Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation

Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed $c$ depending on position $\mathbf{r}$. In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path $\ell^*$, scattering phase function $f$ and anisotropy factor $g$. Discarding the operator term in the wave equation is shown to have a significant impact on $f$ and $g$, yet limited to the low-frequency regime i.e., when the correlation length of the disorder $\ell_c$ is smaller than or comparable to the wavelength $\lambda$. More surprisingly, discarding the operator part has a significant impact on the transport mean-free path $\ell^*$ whatever the frequency regime. When the scalar and operator terms have identical amplitudes, the discrepancy on the transport mean-free path is around $300\,\%$ in the low-frequency regime, and still above $30\,\%$ for $\ell_c/\lambda=10^3$ no matter how weak fluctuations of the disorder are. Analytical results are supported by numerical simulations of the wave equation and Monte Carlo simulations

Pince acoustique : piégeage et manipulation d'un objet par pression de radiation d'une onde progressive

As an acoustic wave impinges an obstacle, a mean force is exerted on its surface. This so-called radiation pressure arises from the non linear interaction between the wave and the object.The early history of this force did not suggest any application of such a feeble effect. Nevertheless, as technological advances improved the prospects of new powerful sound sources, it was rapidly considered to use the acoustic radiation pressure as a mean of non-contact manipulation of small objects. Ever since, standing wave schemes excited in cavities has been the preferred strategy that is becoming considerably popular.In the same time, the radiation pressure of light was also recognised to trap and manipulate very small objects. Using a single focused laser beam, optical tweezers brought a great dexterity to non contact manipulation techniques and rapidly grew to become a fundamental tool in many scientific fields. However, the minuteness of the force, the high intensities required and the smallness of trappable objects are well-known limitations in particular for biological applications.Although optics and acoustics have shown many similarities, an acoustical analogue to optical tweezers using a single beam is yet to be demonstrated. Theoretical and experimental efforts are presented here and shed light on the underpinning mechanisms of single-beam acoustical tweezers. The analysis of a peculiar beam's radiation pressure, i.e. acoustical vortices, unveiled new characteristics for single-beam trapping. Our experimental demonstration along with the low intensities required and the large forces developed show promise for a wide spectrum of new scientific applications.La pression de radiation acoustique est la force moyenne qu'une onde peut exercer sur un obstacle. Initialement, la faible manifestation de cette force ne suggérait pas d'applications potentielles. Néanmoins, avec l'avènement de sources acoustiques de haute puissance, il a rapidement été envisagé de manipuler de petits objets à distance par pression de radiation. Depuis, c'est via l'excitation d'ondes stationnaires dans des cavités que cette méthodologie connait son essor. Parallèlement, la pression de radiation de la lumière a rapidement permis de piéger et de manipuler des petits objets. Grâce à un laser fortement focalisé, la pince optique a donné une grande flexibilité aux techniques de manipulation sans contact et est devenue un outil fondamental pour de nombreuses disciplines scientifiques. Cependant, les faibles forces développées, les importantes intensités lumineuses requises et la petite taille des objets sont d'importantes limites tout particulièrement pour leur application en biologie.A l'heure actuelle, il n'existe pas l'équivalent de la pince optique en acoustique utilisant un unique faisceau. Le travail présenté donne un ensemble d'éléments théoriques et expérimentaux profitables pour la compréhension de la pression de radiation en acoustique et le dimensionnement d'une pince acoustique utilisant un unique faisceau ultrasonore : le vortex acoustique. Ce travail esquisse l'ébauche d'une nouvelle méthode de manipulation sans contact donnant une véritable dextérité de préhension. Les faibles intensités nécessaires associées aux larges forces développées sauront se montrer attractives pour imaginer un large panel de nouvelles applications scientifiques

Spiral-shaped scattered field from incident evanescent acoustic waves on a Mie Particle

We consider theoretically the scattering of an incident evanescent plane wave by a spherical particle. The scattering problem is treated in a classic way by applying the T- matrix formalism and the resulting field is expressed on the basis of the different vibration modes of the particle. Compared to the case of a homogeneous plane incident wave, additional azimuthal scattered modes are excited and their contribution provokes a symmetry breaking of the field. Importantly, if a mode is preferentially excited by choosing the corresponding reduced frequency, the scattered radiation exhibits a spiral structure. The scattered field has a rotating phase around the scatterer which comes from the formation of spiral scattered waves and this effect is accentuated by increasing the evanescence degree of the incident wave. These results could have important implications for the contactless manipulation of objects with acoustic radiation forces and torques

Particle-Size Effect in Airborne Standing-Wave Acoustic Levitation: Trapping Particles at Pressure Antinodes

It is well known that a particle put into an ultrasonic standing wave tends to move towards an equilibrium position, where the acoustic pressure-induced force on its surface compensates the particle weight. We demonstrate, by means of a full three-dimensional numerical analysis and a thorough experimental study, that the acoustic force, and thus the particle’s behavior, critically depends on its size. While particles within certain size ranges, including those smaller than half the wavelength, are trapped on axis around the pressure nodes, particles in other size ranges are trapped off axis nearby the pressure antinodes. This behavior, related with sign inversions of the radiation force, implies that the magnitude of the force, and thus the trapping stiffness, can be maximum or null for some specific sizes. As a case of study, we analyze expanded polystyrene particles levitated in air with an ultrasonic frequency of 40 kHz, a relevant system due to recent applications for the development of volumetric displays. Yet, our results illustrate a general behavior of radiation-based traps with structured wave fields

Genetically encoded nanostructures enable acoustic manipulation of engineered cells

The ability to mechanically manipulate and control the spatial arrangement of biological materials is a critical capability in biomedicine and synthetic biology. Ultrasound has the ability to manipulate objects with high spatial and temporal precision via acoustic radiation force, but has not been used to directly control biomolecules or genetically defined cells. Here, we show that gas vesicles (GVs), a unique class of genetically encoded gas-filled protein nanostructures, can be directly manipulated and patterned by ultrasound and enable acoustic control of genetically engineered GV-expressing cells. Due to their differential density and compressibility relative to water, GVs experience sufficient acoustic radiation force to allow these biomolecules to be moved with acoustic standing waves, as demonstrated within microfluidic devices. Engineered variants of GVs differing in their mechanical properties enable multiplexed actuation and act as sensors of acoustic pressure. Furthermore, when expressed inside genetically engineered bacterial cells, GVs enable these cells to be selectively manipulated with sound waves, allowing patterning, focal trapping and translation with acoustic fields. This work establishes the first genetically encoded nanomaterial compatible with acoustic manipulation, enabling molecular and cellular control in a broad range of contexts

A volumetric display for visual, tactile and audio presentation using acoustic trapping

Science-fiction movies such as Star Wars portray volumetric systems that not only provide visual but also tactile and audible 3D content. Displays, based on swept volume surfaces, holography, optophoretics, plasmonics, or lenticular lenslets, can create 3D visual content without the need for glasses or additional instrumentation. However, they are slow, have limited persistence of vision (POV) capabilities, and, most critically, rely on operating principles that cannot also produce tactile and auditive content. Here, we present for the first time a Multimodal Acoustic Trap Display (MATD): a mid-air volumetric display that can simultaneously deliver visual, auditory, and tactile content, using acoustophoresis as the single operating principle. Our system acoustically traps a particle and illuminates it with red, green, and blue light to control its colour as it quickly scans through our display volume. Using time multiplexing with a secondary trap, amplitude modulation and phase minimization, the MATD delivers simultaneous auditive and tactile content. The system demonstrates particle speeds of up to 8.75m/s and 3.75m/s in the vertical and horizontal directions respectively, offering particle manipulation capabilities superior to other optical or acoustic approaches demonstrated to date. Beyond enabling simultaneous visual, tactile and auditive content, our approach and techniques offer opportunities for non-contact, high-speed manipulation of matter, with applications in computational fabrication and biomedicine

Standing waves for acoustic levitation

Standing waves are the most popular method to achieve acoustic trapping. Particles with greater acoustic impedance than the propagation medium will be trapped at the pressure nodes of a standing wave. Acoustic trapping can be used to hold particles of various materials and sizes, without the need of a close-loop controlling system. Acoustic levitation is a helpful and versatile tool for biomaterials and chemistry, with applications in spectroscopy and lab-on-a-droplet procedures. In this chapter, multiple methods are presented to simulate the acoustic field generated by one or multiple emitters. From the acoustic field, models such as the Gor'kov potential or the Flux Integral are applied to calculate the force exerted on the levitated particles. The position and angle of the acoustic emitters play a fundamental role, thus we analyse commonly used configurations such as emitter and reflector, two opposed emitters, or arrangements using phased arrays

Acoustical tweezers : trapping and manipulation of small objects with the radiation pressure of progressive sound waves

La pression de radiation acoustique est la force moyenne qu'une onde peut exercer sur un obstacle. Initialement, la faible manifestation de cette force ne suggérait pas d'applications potentielles. Néanmoins, avec l'avènement de sources acoustiques de haute puissance, il a rapidement été envisagé de manipuler de petits objets à distance par pression de radiation. Depuis, c'est via l'excitation d'ondes stationnaires dans des cavités que cette méthodologie connait son essor. Parallèlement, la pression de radiation de la lumière a rapidement permis de piéger et de manipuler des petits objets. Grâce à un laser fortement focalisé, la pince optique a donné une grande flexibilité aux techniques de manipulation sans contact et est devenue un outil fondamental pour de nombreuses disciplines scientifiques. Cependant, les faibles forces développées, les importantes intensités lumineuses requises et la petite taille des objets sont d'importantes limites tout particulièrement pour leur application en biologie.A l'heure actuelle, il n'existe pas l'équivalent de la pince optique en acoustique utilisant un unique faisceau. Le travail présenté donne un ensemble d'éléments théoriques et expérimentaux profitables pour la compréhension de la pression de radiation en acoustique et le dimensionnement d'une pince acoustique utilisant un unique faisceau ultrasonore : le vortex acoustique. Ce travail esquisse l'ébauche d'une nouvelle méthode de manipulation sans contact donnant une véritable dextérité de préhension. Les faibles intensités nécessaires associées aux larges forces développées sauront se montrer attractives pour imaginer un large panel de nouvelles applications scientifiques.As an acoustic wave impinges an obstacle, a mean force is exerted on its surface. This so-called radiation pressure arises from the non linear interaction between the wave and the object.The early history of this force did not suggest any application of such a feeble effect. Nevertheless, as technological advances improved the prospects of new powerful sound sources, it was rapidly considered to use the acoustic radiation pressure as a mean of non-contact manipulation of small objects. Ever since, standing wave schemes excited in cavities has been the preferred strategy that is becoming considerably popular.In the same time, the radiation pressure of light was also recognised to trap and manipulate very small objects. Using a single focused laser beam, optical tweezers brought a great dexterity to non contact manipulation techniques and rapidly grew to become a fundamental tool in many scientific fields. However, the minuteness of the force, the high intensities required and the smallness of trappable objects are well-known limitations in particular for biological applications.Although optics and acoustics have shown many similarities, an acoustical analogue to optical tweezers using a single beam is yet to be demonstrated. Theoretical and experimental efforts are presented here and shed light on the underpinning mechanisms of single-beam acoustical tweezers. The analysis of a peculiar beam's radiation pressure, i.e. acoustical vortices, unveiled new characteristics for single-beam trapping. Our experimental demonstration along with the low intensities required and the large forces developed show promise for a wide spectrum of new scientific applications