In acoustofluidic manipulation and sorting devices, Rayleigh streaming flows are typically found in addition to the acoustic radiation forces. However, experimental work from various groups has described acoustic streaming that occurs in planar devices in a plane parallel to the transducer face. This is typically a four-quadrant streaming pattern with the circulation parallel to the transducer. Understanding its origins is essential for creating designs that limit or control this phenomenon. The cause of this kind of streaming pattern has not been previously explained as it is different from the well-known classical streaming patterns such as Rayleigh streaming and Eckart streaming, whose circulation planes are generally perpendicular to the face of the acoustic transducer. In order to gain insight into these patterns we present a numerical method based on Nyborg's limiting velocity boundary condition that includes terms ignored in the Rayleigh analysis, and verify its predictions against experimental PIV results in a simple device. The results show that the modelled particle trajectories match those found experimentally. Analysis of the dominant terms in the driving equations shows that the origin of this kind of streaming pattern is related to the circulation of the acoustic intensity.

Ultrasonic treatment is an effective method for size refinement and dispersion of nanomaterials during their synthesis process. However, the quantitative relationship between ultrasonic conditions and particle size in the synthesis of metal nanoparticles has not been fully revealed. In this study, Cu nanoparticles were synthesized via the wet-chemical redox method under ultrasonic treatment, and statistical analysis on the evolution of particle size distribution was carried out. It was found that the particle size decreased exponentially with increasing ultrasonic power. A quantitative model was then proposed to describe the influence of ultrasonic power on the size distribution of metal nanoparticles from the perspective of the competition between the surface energy and the ultrasonic force. A relational expression of Rc∝γ47P-37 was revealed, and it was proved to fit well with the experimental results. Our study provides new experimental basis and theoretical method for understanding the mechanism of ultrasonic-induced size refinement of metal nanoparticles.

Numerical simulations of acoustic streaming flows can be used not only to explain the complex phenomena observed in acoustofluidic manipulation devices, but also to predict and optimise their performances. In this paper, two numerical methods based on perturbation theory are compared in order to demonstrate their viability and applicability for modelling boundary-driven streaming flows in acoustofluidic systems. It was found that the Reynolds stress method, which predicts the streaming fields from their driving terms, can effectively resolve both the inner and outer streaming fields and can be used to demonstrate the driving mechanisms of a broad range of boundary-driven streaming flows. However, computational efficiency typically limits its useful application to two-dimensional models. We highlight the close relationship between the classical boundary-driven streaming vortices and the rotationality of the Reynolds stress force field. The limiting velocity method, which ignores the acoustic boundary layer and solves the outer streaming fields by applying the ‘limiting velocities’ as boundary conditions, is more computationally efficient and can be used for predicting three-dimensional outer streaming fields and provide insight into their origins, provided that the radius of curvature of the channel surfaces is much greater than the acoustic boundary layer thickness (\(\delta_{v}\)). We also show that for the limiting velocity method to be valid the channel scales must exceed a value of approximately 100 \(\delta_{v}\) (for an error of ~5% on the streaming velocity magnitudes) for the case presented in this paper. Comparisons of these two numerical methods can provide effective guidance for researchers in the field of acoustofluidics on choosing appropriate methods to predict boundary-driven streaming fields in the design of acoustofluidic particle manipulation devices.

This article discusses three-dimensional (3D) boundary-driven streaming in acoustofluidic devices. Firstly, the 3D Rayleigh streaming pattern in a microchannel is simulated and its effect on the movement of microparticles of various sizes is demonstrated. The results obtained from this model show good comparisons with 3D experimental visualisations and demonstrate the fully 3D nature of the acoustic streaming field and the associated acoustophoretic motion of microparticles in acoustofluidic devices. This method is then applied to another acoustofluidic device in order to gain insights into an unusual in-plane streaming pattern. The origin of this streaming has not been fully described and its characteristics cannot be explained from the classical theory of Rayleigh streaming. The simulated in-plane streaming pattern was in good agreement with the experimental visualisation. The mechanism behind it is shown to be related to the active sound intensity field, which supports our previous findings on the mechanism of the in-plane acoustic streaming pattern visualised and modelled in a thin-layered capillary device.

While Chladni patterns in air over vibrating plates at macroscale have been well studied, inverse Chladni patterns in water at microscale have recently been reported. The underlying physics for the focusing of microparticles on the vibrating interface, however, is still unclear. In this paper, we present a quantitative three-dimensional study on the acoustophoretic motion of microparticles on a clamped vibrating circular plate in contact with water with emphasis on the roles of acoustic radiation and streaming-induced drag forces. The numerical simulations show good comparisons with experimental observations and basic theory. While we provide clear demonstrations of three-dimensional particle size-dependent microparticle trajectories in vibrating plate systems, we show that acoustic radiation forces are crucial for the formation of inverse Chladni patterns in liquids on both out-of-plane and in-plane microparticle movements. For out-of-plane microparticle acoustophoresis, out-of-plane acoustic radiation forces are the main driving force in the near-field, which prevent out-of-plane acoustic streaming vortices from dragging particles away from the vibrating interface. For in-plane acoustophoresis on the vibrating interface, acoustic streaming is not the only mechanism that carries microparticles to the vibrating antinodes forming inverse Chladni patterns: In-plane acoustic radiation forces could have a greater contribution. To facilitate the design of lab-on-a-chip devices for a wide range of applications, the effects of many key parameters, including the plate radius R and thickness h and the fluid viscosity μ, on the microparticle acoustophoresis are discussed, which show that the threshold in-plane and out-of-plane particle sizes balanced from the acoustic radiation and streaming-induced drag forces scale linearly with R and \(\sqrt \mu\), but inversely with \(\sqrt h\).

Classical Rayleigh streaming is well known and can be modelled using Nyborg’s limiting velocity method as driven by fluid velocities adjacent to the walls parallel to the axis of the main acoustic resonance. We have demonstrated previously the existence and the mechanism of four-quadrant transducer plane streaming patterns in thin-layered acoustofluidic devices which are driven by the limiting velocities on the walls perpendicular to the axis of the main acoustic propagation. We have recently found experimentally that there is a third case which resembles Rayleigh streaming but is a more complex pattern related to three-dimensional cavity modes of an enclosure. This streaming has vortex sizes related to the effective wavelength in each cavity axis of the modes which can be much larger than those found in the one-dimensional case with Rayleigh streaming. We will call this here modal Rayleigh-like streaming and show that it can be important in layered acoustofluidic manipulation devices. This paper seeks to establish the conditions under which each of these is dominant and shows how the limiting velocity field for each relates to different parts of the complex acoustic intensity patterns at the driving boundaries.