Nonlinear change of on-axis pressure and intensity maxima positions and its relation with the linear focal shift effect

A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f = 1 MHz, aperture radius a = 1.5 cm and geometrical focal distance R = 11.7 cm, corresponding to a Fresnel number N_F = 1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1 cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions.     

A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller-Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 mum diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.     

Dispersion and frequency dependent nonlinearity parameters in a graphite-epoxy composite

Longitudinal phase velocity and nonlinearity parameter have been measured as a function of frequency in the low megaHertz range in a laminate graphite-fiber-epoxy-resin composite. Amplitudes of both the fundamental and generated second harmonics were measured absolutely with a capacitive receiver. Phase velocity and nonlinearity parameter vary with frequency. The extent of the variance depends on the orientation of the fiber layers. Comparison is made between the nonlinear differential equation appropriate for crystals and a new equation that accounts for frequency dependence of phase velocity and nonlinearity parameter. The newer equation describes the data more accurately than the crystalline model does, but appears to require additional terms.     

Evolution of acoustic waves in microinhomogeneous media with quadratic elastic nonlinearity and relaxation

A nonlinear wave equation for the velocity “relaxator” is derived in the framework of the rheological model and the corresponding equation of state of a microinhomogeneous medium containing viscoelastic defects with quadratic nonlinear elasticity. The equation is qualitatively analyzed, and numerical solutions to it are presented for a stationary symmetric shock wave and the evolution of initially harmonic waves.     

The transmission of finite amplitude sound beam in multi-layered biological media

Based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, a model in the frequency domain is given to describe the transmission of finite amplitude sound beam in multi-layered biological media. Favorable agreement between the theoretical analyses and the measured results shows this approach could effectively describe the transmission of finite amplitude sound wave in multi-layered biological media.     

Numerical simulation of particle motion in an ultrasound field using the lattice Boltzmann model

In this paper we investigate the motion of small particles suspended in a fluid through which an ultrasound field is propagating. The application of the lattice Boltzmann model to this problem is considered using a two dimensional model. Particles in an ultrasound field are observed to move with a mean particle motion. Further, the time-averaged force on a fixed cylinder is computed and found to be in good agreement with a theoretical expression for the radiation force. Simulations are performed with a single particle, although the approach can equally be applied for a larger number of particles.     

Spatial confinement of ultrasonic force fields in microfluidic channels

We demonstrate and investigate multiple localized ultrasonic manipulation functions in series in microfluidic chips. The manipulation functions are based on spatially separated and confined ultrasonic primary radiation force fields, obtained by local matching of the resonance condition of the microfluidic channel. The channel segments are remotely actuated by the use of frequency-specific external transducers with refracting wedges placed on top of the chips. The force field in each channel segment is characterized by the use of micrometer-resolution particle image velocimetry (micro-PIV). The confinement of the ultrasonic fields during single- or dual-segment actuation, as well as the cross-talk between two adjacent fields, is characterized and quantified. Our results show that the field confinement typically scales with the acoustic wavelength, and that the cross-talk is insignificant between adjacent fields. The goal is to define design strategies for implementing several spatially separated ultrasonic manipulation functions in series for use in advanced particle or cell handling and processing applications. One such proof-of-concept application is demonstrated, where flow-through-mode operation of a chip with flow splitting elements is used for two-dimensional pre-alignment and addressable merging of particle tracks.     

Magnetic resonance imaging of acoustic streaming: absorption coefficient and acoustic field shape estimation

In this study, magnetic resonance imaging (MRI) is used to visualize acoustic streaming in liquids. A single-shot spin echo sequence (HASTE) with a saturation band perpendicular to the acoustic beam permits the acquisition of an instantaneous image of the flow due to the application of ultrasound. An average acoustic streaming velocity can be estimated from the MR images, from which the ultrasonic absorption coefficient and the bulk viscosity of different glycerol-water mixtures can be deduced. In the same way, this MRI method could be used to assess the acoustic field and time-average power of ultrasonic transducers in water (or other liquids with known physical properties), after calibration of a geometrical parameter that is dependent on the experimental setup.     

Translational instability of a spherical bubble in a standing ultrasound wave

Translational bubble dynamics is much less studied than the dynamics of radial bubble oscillation, while in many scientific and engineering applications the control of space location of cavitation bubbles is of great practical importance. This paper aims at the theoretical study of various aspects of the translational motion of a spherical gas bubble in a high-frequency standing wave. In particular, it is shown that the translational instability that gives rise to the reciprocal translation of a spherical bubble between the pressure antinode and the pressure node is caused by the hysteresis in the main resonance of the bubble. Different types of translational trajectories that can occur in a standing wave are illustrated by numerical simulations. A general classification of the observed translational trajectories is proposed.     

Mode-switching: A new technique for electronically varying the agglomeration position in an acoustic particle manipulator

Acoustic radiation forces offer a means of manipulating particles within a fluid. Much interest in recent years has focussed on the use of radiation forces in microfluidic (or “lab on a chip”) devices. Such devices are well matched to the use of ultrasonic standing waves in which the resonant dimensions of the chamber are smaller than the ultrasonic wavelength in use. However, such devices have typically been limited to moving particles to one or two predetermined planes, whose positions are determined by acoustic pressure nodes/anti-nodes set up in the ultrasonic standing wave. In most cases devices have been designed to move particles to either the centre or (more recently) the side of a flow channel using ultrasonic frequencies that produce a half or quarter wavelength over the channel, respectively.It is demonstrated here that by rapidly switching back and forth between half and quarter wavelength frequencies - mode-switching - a new agglomeration position is established that permits beads to be brought to any arbitrary point between the half and quarter-wave nodes. This new agglomeration position is effectively a position of stable equilibrium. This has many potential applications, particularly in cell sorting and manipulation. It should also enable precise control of agglomeration position to be maintained regardless of manufacturing tolerances, temperature variations, fluid medium characteristics and particle concentration.     

Real-Time Measurements and Modelling on Dynamic Behaviour of SonoVue Bubbles Based on Light Scattering Technology

The dynamic behaviour of SonoVue microbubbles, a new generation ultrasound contrast agent, is investigated in real time with light scattering method. Highly diluted SonoVue microbubbles are injected into a diluted gel made of xanthan gum and water. The responses of individual SonoVue bubbles to driven ultrasound pulses are measured. Both linear and nonlinear bubble oscillations are observed and the results suggest that SonoVue microbubbles can generate strong nonlinear responses. By fitting the experimental data of individual bubble responses with Sarkar＇s model, the shell coating parameter of the bubbles and dilatational viscosity is estimated to be 7.0 nm-s-Pa.     

Dynamic acoustic radiation force acting on cylindrical shells: theory and simulations

An object placed in an acoustic field is known to experience a force due to the transfer of momentum from the wave to the object itself. This force is known to be steady when the incident field is considered to be continuous with constant amplitude. One may define the dynamic (oscillatory) radiation force for a continuous wave-field whose intensity varies slowly with time. This paper extends the theory of the dynamic acoustic radiation force resulting from an amplitude-modulated progressive plane wave-field incident on solid cylinders to the case of solid cylindrical shells with particular emphasis on their thickness and contents of their hollow regions. A new factor corresponding to the dynamic radiation force is defined as Y(d) and stands for the dynamic radiation force per unit energy density and unit cross sectional surface. The results of numerical calculations are presented, indicating the ways in which the form of the dynamic radiation force function curves are affected by variations in the material mechanical parameters and by changes in the interior fluid inside the shell's hollow region. It was shown that the dynamic radiation force function Y(d) deviates from the static radiation force function for progressive waves Y(p) when the modulation frequency increases. These results indicate that the theory presented here is broader than the existing theory on cylinders.     

Space distribution of harmonic mode vibration amplitudes in nonlinear finite piezoelectric transducer

Nonlinear elastic vibrations of cylindrical piezoelectric transducers are investigated both experimentally and theoretically. A particular behaviour, that relates the space distribution of the fundamental mode vibration to those of the second and third harmonic components, is observed. A simplified physical interpretation of the phenomenon is given.     

Evanescent modes and anomalous streaming in a thermoacoustic device

An oil-heated thermoacoustic refrigerator was constructed in order to investigate the use of waste-heat sources to operate a refrigerator. Fluid flows within the resonator in the vicinity of the stack/heat exchanger assemblies were measured through optical means. During the course of the experiment, anomalous centerline steady flows were observed at magnitudes of up to three times the acoustic amplitudes within the resonator of the thermoacoustic device. An evanescent component of the acoustic field was also measured at the same location. An order of magnitude calculation indicates that the body force induced by the evanescent mode is of sufficient magnitude and structure to be the source of the streaming.     

Experimental and theoretical investigation of photoacoustic-signal generation by wavelength-modulated diode lasers

The dependence of photoacoustic spectra on different experimental parameters was investigated by both theoretical and experimental means. The experiments were carried out with an inexpensive resonant optoacoustic system based on near-infrared laser diodes, which allowed photoacoustic and direct absorption spectra to be recorded simultaneously. The experimental observations were compared to theoretical predictions. It was also demonstrated that source-frequency (wavelength) modulation at the resonance frequency of the cell provides superior signal to noise ratio compared to amplitude modulation and eliminates background drifts and fluctuations.     

Impact of acoustic pressure on ambient pressure estimation using ultrasound contrast agent

Local blood pressure measurements provide important information on the state of health of organs in the body and can be used to diagnose diseases in the heart, lungs, and kidneys. This paper presents an approach for investigating the ambient pressure sensitivity of a contrast agent using diagnostic ultrasound. The experimental setup resembles a realistic clinical setup utilizing a single array transducer for transmit and receive. The ambient pressure sensitivity of SonoVue (Bracco, Milano, Italy) was measured twice using two different acoustic driving pressures, which were selected based on a preliminary experiment. To compensate for variations in bubble response and to make the estimates more robust, the relation between the energy of the subharmonic and the fundamental component was chosen as a measure over the subharmonic peak amplitude. The preliminary study revealed the growth stage of the subharmonic component to occur at acoustic driving pressures between 300 and 500 kPa. Based on this, the pressure sensitivity was investigated using a driving pressure of 485 and 500 kPa. At 485 kPa, a linear pressure sensitivity of 0.42 dB/kPa was found having a linear correlation coefficient of 0.94. The second measurement series at 485 kPa showed a sensitivity of 0.41 dB/kPa with a correlation coefficient of 0.89. Based on the measurements at 500 kPa, this acoustic driving pressure was concluded to be too high causing the bubbles to be destroyed. The pressure sensitivity for these two measurement series were 0.42 and 0.25 dB/kPa with linear correlation coefficients of 0.98 and 0.93, respectively.     

The Rayleigh-Plesset equation in terms of volume with explicit shear losses

The most common nonlinear equation of motion for the damped pulsation of a spherical gas bubble in an infinite body of liquid is the Rayleigh-Plesset equation, expressed in terms of the dependency of the bubble radius on the conditions pertaining in the gas and liquid (the so-called ‘radius frame’). However over the past few decades several important analyses have been based on a heuristically derived small-amplitude expansion of the Rayleigh-Plesset equation which considers the bubble volume, instead of the radius, as the parameter of interest, and for which the dissipation term is not derived from first principles. So common is the use of this equation in some fields that the inherent differences between it and the ‘radius frame’ Rayleigh-Plesset equation are not emphasised, and it is important in comparing the results of the two equations to understand that they differ both in terms of damping, and in the extent to which they neglect higher order terms. This paper highlights these differences. Furthermore, it derives a ‘volume frame’ version of the Rayleigh-Plesset equation which contains exactly the same basic physics for dissipation, and retains terms to the same high order, as does the ‘radius frame’ Rayleigh-Plesset equation. Use of this equation will allow like-with-like comparisons between predictions in the two frames.     

Microfoam formation in a capillary

The ultrasound-induced formation of bubble clusters may be of interest as a therapeutic means. If the clusters behave as one entity, i.e., one mega-bubble, its ultrasonic manipulation towards a boundary is straightforward and quick. If the clusters can be forced to accumulate to a microfoam, entire vessels might be blocked on purpose using an ultrasound contrast agent and a sound source.In this paper, we analyse how ultrasound contrast agent clusters are formed in a capillary and what happens to the clusters if sonication is continued, using continuous driving frequencies in the range 1-10 MHz. Furthermore, we show high-speed camera footage of microbubble clustering phenomena.We observed the following stages of microfoam formation within a dense population of microbubbles before ultrasound arrival. After the sonication started, contrast microbubbles collided, forming small clusters, owing to secondary radiation forces. These clusters coalesced within the space of a quarter of the ultrasonic wavelength, owing to primary radiation forces. The resulting microfoams translated in the direction of the ultrasound field, hitting the capillary wall, also owing to primary radiation forces.We have demonstrated that as soon as the bubble clusters are formed and as long as they are in the sound field, they behave as one entity. At our acoustic settings, it takes seconds to force the bubble clusters to positions approximately a quarter wavelength apart. It also just takes seconds to drive the clusters towards the capillary wall.Subjecting an ultrasound contrast agent of given concentration to a continuous low-amplitude signal makes it cluster to a microfoam of known position and known size, allowing for sonic manipulation.     

Acoustic measurements and computational results on material specimens with harmonic variation of the cross section

The present work represents both an experimental and theoretical investigation of the behavior of finite cylindrical rods with harmonic variation of the cross section. The matrix method was used to compute the transfer power spectra of elastic rods with uniform circular cross section and of rods with harmonic variation of the cross section with distance. Theoretical and experimental results show that for a rod with periodical variation of the cross section, a new set of supplementary frequencies appear for which the transfer power coefficient has significant values, which are in relation with the space period of the inhomogeneity. Also, due to the radial component of the displacement certain modes are enhanced which satisfy boundary conditions on the surface and are obtained from the zeroes of Bessel functions.     

Experimental study of nonlinear acoustical effects in limestone

Results of an experimental and theoretical study of nonlinear acoustic effects (amplitude-dependent loss, resonance frequency shift, second and third harmonic generation, and sound by sound damping) in a limestone bar resonator are reported. The observed effects are analytically described in the framework of phenomenological equations of state with allowance for the low-frequency hysteretic nonlinearity and the high-frequency dissipative nonlinearity. Experimental and analytical dependences of nonlinear effects are compared to find the parameters of the hysteretic and dissipative nonlinearities of the limestone sample studied.