Acoustophoresis of disk-shaped microparticles: A numerical and experimental study of acoustic radiation forces and torques

Acoustic manipulation of multi-body structures and dynamics

Sound can exert forces on objects of any material and shape. This has made the contactless manipulation of objects by intense ultrasound a fascinating area of research with wide-ranging applications. While much is understood for acoustic forcing of individual objects, sound-mediated interactions among multiple objects at close range gives rise to a rich set of structures and dynamics that are less explored and have been emerging as a frontier for research. We introduce the basic mechanisms giving rise to sound-mediated interactions among rigid as well as deformable particles, focusing on the regime where the particles' size and spacing are much smaller than the sound wavelength. The interplay of secondary acoustic scattering, Bjerknes forces, and micro-streaming is discussed and the role of particle shape is highlighted. Furthermore, we present recent advances in characterizing non-conservative and non-pairwise additive contributions to the particle interactions, along with instabilities and active fluctuations. These excitations emerge at sufficiently strong sound energy density and can act as an effective temperature in otherwise athermal systems.

Willis Coupling-Induced Acoustic Radiation Force and Torque Reversal

Acoustic meta-atoms serve as the building blocks of metamaterials, with linear properties designed to achieve functions such as beam steering, cloaking, and focusing. They have also been used to shape the characteristics of incident acoustic fields, which led to the manipulation of acoustic radiation force and torque for development of acoustic tweezers with improved spatial resolution. However, acoustic radiation force and torque also depend on the shape of the object, which strongly affects its scattering properties. We show that by designing linear properties of an object using metamaterial concepts, the nonlinear acoustic effects of radiation force and torque can be controlled. Trapped objects are typically small compared with the wavelength, and are described as particles, inducing monopole and dipole scattering. We extend such models to a polarizability tensor including Willis coupling terms, as a measure of asymmetry, capturing the significance of geometrical features. We apply our model to a three-dimensional, subwavelength meta-atom with maximal Willis coupling, demonstrating that the force and the torque can be reversed relative to an equivalent symmetrical particle. By considering shape asymmetry in the acoustic radiation force and torque, Gorkov's fundamental theory of acoustophoresis is thereby extended. Asymmetrical shapes influence the acoustic fields by shifting the stable trapping location, highlighting a potential for tunable, shape-dependent particle sorting.

Acoustofluidics 24: theory and experimental measurements of acoustic interaction force

The motion of small objects in acoustophoresis depends on the acoustic radiation force and torque. These are nonlinear phenomena originating from wave scattering, and consist of primary and secondary components. The primary radiation force is the force acting on an object due to the incident field, in the absence of other objects. The secondary component, known as acoustic interaction force, accounts for the interaction among objects, and contributes to the clustering patterns of objects, as commonly observed in experiments. In this tutorial, the theory of acoustic interaction forces is presented using the force potential and partial-wave expansion approaches, and the distinguishing features of these forces such as rotational coupling and non-reciprocity are described. Theoretical results are compared to experimental measurements of interaction forces using a glass micro-capillary setup to explain the practical challenges. Finally, the phenomenon of clustering patterns induced by the close-range interaction of objects is demonstrated to point out the considerations about multiple collision and the predicted clustering patterns entirely due to the interaction force. Understanding the principles of acoustic interaction enables us to develop novel acoustofluidic applications beyond the typical processing of large populations of particles and with focus on the controlled manipulation of small clusters.

Influence of particle shape and material on the acoustic radiation force and microstreaming in a standing wave

In view of its influence on the acoustic radiation force, we investigate the microstreaming around a small solid elastic particle in an ultrasonic standing wave in dependence of its material properties and shape. The configuration is axisymmetric, making it accessible to numerical methods, such as the finite element method. The results reveal a transition from viscous scattering- to microstreaming-dominated acoustic radiation force that depends on the particle density. When a deviation of the particle shape from a sphere becomes smaller than the viscous boundary layer thickness, we show that the influence of the shape on the viscous contributions to the acoustic radiation force diminishes, allowing the use of theoretical models for a spherical particle. However, extreme asymmetric shape perturbations, such as crowns with sharp edges, can give rise to noticeable viscous contributions for a dense particle that is larger than the viscous boundary layer thickness. We also introduce a hybrid analytical model for the acoustic radiation force on a spherical particle that accounts for the microstreaming and particle compressibility and shows a good agreement with numerical simulations for an arbitrary particle size and density.

Acoustophoresis of a resonant elastic microparticle in a viscous fluid medium

This work presents three-dimensional (3D) numerical analysis of acoustic radiation force on an elastic microsphere suspended in a viscous fluid. Acoustophoresis of finite-sized, neutrally buoyant, nearly incompressible soft particles may improve by orders of magnitude and change directions when going through resonant vibrations. These findings offer the potential to manipulate and separate microparticles based on their resonance frequency. This concept has profound implications in cell and microparticle handling, 3D printing, and enrichment in lab-on-chip applications. The existing analytical body of work can predict spheroidal harmonics of an elastic sphere and acoustic radiation force based on monopole and dipole scatter in an ideal fluid. However, little attention is given to the complex interplay of resonant fluid and solid bodies that generate acoustic radiation. The finite element method is used to find resonant modes, damping factors, and acoustic forces of an elastic sphere subject to a standing acoustic wave. Under fundamental spheroidal modes, the radiation force fluctuates significantly around analytical values due to constructive or destructive scatter-incident wave interference. This suggests that for certain materials, relevant to acoustofluidic applications, particle resonances are an important scattering mechanism and design parameter. The 3D model may be applied to any number of particles regardless of geometry or background acoustic field.

Acoustically manipulating internal structure of disk-in-sphere endoskeletal droplets

Manipulation of micro/nano particles has been well studied and demonstrated by optical, electromagnetic, and acoustic approaches, or their combinations. Manipulation of internal structure of droplet/particle is rarely explored and remains challenging due to its complicated nature. Here we demonstrated the manipulation of internal structure of disk-in-sphere endoskeletal droplets using acoustic wave. We developed a model to investigate the physical mechanisms behind this interesting phenomenon. Theoretical analysis of the acoustic interactions indicated that these assembly dynamics arise from a balance of the primary and secondary radiation forces. Additionally, the disk orientation was found to change with acoustic driving frequency, which allowed on-demand, reversible adjustment of the disk orientations with respect to the substrate. This dynamic behavior leads to unique reversible arrangements of the endoskeletal droplets and their internal architecture, which may provide an avenue for directed assembly of novel hierarchical colloidal architectures and intracellular organelles or intra-organoid structures.

Endoskeletal droplets are a class of complex colloids containing a solid internal phase cast within a liquid emulsion droplet. Here, authors show acoustic manipulation of solid disks inside liquid droplets whose orientation can be externally controlled with the frequency.

Magnetically driven in-plane modulation of the 3D orientation of vertical ferromagnetic flakes

External magnetic fields are known to attract and orient magnetically responsive colloidal particles. In the case of 2D microplatelets, rotating magnetic fields are typically used to orient them parallel to each other in a brick-and-mortar fashion. Thanks to this microstructure, the resulting composites achieve enhanced mechanical and functional properties. However, parts with complex geometries require their microstructure to be specifically tuned and controlled locally in 3D. Although the tunability of the microstructure along the vertical direction has already been demonstrated using magnetic orientation combined with sequential or continuous casting, controlling the particle orientation in the horizontal plane in a fast and effective fashion remains challenging. Here, we propose to use rotating magnetic arrays to control the in-plane orientation of ferromagnetic nickel flakes distributed in curable polymeric matrices. We experimentally studied the orientation of the flakes in response to magnets rotating at various frequencies and precessing angles. Then, we used COMSOL to model the magnetic field from rotating magnetic arrays and predicted the resulting in-plane orientations. To validate the approach, we created composites with locally oriented flakes. This work could initiate reverse-engineering methods to design the microstructure in composite materials with intricate geometrical shapes for structural or functional applications.

Acoustic radiation force and radiation torque beyond particles: Effects of nonspherical shape and Willis coupling

Acoustophoresis mainly deals with the manipulation of subwavelength scatterers in an incident acoustic field. The geometric details of manipulated particles are often neglected by replacing them with equivalent symmetric geometries such as spheres, spheroids, cylinders, or disks. It has been demonstrated that geometric asymmetry, represented by Willis coupling terms, can strongly affect the scattering of a small object; hence neglecting these terms may miss important force contributions. In this work, we present a generalized formalism of acoustic radiation force and radiation torque based on the polarizability tensor, where Willis coupling terms are included to account for geometric asymmetry. Following Gorkov's approach, the effects of geometric asymmetry are explicitly formulated as additional terms in the radiation force and torque expressions. By breaking the symmetry of a sphere along one axis using intrusion and protrusion, we characterize the changes in the force and torque in terms of partial components, associated with the direct and Willis coupling coefficients of the polarizability tensor. We investigate the cases of standing and traveling plane waves and show how the equilibrium positions and angles are shifted by these additional terms. We show that while the contributions of asymmetry to the force are often negligible for small particles, these terms greatly affect the radiation torque. Our presented theory, providing a way of calculating radiation force and torque directly from polarizability coefficients, shows that it is essential to account for shape of objects undergoing acoustophoretic manipulation, with important implications for applications such as the manipulation of biological cells.

Mean acoustic fields exerted on a subwavelength axisymmetric particle

The acoustic radiation force produced by ultrasonic waves is the "workhorse" of particle manipulation in acoustofluidics. Nonspherical particles are also subjected to a mean torque known as the acoustic radiation torque. Together they constitute the mean acoustic fields exerted on the particle. Analytical methods alone cannot calculate these fields on arbitrarily shaped particles in actual fluids and are no longer fit for purpose. Here, a semi-analytical approach is introduced for handling subwavelength axisymmetric particles immersed in an isotropic Newtonian fluid. The obtained mean acoustic fields depend on the scattering coefficients that reflect the monopole and dipole modes. These coefficients are determined by numerically solving the scattering problem. Our method is benchmarked by comparison with the exact result for a subwavelength rigid sphere in water. Besides, a more realistic case of a red blood cell immersed in blood plasma under a standing ultrasonic wave is investigated with our methodology.

Bio-inspired Acousto-magnetic Microswarm Robots with Upstream Motility

The ability to propel against flows, i.e., to perform positive rheotaxis, can provide exciting opportunities for applications in targeted therapeutics and non-invasive surgery. To date, no biocompatible technologies exist for navigating microparticles upstream when they are in a background fluid flow. Inspired by many naturally- occurring microswimmers such as bacteria, spermatozoa, and plankton that utilize the non-slip boundary conditions of the wall to exhibit upstream propulsion, here, we report on the design and characterization of self-assembled microswarms that can execute upstream motility in a combination of external acoustic and magnetic fields. Both acoustic and magnetic fields are safe to humans, non-invasive, can penetrate deeply into the human body, and are well-developed in clinical settings. The combination of both fields can overcome the limitations encountered by single actuation methods. The design criteria of the acoustically-induced reaction force of the microswarms, which is needed to perform rolling-type motion, are discussed. We show quantitative agreement between experimental data and our model that captures the rolling behaviour. The upstream capability provides a design strategy for delivering small drug molecules to hard-to-reach sites and represents a fundamental step toward the realization of micro- and nanosystem-navigation against the blood flow.

Influence of the temperature on the opto-acoustophoretic effect

Opto-acoustophoretic mobility has been demonstrated recently for fluorescent and colored particles acoustically levitated in a stationary ultrasonic field when illuminated with the appropriate optical wavelength [Dumy, Hoyos, and Aider, J. Acoust. Soc. Am. 146, 4557-4568 (2019); Zhou, Gao, Yang, Li, Shao, Zhang, Li, and Li, Adv. Sci. 5, 1800122 (2018)]. It is a repeatable phenomenon, needing both acoustic trapping and specific optic excitation to occur. However, the physical origin of the phenomenon is still debated. In this study, we provide more insights into the probable origin of this phenomenon by confronting numerical simulations with temperature controlled experiments. The phenomenon properties are well reproduced by our model, relying on a thermofluidic instability, hinting at the potential thermally induced fluid density gradient as a drag source for the observed ejection of particles. Thermostated experiments exhibit a surprising threshold above which the phenomenon is not observed anymore no matter how large the optic or acoustic energies used. This exciting observation differs from the initial interpretation of the phenomenon, altering its potential application without removing its interest because it suggests the possible contactless generation of customized flows by acoustically trapped particles.

Acoustically modulated biomechanical stimulation for human cartilage tissue engineering

Bioacoustofluidics can be used to trap and levitate cells within a fluid channel, thereby facilitating scaffold-free tissue engineering in a 3D environment. In the present study, we have designed and characterised an acoustofluidic bioreactor platform, which applies acoustic forces to mechanically stimulate aggregates of human articular chondrocytes in long-term levitated culture. By varying the acoustic parameters (amplitude, frequency sweep, and sweep repetition rate), cells were stimulated by oscillatory fluid shear stresses, which were dynamically modulated at different sweep repetition rates (1-50 Hz). Furthermore, in combination with appropriate biochemical cues, the acoustic stimulation was tuned to engineer human cartilage constructs with structural and mechanical properties comparable to those of native human cartilage, as assessed by immunohistology and nano-indentation, respectively. The findings of this study demonstrate the capability of acoustofluidics to provide a tuneable biomechanical force for the culture and development of hyaline-like human cartilage constructs in vitro.

Acoustofluidic particle dynamics: Beyond the Rayleigh limit

In this work a numerical model to calculate the trajectories of multiple acoustically and hydrodynamically interacting spherical particles is presented. The acoustic forces are calculated by solving the fully coupled three-dimensional scattering problem using finite element software. The method is not restricted to single re-scattering events, mono- and dipole radiation, and long wavelengths with respect to the particle diameter, thus expanding current models. High frequency surface acoustic waves have been used in the one cell per well technology to focus individual cells in a two-dimensional wave-field. Sometimes the cells started forming clumps and it was not possible to focus on individual cells. Due to a lack of existing theory, this could not be fully investigated. Here, the authors use the full dynamic simulations to identify limiting factors of the one-cell-per-well technology. At first, the authors demonstrate good agreement of the numerical model with analytical results in the Rayleigh limiting case. A frequency dependent stability exchange between the pressure and velocity was then demonstrated. The numerical formulation presented in this work is relatively general and can be used for a multitude of different high frequency applications. It is a powerful tool in the analysis of microscale acoustofluidic devices and processes.

Controlled rotation and translation of spherical particles or living cells by surface acoustic waves

We show experimental evidence of the acoustically-assisted micromanipulation of small objects like solid particles or blood cells, combining rotation and translation, using high frequency surface acoustic waves. This was obtained from the leakage in a microfluidic channel of two standing waves arranged perpendicularly in a LiNbO₃ piezoelectric substrate working at 36.3 MHz. By controlling the phase lag between the emitters, we could, in addition to translation, generate a swirling motion of the emitting surface which, in turn, led to the rapid rotation of spherical polystyrene Janus beads suspended in the channel and of human red and white blood cells up to several rounds per second. We show that these revolution velocities are compatible with a torque caused by the acoustic streaming that develops at the particles surface, like that first described by [F. Busse et al., J. Acoust. Soc. Am., 1981, 69(6), 1634-1638]. This device, based on standard interdigitated transducers (IDTs) adjusted to emit at equal frequencies, opens a way to a large range of applications since it allows the simultaneous control of the translation and rotation of hard objects, as well as the investigation of the response of cells to shear stress.

Multibody dynamics in acoustophoresis

Determining the trajectories of multiple acoustically and hydrodynamically interacting as well as colliding particles is one of the challenges in numerical acoustophoresis. Although the acoustic forces between multiple small spherical particles can be obtained analytically, previous research did not address the particle-particle contacts in a rigorous way. This article extends existing methods by presenting an algorithm on displacement level which models the hard contacts using set-valued force laws, hence allowing for the first time the computation of a first approximation of complete trajectories of multiple hydrodynamically and acoustically interacting particles. This work uses a semi-analytical method to determine the acoustic forces, which is accurate up to the dipole contributions of the multipole expansion. The hydrodynamic interactions are modeled using the resistance and mobility functions of the Stokes' flow. In previous experimental work particles have been reported to interact acoustically, ultimately forming stacked lines near the pressure nodes of a standing wave. This phenomenon is examined experimentally and numerically, the simulation shows good agreement with the experimental results. To demonstrate the capabilities of the method, the rotation of a particle clump in two orthogonal waves is simulated. The presented method allows further insight in self-assembly applications and acoustic particle manipulation.