident waves, plane traveling wave, plane standing wave, and dual orthogonal standing waves, are investigated in detail. It is found that for a small particle, the viscous effects for an incident standing wave may be neglected but those for an incident traveling wave are notable. A nonzero viscous torque is experienced by the rigid cylinder when subjected to dual orthogonal standing waves with a phase shift even when the cylinder is located at equilibrium positions without imposed acoustic forces. Furthermore, numerical simulations are carried out based on the FVM algorithm to verify the proposed theoretical formulas. The theoretical results and the numerical ones agree with each other very well in all the cases considered.     

驻波声场中单分散细颗粒的相互作用特性

利用外加声场促进悬浮在气相中的细颗粒发生相互作用,进而引起颗粒的碰撞和凝并,使得颗粒平均粒径增大、数目浓度降低,是控制细颗粒排放的重要技术途径.为探究驻波声场中单分散细颗粒的相互作用,建立包含曳力、重力、声尾流效应的颗粒相互作用模型,采用四阶经典龙格-库塔算法和二阶隐式亚当斯插值算法对模型进行求解.将数值模拟得到的颗粒声波夹带速度和相互作用过程与相应的解析解和实验结果进行对比,验证模型的准确性.进而研究颗粒初始条件和直径对相互作用特性的影响.结果表明,初始时刻颗粒中心连线越接近声波波动方向、颗粒位置越接近波腹点,颗粒间的声尾流效应就越强,颗粒发生碰撞所需要的时间就越短.研究还发现,颗粒直径对颗粒相互作用的影响取决于初始时刻颗粒中心连线偏离声波波动方向的程度.当偏离较小时,颗粒直径越大,颗粒发生碰撞所需要的时间越短;当偏离很大时,直径较小的颗粒能够发生碰撞,而直径较大的颗粒则无法发生碰撞.