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.     

The use of ultrasonic standing waves to enhance optical particle sizing equipment

Fluid dynamics modelling augmented with routines to simulate acoustic forces on aerosol particles has been used to investigate the potential of combining ultrasonic standing wave fields with optical particle analysis equipment. Simulations of particle dynamics in airstreams incorporating acoustic forces predict that particles in the 1-10 microns diameter range may be effectively focused to the velocity nodes of the standing wave field. Particles move to the velocity nodes within tens of milliseconds for acoustic frequencies of 10-100 kHz and at an acoustic energy density of 100 Jm-3. Larger particles are predicted to move to the velocity antinodes within similar times; however, there is a crossover region at approximately 15-20 microns particle diameter where longer times are predicted due to the competing forces driving particles to the vibration node and antinode. With sufficient transverse flow velocities the models predict that disturbances due to acoustic streaming can be overcome and a useful degree of focusing achieved for the aerosol particles. Results from a model demonstrating sampling and acoustic focusing of 3-9 microns aerosol particles to a 200 microns wide analysis area are presented.     

Measurement of Inherent Material Density of Nanoparticle Agglomerates

We describe a new technique to measure the size dependent inherent material density of chain agglomerate particles. Measurements were carried out for diesel soot and aluminum/alumina agglomerate particles in the nanometer size range. Transmission electron microscopy was used to measure the volumes of agglomerate particles that were preselected by mass using an aerosol particle mass analyzer. We found that the density of diesel exhaust particles increased from 1.27 to 1.78g/cm³ as particle mobility size increased from 50 to 220nm. When particles are preheated to remove volatile components, the density was 1.77±0.07g/cm³, independent of particle size. The densities measured after heating correspond to the inherent material density of diesel soot. Measurements with aluminum nanoparticles were made downstream of a furnace where aluminum (Al) was converted to alumina (Al₂O₃). From measurements of inherent material density we were able to infer the extent of reaction, which varied with furnace temperature.     

Investigation of airborne nanopowder agglomerate stability in an orifice under various differential pressure conditions

The stability of agglomerates is not only an important material parameter of powders but also of interest for estimating the particle size upon accidental release into the atmosphere. This is especially important when the size of primary particles is well below the agglomerate size, which is usually the case when the size of primary particles is below 100 nm. During production or airborne transportation in pipes, high particle concentrations lead to particle coagulation and the formation of agglomerates in a size range of up to some micrometers. Binding between the primary particles in the agglomerates is usually due to van der Waals forces. In the case of a leak in a pressurized vessel (e.g. reactor, transport pipe, etc.), these agglomerates can be emitted and shear forces within the leak can cause agglomerates to breakup. In order to simulate such shear forces and study their effect on agglomerate stability within the airborne state, a method was developed where agglomerate powders can be aerosolized and passed through an orifice under various differential pressure conditions. First results show that a higher differential pressure across the orifice causes a stronger fragmentation of the agglomerates, which furthermore seems to be material dependent.     

基于分形理论的驻波声场中颗粒团运动特性数值预测*

基于分形理论,建立驻波声场中颗粒团动力学模型,对颗粒团的夹带系数、相位滞后和漂移系数进行数值预测。将预测结果和实验进行对比,二者吻合良好。在此基础上,研究了组成颗粒团的原生颗粒半径、数目以及排列情况对于颗粒团运动特性参数的影响。结果表明,对于由两个原生颗粒组成的颗粒团,原生颗粒半径越接近,颗粒团与等体积球形颗粒运动特性的差异越大;在分形维数一定时,随着原生颗粒数目的增多,颗粒团的夹带系数减小,相位滞后增加,漂移系数先增大后减小,颗粒团与等体积球形颗粒的动力学行为存在显著差异;原生颗粒排列趋于致密时,颗粒团的夹带系数增大,相位滞后减小,漂移系数发生单调变化,与等体积球形颗粒运动特性的差异缩小。     

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.     

Agglomeration of particles by a converging ultrasound field and their quantitative assessments

The acoustic radiation force resulting from acoustic waves have been extensively studied for the contact-free generation of organized patterning arrays. The precise arrangement of microscopic objects clustered at the pressure nodes is critical to the development of functional structures and patterned surfaces. However, the size of the clusters is restricted by the saturation limit of the acoustic nodes. Here, we present a bulk acoustic wave (BAW) platform, which employs a two-dimensional acoustic wave to propel particles of various sizes. Experimentally, when particles are large, significant acoustic energy is scattered and partly absorbed by the matched layers in front of the sensors. The acoustic radiation force from a convergent acoustic pressure field agglomerates the large polystyrene (PS) particles towards the central region instead of the pressure nodes. The parametric analysis has been performed to assess the transition in the particles from clustering at the organized nodal arrays to agglomerating in the central region, which is a function of particle size, particle concentration, and load voltage. Statistically, the particles can agglomerate with a cluster ratio greater than 70%, and this ratio can be improved by increasing the load power/voltage supplied to the transducers. With its ability to perform biocompatible, label-free, and contact-free self-assembly, this concept offers a new possibility in the fabrication of colloidal layers, the recreation of tissue microstructure, the development of organoid spheroid cultures, the migration of microorganisms, and the assembly of bioprinting materials.     

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.     

Microparticle column geometry in acoustic stationary fields

Particles suspended in a fluid will experience forces from stationary acoustic fields. The magnitude of the force depends on the time-averaged energy density of the field and the material properties of the particles and fluid. Forces acting on known particles smaller than 20 microm were studied. Within a 500 kHz acoustic beam generated by a plane-piston circular source, observations were made of the geometry of the particle column that is formed. Varying the acoustic energy altered the column width in a manner predicted by equations for the primary acoustic radiation force from scattering of particles in the long-wavelength limit. The minimum pressures required to trap gas, solid, and liquid particles in a water medium at room temperature were also estimated to within 12%. These results highlight the ability of stationary acoustic fields from a plane-piston radiator to impose nano-Newton-scale forces onto fluid particles with properties similar to biological cells, and suggest that it is possible to accurately quantify these forces.     

In-Line Particle Size Determination for Jet Agglomeration Processes

In jet agglomeration plants, powders are agglomerated to obtain good instant properties. The free-falling initial material is wetted in a spray cone by droplets or in a steam jet by condensation at the particle surface. In a subsequent region of high particle concentration, collision between particles occurs and agglomerates form, if the forces of adhesion are strong enough. A commercial measurement device, working according to the principle of Fraunhofer diffraction, was modified for in-line application. It was used to measure particle size distributions and concentrations of solid particles and droplets in jets. A model is presented to calculate local particle sizes by means of mass balances from integral measurements over large volumes. The results of in-line particle size and agglomerate size analyses show the practical importance of dry agglomeration during transport and lead to a better understanding of the subsequent wet agglomeration process.     

Multiphysics modelling of the separation of suspended particles via frequency ramping of ultrasonic standing waves

A model was developed to determine the local changes of concentration of particles and the formations of bands induced by a standing acoustic wave field subjected to a sawtooth frequency ramping pattern. The mass transport equation was modified to incorporate the effect of acoustic forces on the concentration of particles. This was achieved by balancing the forces acting on particles. The frequency ramping was implemented as a parametric sweep for the time harmonic frequency response in time steps of 0.1 s. The physics phenomena of piezoelectricity, acoustic fields and diffusion of particles were coupled and solved in COMSOL Multiphysics? (COMSOL AB, Stockholm, Sweden) following a three step approach. The first step solves the governing partial differential equations describing the acoustic field by assuming that the pressure field achieves a pseudo steady state. In the second step, the acoustic radiation force is calculated from the pressure field. The final step allows calculating the locally changing concentration of particles as a function of time by solving the modified equation of particle transport. The diffusivity was calculated as function of concentration following the Garg and Ruthven [1] equation which describes the steep increase of diffusivity when the concentration approaches saturation. However, it was found that this steep increase creates numerical instabilities at high voltages (in the piezoelectricity equations) and high initial particle concentration. The model was simplified to a pseudo one-dimensional case due to computation power limitations. The predicted particle distribution calculated with the model is in good agreement with the experimental data as it follows accurately the movement of the bands in the centre of the chamber.     

Sonochemical coating of magnetite nanoparticles with silica

Magnetite nanoparticles were coated with silica through the hydrolysis and condensation of tetraethyl orthosilicate (TEOS) under ultrasonic irradiation. The ultrasonic irradiation was used to prevent the agglomeration of the magnetite particles and accelerate the hydrolysis and condensation of TEOS. TEM, DLS, XRF, VSM, TG and sedimentation test were used to characterize the silica-coated magnetite particles. The dispersibility of silica-coated magnetite particles in aqueous solution was improved significantly and the agglomerate particle size was decreased to 110 nm. It was found that the agglomerate particle size of silica-coated magnetite particles was mainly decided by the coating temperature and the pH value in the silica-coating process. The weight ratio of silica in silica-coated magnetite particles was mainly decided by the pH value in the silica-coating process. The dispersibility of silica-coated magnetite particles was mainly decided by the agglomerate particle size of the suspension. The oxidation of magnetite particles in air was limited through the coated silica. The magnetism of silica-coated magnetite particles decreased slightly after silica-coating.     

Trapping of microparticles in the near field of an ultrasonic transducer

We are investigating means of handling microparticles in microfluidic systems, in particular localized acoustic trapping of microparticles in a flow-through device. Standing ultrasonic waves were generated across a microfluidic channel by ultrasonic microtransducers integrated in one of the channel walls. Particles in a fluid passing a transducer were drawn to pressure minima in the acoustic field, thereby being trapped and confined at the lateral position of the transducer. The spatial distribution of trapped particles was evaluated and compared with calculated acoustic intensity distributions. The particle trapping was found to be strongly affected by near field pressure variations due to diffraction effects associated with the finite sized transducer element. Since laterally confining radiation forces are proportional to gradients in the acoustic energy density, these near field pressure variations may be used to get strong trapping forces, thus increasing the lateral trapping efficiency of the device. In the experiments, particles were successfully trapped in linear fluid flow rates up to 1mm/s. It is anticipated that acoustic trapping using integrated transducers can be exploited in miniaturised total chemical analysis systems (microTAS), where e.g. microbeads with immobilised antibodies can be trapped in arrays and subjected to minute amounts of sample followed by a reaction, detected using fluorescence.     

Towards the automation of micron-sized particle handling by use of acoustic manipulation assisted by microfluidics

The use of acoustic radiation forces for the manipulation and positioning of micrometer sized particles has shown to be a promising approach. Resonant excitation of a system containing a particle laden fluid filled cavity, can (depending on the mode excited) result in positioning of the particles in parallel lines (1-D) or distinct clumps in a grid formation (2-D) due to the high amplitude standing pressure fields that arise in the fluid. In a broader context, the alignment of particles using acoustic forces can be used to assist manipulation processes which utilise an external mechanical tool, for instance a microgripper. In such a system, particles can be removed sequentially from a line formed by acoustic forces within a microfluidic channel, hence allowing a degree of automation. In order to fully automate the gripping process, the particles must be confined to a repeatable and accurate location in two dimensions (assuming that in the third dimension they sit on the lower surface of the channel). Only in this way it is possible to remove subsequent particles by simply bringing the gripper to a known location and activating its fingers. This combined use of acoustic forces and mechanical gripping requires that one extremity of the channel is open. However, the presence of the liquid-air interface which occurs at this opening, causes the standing pressure field to decay to zero towards the opening. In a volume of liquid in proximity to the interface positioning of particles by acoustic forces is therefore no longer possible. In addition, the longitudinal gradient of the field can cause a drift of particles towards the longitudinal center of the channel at some frequencies, undesirably moving them further away from the interface, and so further from the gripper. As a solution the use of microfluidic flow induced drag forces in addition to the acoustic force potential has been investigated.     

Influence of the Particle Morphology on the Activity of Nanometer Platinum Aerosol Catalysts

For nanoparticle agglomerates, the catalytic activity may depend strongly on their structure. The influence of different parameters such as agglomerate structure, primary particle temperature history and surface preconditioning on the catalytic activity of nanoparticles was investigated. The fraction of agglomerate surface contributing to the reaction depends on the agglomerate structure and on the velocity of the reaction under investigation. For extremely fast reactions such as the oxidation of hydrogen on Pt nanoparticles, only the outermost surface (exposed surface) contributes substantially to the formation of water. For the system investigated here, the inner surface not substantially contributing to the reaction accounted for at least 70% of the total particle surface as determined from oxygen presaturation experiments of the agglomerate surface. A considerable activity loss of the platinum particles was observed on preheating the nanoparticle agglomerates. The preheating leads to an increase in the nanoparticle size by an order of magnitude due to sintering. It is unclear if this activity reduction is due to changes in the particle surface state or to a real size effect of the nanoparticles.     

Strategies for single particle manipulation using acoustic and flow fields

Acoustic radiation forces have often been used for the manipulation of large amounts of micrometer sized suspended particles. The nature of acoustic standing wave fields is such that they are present throughout the whole fluidic volume; this means they are well suited to such operations, with all suspended particles reacting at the same time upon exposure. Here, this simultaneous positioning capability is exploited to pre-align particles along the centerline of channels, so that they can successively be removed by means of an external tool for further analysis. This permits a certain degree of automation in single particle manipulation processes to be achieved as initial identification of particles’ location is no longer necessary, rather predetermined. Two research fields in which applications are found have been identified. First, the manipulation of copolymer beads and cells using a microgripper is presented. Then, sample preparation for crystallographic analysis by positioning crystals into a loop using acoustic manipulation and a laminar flow will be presented.     

The effect of high-frequency acoustic wave vibration pattern on HKUST’s multi-level pore structure

The physical properties of materials are critical to their functionality, and the ability to control these properties using external forces is a significant challenge. In this study, we investigate the effect of three high frequency acoustic wave vibration patterns on the structure and morphology of MOF particles. Our results indicate that while regular vibration patterns generated by SAW can alter particle morphology, hybrid waves and Lamb waves with irregular vibration patterns can synthesise MOF crystals with multi-level pores. The vibration pattern of acoustic waves is shown to be a critical factor in controlling the particle morphology process. These results provide new insights into the precise control of crystal structure and the theory of crystallisation by particle attachment (CPA).     

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.     

A Survey of Complementary Methods for the Characterization of Dense Colloidal Silica

The aim of this study is to enhance existing knowledge of different techniques developed for the characterization of stability and particle sizing of nanoparticles in dense dispersions subjected to interparticulate and hydrodynamic forces. Silica suspension, commercially known as Klebosol^® 30R50 and consisting of a particle size of 80 nm on average, was investigated in the study over a wide range of concentrations. The investigations were carried out using different optical and acoustic techniques such as laser diffraction, multiple light scattering, photon correlation spectroscopy and acoustic spectroscopy. The study details the capabilities and limitations of these modern techniques based on the different physical principles behind the characterization of the size distribution of particles in suspensions. The results are presented in terms of particle size ranges, solid concentration and technological aspects such as online and offline analysis. An important finding is that many of these modern techniques need to be improved for applications at higher concentrations since the standard models become practically invalid because of the complex interaction of acoustic and optical waves with particles in suspensions of silica.     

Characterization of SiC and Si<Subscript>3</Subscript>N<Subscript>4</Subscript> nanoparticles and their aqueous dispersions

Nanoparticles of SiC and Si₃N₄ were previously used to obtain electroless NiP/particles nanocomposites. The incorporation process was very different, depending on the particle: SiC tended to agglomerate and had a high incorporation level; Si₃N₄ particles were not aggregated, but their incorporation level was very low. To try to explain these differences, the particles and their aqueous dispersions were characterized. Although the as-received products were both oxidized and of the identical mean size, results showed that the size distributions and the surface oxidation products were rather different. The zeta potential in water dispersions was similar and negative for both particles but, as the electrolyte ions were introduced, it showed a different evolution: nitride particles retained a small negative charge and carbide was almost uncharged. The overall results obtained in this study explain the different behavior of both ceramic particles and provide possible solutions to improve their co-deposition with nickel.