Acoustic levitation and high-resolution synchrotron X-ray powder diffraction: A fast screening approach of niclosamide amorphous solid dispersions.

The levitation of samples in an acoustic field has been of interest in the preparation and study of amorphous solid dispersions (ASD). Here, niclosamide-polymer solutions were levitated in a multi-emitter single-axis acoustic levitator and analyzed for 10 min at a High-resolution synchrotron X-ray powder diffraction beamline. This assembly enabled high-quality and fast time-resolved measurements with microliter sample size and measurement of solvent evaporation and recrystallization of niclosamide (NCL). Polymers HPMCP-55S, HPMCP-50, HPMCP-55, Klucel®, and poloxamers were not able to form amorphous dispersions with NCL. Plasdone® and Soluplus® demonstrated excellent properties to form NCL amorphous dispersions, with the last showing superior solubility enhancement. Furthermore, this fast levitation polymer screening showed good agreement with results obtained by conventional solvent evaporation screening evaluated for five days in a stability study, carried out at 40 °C/75% RH. The study showed that acoustic levitation and high-resolution synchrotron combination opens up a new horizon with great potential for accelerating ASD formulation screening and analysis.

Bandpass sorting of heterogeneous cells using a single surface acoustic wave transducer pair.

Separation and sorting of biological entities (viruses, bacteria, and cells) is a critical step in any microfluidic lab-on-a-chip device. Acoustofluidics platforms have demonstrated their ability to use physical characteristics of cells to perform label-free separation. Bandpass-type sorting methods of medium-sized entities from a mixture have been presented using acoustic techniques; however, they require multiple transducers, lack support for various target populations, can be sensitive to flow variations, or have not been verified for continuous flow sorting of biological cells. To our knowledge, this paper presents the first acoustic bandpass method that overcomes all these limitations and presents an inherently reconfigurable technique with a single transducer pair for stable continuous flow sorting of blood cells. The sorting method is first demonstrated for polystyrene particles of sizes 6, 10, and 14.5 µm in diameter with measured purity and efficiency coefficients above 75 ± 6% and 85 ± 9%, respectively. The sorting strategy was further validated in the separation of red blood cells from white blood cells and 1 µm polystyrene particles with 78 ± 8% efficiency and 74 ± 6% purity, respectively, at a flow rate of at least 1 µl/min, enabling to process finger prick blood samples within minutes.

Numerical Determination of the Secondary Acoustic Radiation Force on a Small Sphere in a Plane Standing Wave Field.

Two numerical methods based on the Finite Element Method are presented for calculating the secondary acoustic radiation force between interacting spherical particles. The first model only considers the acoustic waves scattering off a single particle, while the second model includes re-scattering effects between the two interacting spheres. The 2D axisymmetric simplified model combines the Gor'kov potential approach with acoustic simulations to find the interacting forces between two small compressible spheres in an inviscid fluid. The second model is based on 3D simulations of the acoustic field and uses the tensor integral method for direct calculation of the force. The results obtained by both models are compared with analytical equations, showing good agreement between them. The 2D and 3D models take, respectively, seconds and tens of seconds to achieve a convergence error of less than 1%. In comparison with previous models, the numerical methods presented herein can be easily implemented in commercial Finite Element software packages, where surface integrals are available, making it a suitable tool for investigating interparticle forces in acoustic manipulation devices.

Automatic contactless injection, transportation, merging, and ejection of droplets with a multifocal point acoustic levitator.

We present an acoustic levitation system that automatically injects, transports, merges and ejects liquid droplets in mid-air. The system consists of a phased array operating at 40 kHz on top of a plane reflector. The phase array generates multiple focal points at independent positions that form standing waves between the array and the reflector. In the reflector there is an inlet for a piezoelectric droplet injector which automatically inserts liquid droplets at the lower pressure nodes of the standing waves, and a hole that serves as an outlet for ejecting the processed droplets out of the system. Simulations of the acoustic radiation potential acting on the levitating droplets are in good agreement with the experiments. High-speed footage captured the functioning of the system in four fluidic operations: injection, transport, merging and ejection of liquid droplets. Having these operations integrated reliably into a single automatic system paves the way for the adoption of mid-air acoustophoretic processing in biological, chemical and pharmaceutical applications.

Particle separation by phase modulated surface acoustic waves.

High efficiency isolation of cells or particles from a heterogeneous mixture is a critical processing step in lab-on-a-chip devices. Acoustic techniques offer contactless and label-free manipulation, preserve viability of biological cells, and provide versatility as the applied electrical signal can be adapted to various scenarios. Conventional acoustic separation methods use time-of-flight and achieve separation up to distances of quarter wavelength with limited separation power due to slow gradients in the force. The method proposed here allows separation by half of the wavelength and can be extended by repeating the modulation pattern and can ensure maximum force acting on the particles. In this work, we propose an optimised phase modulation scheme for particle separation in a surface acoustic wave microfluidic device. An expression for the acoustic radiation force arising from the interaction between acoustic waves in the fluid was derived. We demonstrated, for the first time, that the expression of the acoustic radiation force differs in surface acoustic wave and bulk devices, due to the presence of a geometric scaling factor. Two phase modulation schemes are investigated theoretically and experimentally. Theoretical findings were experimentally validated for different mixtures of polystyrene particles confirming that the method offers high selectivity. A Monte-Carlo simulation enabled us to assess performance in real situations, including the effects of particle size variation and non-uniform acoustic field on sorting efficiency and purity, validating the ability to separate particles with high purity and high resolution.

Acoustic levitation of an object larger than the acoustic wavelength.

Levitation and manipulation of objects by sound waves have a wide range of applications in chemistry, biology, material sciences, and engineering. However, the current acoustic levitation techniques are mainly restricted to particles that are much smaller than the acoustic wavelength. In this work, it is shown that acoustic standing waves can be employed to stably levitate an object much larger than the acoustic wavelength in air. The levitation of a large slightly curved object weighting 2.3 g is demonstrated by using a device formed by two 25 kHz ultrasonic Langevin transducers connected to an aluminum plate. The sound wave emitted by the device provides a vertical acoustic radiation force to counteract gravity and a lateral restoring force that ensure horizontal stability to the levitated object. In order to understand the levitation stability, a numerical model based on the finite element method is used to determine the acoustic radiation force that acts on the object.

Development of an Acoustic Levitation Linear Transportation System Based on a Ring-Type Structure.

A linear acoustic levitation transportation system based on a ring-type vibrator is presented. The system is composed by two 21-kHz Langevin transducers connected to a ring-shaped structure formed by two semicircular sections and two flat plates. In this system, a flexural standing wave is generated along the ring structure, producing an acoustic standing wave between the vibrating ring and a plane reflector located at a distance of approximately a half wavelength from the ring. The acoustic standing wave in air has a series of pressure nodes, where small particles can be levitated and transported. The ring-type transportation system was designed and analyzed by using the finite element method. Additionally, a prototype was built and the acoustic levitation and transport of a small polystyrene particle was demonstrated.

Contactless Acoustic Manipulation and Sorting of Particles by Dynamic Acoustic Fields.

This paper presents a contactless, acoustic technique to manipulate and sort particles of varying size in both liquid and air media. An acoustic standing wave is generated by the superposition of counterpropagating waves emitted by two opposing emitters. The acoustic radiation force traps the smallest particles at the pressure nodes of the acoustic standing wave. The position of the particles can be manipulated by dynamically changing the phase difference between the two emitters. By applying a dynamic acoustic field (DAF), it is demonstrated that particles can be manipulated spatially and sorted according to size. The discrimination (sorting dynamic range) capability is initially demonstrated in liquid media by separating three different sets of polystyrene particles, ranging in size from 5 to 45µm in diameter. The separation between particles was performed up to a ratio of 5/6 in diameter (20% diameter difference). Finally, the scalability of the DAF method is demonstrated by sorting expanded polystyrene particles of 2 and 5 mm diameter in air.

Experimental study of the oscillation of spheres in an acoustic levitator.

The spontaneous oscillation of solid spheres in a single-axis acoustic levitator is experimentally investigated by using a high speed camera to record the position of the levitated sphere as a function of time. The oscillations in the axial and radial directions are systematically studied by changing the sphere density and the acoustic pressure amplitude. In order to interpret the experimental results, a simple model based on a spring-mass system is applied in the analysis of the sphere oscillatory behavior. This model requires the knowledge of the acoustic pressure distribution, which was obtained numerically by using a linear finite element method (FEM). Additionally, the linear acoustic pressure distribution obtained by FEM was compared with that measured with a laser Doppler vibrometer. The comparison between numerical and experimental pressure distributions shows good agreement for low values of pressure amplitude. When the pressure amplitude is increased, the acoustic pressure distribution becomes nonlinear, producing harmonics of the fundamental frequency. The experimental results of the spheres oscillations for low pressure amplitudes are consistent with the results predicted by the simple model based on a spring-mass system.

Nonlinear characterization of a single-axis acoustic levitator.

The nonlinear behavior of a 20.3 kHz single-axis acoustic levitator formed by a Langevin transducer with a concave radiating surface and a concave reflector is experimentally investigated. In this study, a laser Doppler vibrometer is applied to measure the nonlinear sound field in the air gap between the transducer and the reflector. Additionally, an electronic balance is used in the measurement of the acoustic radiation force on the reflector as a function of the distance between the transducer and the reflector. The experimental results show some effects that cannot be described by the linear acoustic theory, such as the jump phenomenon, harmonic generation, and the hysteresis effect. The influence of these nonlinear effects on the acoustic levitation of small particles is discussed.

Analysis of the particle stability in a new designed ultrasonic levitation device.

The use of acoustic levitation in the fields of analytical chemistry and in the containerless processing of materials requires a good stability of the levitated particle. However, spontaneous oscillations and rotation of the levitated particle have been reported in literature, which can reduce the applicability of the acoustic levitation technique. Aiming to reduce the particle oscillations, this paper presents the analysis of the particle stability in a new acoustic levitator device. The new acoustic levitator consists of a piezoelectric transducer with a concave radiating surface and a concave reflector. The analysis is conducted by determining numerically the axial and lateral forces that act on the levitated object and by measuring the oscillations of a sphere particle by a laser Doppler vibrometer. It is shown that the new levitator design allows to increase the lateral forces and reduce significantly the lateral oscillations of the levitated object.

Matrix method for acoustic levitation simulation.

A matrix method is presented for simulating acoustic levitators. A typical acoustic levitator consists of an ultrasonic transducer and a reflector. The matrix method is used to determine the potential for acoustic radiation force that acts on a small sphere in the standing wave field produced by the levitator. The method is based on the Rayleigh integral and it takes into account the multiple reflections that occur between the transducer and the reflector. The potential for acoustic radiation force obtained by the matrix method is validated by comparing the matrix method results with those obtained by the finite element method when using an axisymmetric model of a single-axis acoustic levitator. After validation, the method is applied in the simulation of a noncontact manipulation system consisting of two 37.9-kHz Langevin-type transducers and a plane reflector. The manipulation system allows control of the horizontal position of a small levitated sphere from -6 mm to 6 mm, which is done by changing the phase difference between the two transducers. The horizontal position of the sphere predicted by the matrix method agrees with the horizontal positions measured experimentally with a charge-coupled device camera. The main advantage of the matrix method is that it allows simulation of non-symmetric acoustic levitators without requiring much computational effort.

Identification of elastic, dielectric, and piezoelectric constants in piezoceramic disks.

Three-dimensional modeling of piezoelectric devices requires a precise knowledge of piezoelectric material parameters. The commonly used piezoelectric materials belong to the 6mm symmetry class, which have ten independent constants. In this work, a methodology to obtain precise material constants over a wide frequency band through finite element analysis of a piezoceramic disk is presented. Given an experimental electrical impedance curve and a first estimate for the piezoelectric material properties, the objective is to find the material properties that minimize the difference between the electrical impedance calculated by the finite element method and that obtained experimentally by an electrical impedance analyzer. The methodology consists of four basic steps: experimental measurement, identification of vibration modes and their sensitivity to material constants, a preliminary identification algorithm, and final refinement of the material constants using an optimization algorithm. The application of the methodology is exemplified using a hard lead zirconate titanate piezoceramic. The same methodology is applied to a soft piezoceramic. The errors in the identification of each parameter are statistically estimated in both cases, and are less than 0.6% for elastic constants, and less than 6.3% for dielectric and piezoelectric constants.

Finite element analysis and optimization of a single-axis acoustic levitator.

A finite element analysis and a parametric optimization of single-axis acoustic levitators are presented. The finite element method is used to simulate a levitator consisting of a Langevin ultrasonic transducer with a plane radiating surface and a plane reflector. The transducer electrical impedance, the transducer face displacement, and the acoustic radiation potential that acts on small spheres are determined by the finite element method. The numerical electrical impedance is compared with that acquired experimentally by an impedance analyzer, and the predicted displacement is compared with that obtained by a fiber-optic vibration sensor. The numerical acoustic radiation potential is verified experimentally by placing small spheres in the levitator. The same procedure is used to optimize a levitator consisting of a curved reflector and a concave-faced transducer. The numerical results show that the acoustic radiation force in the new levitator is enhanced 604 times compared with the levitator consisting of a plane transducer and a plane reflector. The optimized levitator is able to levitate 3, 2.5-mm diameter steel spheres with a power consumption of only 0.9 W.