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.     

Acoustic streaming in a rotating fluid

Acoustic streaming theory is derived that is applicable to a fluid that is slow moving in a reference frame that rotates with a constant angular velocity omega. A simplified streaming equation is obtained for the special case in which the acoustic angular frequency omega is large relative to omega, and the change in fluid density due to rotation alone is negligible. For this special case it is shown that the "driving force" for the acoustic streaming is independent of omega. Thus, if no acoustic streaming is present in a fluid system that is stationary, then no steady-state acoustic streaming is predicted for a similar system that rotates with constant angular velocity. For a system in which acoustic streaming is present, the flow behavior depends on the relative magnitudes of the Coriolis forces and the viscous forces. If the Ekman number is large (that is, the viscous force dominates) then the predicted flow is identical to that which would exist in a stationary system. If, on the other hand, the Ekman number is small then the Coriolis force dominates and the component of flow in the direction of the axis of rotation can be much smaller in the rotating system than in a similar system at rest.     

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.     

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.     

Axisymmetric acoustophoresis for paper pulp concentration

In pulp and paper mills, mechanical processes such as screening and washing are commonly used to remove accumulated solid suspensions and concentrate the pulp. For environmental reasons and to optimize paper production, an emerging challenge is to develop alternative methods to concentrate paper pulp between 3 % and 6 % consistency for which the mixed pulp-water flow is complex. Among the proposed solutions in the literature, solutions based on acoustic levitation, also referred as acoustophoresis, of low-consistency pulp have been demonstrated as a potential solution for efficient pulp concentration and water recirculation. However, no sensitivity analysis on the ultrasound and physical parameters was proposed, limiting the extension to a realistic application. Thus, this paper presents a numerical modeling of acoustophoresis for pulp flow concentration in a pipe. For this purpose, the pulp flow is defined as a pseudo-homogenous fluid with a turbulent Low Re k- ∊ formalism, and the pulp particles are considered spherical and deflected by two acoustic forces, namely the acoustic radiation force and the Stokes drag force, both induced by an ultrasound wave generated along the walls of a circular pipe. The combined action of these two forces in the pulp flow enables to concentrate the particles at the center of the pipe. The influences of particle size and mechanical properties, fluid properties and ultrasound parameters are analyzed within a parametric study to optimize the particle deflection and the pulp concentration. The experimental feasibility of the industrial use of acoustophoresis for the concentration of paper pulp is demonstrated with a concentration gain up to 15 %.     

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.     

Scattering forces and electromagnetic momentum density in crossed circularly polarized standing waves

We analyze the forces on a small dipolar particle and the electromagnetic momentum density in a configuration consisting in two perpendicular circularly polarized stationary waves. The field distribution shows regions in which the electric and magnetic fields are parallel corresponding to a null Poynting vector. Although the average value of the momentum density, proportional to the Poynting vector, is zero in these regions, there are scattering forces acting on small particles due to light's spin force. The total scattering force suggests a new definition of the average value of the momentum density for free propagating electromagnetic fields.     

自由空间中球形粒子的负向声辐射力

针对一定声场作用下自由空间中的球形粒子,首先分析了声散射过程中的吸收声功率、散射声功率和损失声功率以及三者之间的关系,并通过计算发现了由于参数选取不当导致的负吸收现象。接着从动量守恒定律出发推导了声辐射力的一般表达式,阐释了声辐射力与声能流之间的关系,并从理论和计算两方面验证了负向声辐射力的存在。当负向声辐射力产生时,声波的背向散射被抑制。在此基础上,进一步研究了粒子的偏心特性和流体的黏度这两种常见因素对负向声辐射力的影响。利用球函数的加法公式推导了偏心球的散射系数和声辐射力公式,结果显示偏心距离、粒子的材料等都会显著改变负向声辐射力的产生条件。在低频近似下,由于流体黏度附加的正向声辐射力是否能完全抵消原来的负向声辐射力将决定最终的声辐射力方向。该结果对利用负向声辐射力制成单行波声学镊子来实现对特定粒子的操控有着理论指导意义。      

Scattering forces and electromagnetic momentum density in crossed circularly polarized standing waves

We analyze the forces on a small dipolar particle and the electromagnetic momentum density in a configuration consisting in two perpendicular circularly polarized stationary waves. The field distribution shows regions in which the electric and magnetic fields are parallel corresponding to a null Poynting vector. Although the average value of the momentum density, proportional to the Poynting vector, is zero in these regions, there are scattering forces acting on small particles due to light's spin force. The total scattering force suggests a new definition of the average value of the momentum density for free propagating electromagnetic fields.     

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.     

Performance of a quarter-wavelength particle concentrator

A series of devices have been investigated which use acoustic radiation forces to concentrate micron sized particles. These multi-layered resonators use a quarter-wavelength resonance in order to position an acoustic pressure node close to the top surface of a fluid layer such that particles migrate towards this surface. As flow-through devices, it is then possible to collect a concentrate of particulates by drawing off the particle stream and separating it from the clarified fluid and so can operate continuously as opposed to batch processes such as centrifugation. The methods of construction are described which include a micro-fabricated, wet-etched device and a modular device fabricated using a micro-mill. These use silicon and macor, a machinable glass ceramic, as a carrier layer between the transducer and fluid channel, respectively. Simulations using an acoustic impedance transfer model are used to determine the influence of various design parameters on the acoustic energy density within the fluid layer and the nodal position. Concentration tests have shown up to 4.4-, 6.0- and 3.2-fold increases in concentration for 9, 3 and 1 microm diameter polystyrene particles, respectively. The effect of voltage and fluid flow rates on concentration performance is investigated and helps demonstrate the various factors which determine the increase in concentration possible.     

湿颗粒堆力学特性的离散元法模拟研究

利用基于线性黏聚接触模型的离散元法对不同颗粒系统的堆积过程进行了数值模拟研究,分析了颗粒形状和湿颗粒间液桥力对颗粒堆积形态的影响机理,获得了球形和块状湿颗粒堆基底表面所受的法向力以及堆中颗粒间的法向力和切向力"中心凹陷"式的分布规律,讨论了颗粒形状和黏聚能量密度对基底表面作用力和颗粒间作用力的影响.研究结果表明,颗粒形状和液桥力对颗粒堆的堆积形态具有显著的影响.堆积角随着黏聚能量密度的增加而增大,并且相同条件下的块状颗粒堆积角大于球形颗粒.颗粒形状和黏聚能量密度对基底表面所受作用力和堆中颗粒间的作用力变化及最大幅值均有影响作用.当黏聚能量密度值逐渐增大时,颗粒堆的作用力最大幅值均逐渐增大,并且块状颗粒堆的作用力最大幅值大于球形颗粒堆.当黏聚能量密度值过大时,颗粒堆力学特性更加复杂,液桥力对颗粒堆积特性的影响作用大于颗粒形状的影响.     

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.     

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.     

Dynamic forces on agglomerated particles caused by high-intensity ultrasound

In this paper the acoustic forces on particles and agglomerates caused by high-intensity ultrasound in gaseous atmosphere are derived by means of computational fluid dynamics (CFD). Sound induced forces cause an oscillating stress scenario where the primary particles of an agglomerate are alternatingly pressed together and torn apart with the frequency of the applied wave. A comparison of the calculated acoustic forces with respect to the inter particle adhesion forces from Van-der-Waals and liquid bridge interactions reveals that the separation forces may reach the same order of magnitude for 80 μm sized SiO₂-particles. Hence, with finite probability acoustically agitated gases may de-agglomerate/disperse solid agglomerate structures. This effect is confirmed by dispersion experiments in an acoustic particle levitation setup.     

Using streamlines to visualize acoustic energy flow across boundaries

For spherical waves that radiate from a point source in a homogeneous fluid and propagate across a plane boundary into a dissimilar homogeneous fluid, the acoustic field may differ significantly from the geometric acoustic approximation if either the source or receiver is near the interface (in acoustic wavelengths) or if the stationary phase path is near the critical angle. In such cases, the entire acoustic field must be considered, including inhomogeneous waves associated with diffraction (i.e., those components that vanish with increasing frequency). The energy flow from a continuous-wave monopole point source across the boundary is visualized by tracing acoustic streamlines: those curves whose tangent at every point is parallel to the local acoustic intensity vector, averaged over a wave cycle. It is seen that the acoustic energy flow is not always in line with the "Snell's law" or stationary phase path. Also, plots of acoustic energy streamlines do not display unusual behavior in the vicinity of the critical angle. Finally, it is shown that there exists a law of refraction of acoustic energy streamlines at boundaries with density discontinuities analogous to Snell's law of refraction of ray paths across sound speed discontinuities. Examples include water-to-seabed transmission and water-to-air transmission.     

Finite element modeling of a microparticle manipulator

The contactless movement of microparticles and cells to known locations within a fluid volume is of interest in the fields of microtechnology and life sciences. A device which can position such inhomogeneities suspended in a fluid at multiple locations is described and modeled. The device consists of a thin fluid layer contained in a channel etched into a silicon wafer. Waves are excited by a macro-piezoelectric plate with electrodes on the top and bottom surfaces and, as a result, waves propagate into the adjacent fluid. The result is a pressure field throughout the fluidic volume. When an inhomogeneity in a fluid is exposed to an ultrasonic field the acoustic radiation force results; this is found by integrating the pressure over the surface of the particle, retaining second order terms, and taking the time average. Thus, due to the presence of a pressure field in the fluid in which the particles are suspended, a force field is created. The particles are then collected at the locations of the force potential minima. In the device described here, the force field is used to position particles into lines. The locations of the particles are predicted by using a finite element model of the system. The experimental and modeling results, presented here, are in good agreement.     

A theoretical study of the feasibility of acoustical tweezers: ray acoustics approach

The optical tweezer has been found to have many biomedical applications in trapping macromolecules and cells. For the trapping mechanism, there has to be a sharp spatial change in axial optical intensity and the particle size must be much greater than the wavelength. Similar phenomenon may exist in acoustics. This work was undertaken to demonstrate theoretically that it is possible to acoustically trap particles near the focal point where most of the acoustic energy is concentrated if certain conditions are met. Acoustic force exerted on a fluid particle in ultrasonic fields is analyzed in a ray acoustics regime where the wavelength of acoustic beam is much smaller than the size of the particle. In order to apply the acoustical tweezer to manipulating macromolecules and cells whose size is in the order of a few microns or less, a prerequisite is that the ultrasound wavelength has to be much smaller than a few microns. In this paper, the analysis is therefore based on the field pattern produced by a strongly focused 100 MHz ultrasonic transducer with Gaussian intensity distribution. For the realization of acoustic trapping, negative axial radiation force has to be generated to pull a particle towards a focus. The fat particle considered for acoustic trapping in this paper has an acoustic impedance of 1.4 MRayls. The magnitude of the acoustic axial radiation force that has been calculated as the size of the fat particle is varied from 8lambda to 14lambda. In addition, both Fresnel coefficients at various positions are also calculated to assess the interaction of reflection and refraction and their relative contribution to the effect of the acoustical tweezer. The simulation results show that the feasibility of the acoustical tweezer depends on both the degree of acoustic impedance mismatch and the degree of focusing relative to the particle size.     

Requirements on borehole radiators based on analytical estimation of radiated acoustic fields

Acoustic action on a productive stratum is one method for intensification of hydrocarbon mining. The physical mechanisms of acoustic action can be divided into two main groups: force and energy. The effect of any mechanism is associated with the structure and characteristics of the acoustic fields created by the radiation sources in the borehole. Therefore, the force and energy characteristics of the acoustic fields in the vicinity of a borehole are of high importance. These characteristics make it possible to estimate the prospects of applying the acoustic action under different conditions. The analytical estimates of the force and energy characteristics of the acoustic fields in the vicinity of a borehole are presented, and the requirements imposed on new-generation of borehole radiators are formulated on this basis, the use of which would help to more effectively develop deposits of highly viscous oils and residual gas condensates.