Derivation of acoustical streaming equations for nonlinear and dispersive fluids

The equations of streaming generated by an acoustic mod propagating in a nonlinear dispersive medium (exhibiting absorption and dispersion of phase sound speed) are derived with an arbitrarily shaped incident acoustical field assumed. This field may be periodic or non-periodic. A general dispersion model represented by a convolution operator taking into account relaxation effects was taken into account. Making the assumption of a periodic acoustic field from the general streaming equation. The quasi-stationary flow is driven by a force given by the average value of the dispersion operator with respect to the velocity and acoustic pressure fields. In the spectral representation, it is given by the weighted spectral power density distribution of the acoustic field. The weight of the distribution is the dispersion coefficient - the eigenvalue of the dispersion operator. A new result also reveals the effect of the refractive index deviation on the driving force of streaming. The possibility of generalizing the description of streaming in the simplest case of a non-Newtonian fluid was analyzed. The Reiner-Revlin model of a simple liquid was assumed. It was also noted that the streaming model in the Maxwell liquid is analytically solvable. It was found that asymptotic states of streaming in this model and the Navier-Stokes model are identical. The derivations use new methods different from those used so far. They are based on the separation of nonlinear modes in the momentum transport equation and on the properties of the Gauss-Weierstrass function for the Fick diffusion operator. So far, the method of successive approximations has been used. The consistency of the obtained equations with the assumptions was checked. The obtained formulas generalize the known descriptions of the form of forces driving streaming and extend their application to the case of nonlinear propagation.

Analytical solution of the nonlinear equations of acoustic in the form of Gaussian beam

The nonlinear acoustics equation for a dissipative medium is analytically solved. Continuous wave stimulation and an axisymmetric Gaussian spatial profile of the boundary conditions were assumed. The approximation of the D'Alambert operator by the wave diffusion operator was applied and justified. In this approximation and assuming classical absorption (dispersion), the equation to be solved is presented by the Khokhlov-Zabolotskaya-Kuznetsov model. A sequence of functions describing the spatial distribution of the harmonic components of the disturbance was determined. They are the form of spatially modulated Gauss functions for harmonic wave numbers (frequencies). For a lossless medium a universal numerical sequence describing non-linear interactions and harmonic generations was determined. In other cases, the description of the cooperation of dispersion and non-linear interactions in the harmonic generation process is given by a sequence of functions dependent on the dispersion coefficient and with boundary values given by the universal sequence mentioned above. It was unexpectedly discovered that the influence of geometrical parameters of the beam on nonlinear interactions depends on dispersion, and component of the dispersion, absorption may strengthen harmonic generation. In general, dispersion spatially modulates the amplitude and phase of nonlinear interactions. This is not against the law of conservation of energy. The energy exchange between the fundamental (initiating) component and other harmonics is described. The analytical solution was compared with the numerical one. The numerical solution was obtained in the scheme implementing the full Helmholtz operator (no axial - wave diffusion- approximation).

Experimental and simulation study of harmonic components generated by plane and focused waves

Although there is increasing interest in the use of plane waves (PW) in high-frame-rate imaging, not much experimental data is available about their behavior in terms of nonlinear propagation. This paper presents a detailed study of fundamental and harmonic components of the ultrasound beam associated to PW transmission from a linear array. Simulations and hydrophone measurements of PW propagation in water were performed and compared to the results obtained for focused waves (FWs) at various levels of peak negative pressure (PNP). Experimental results confirm that, at comparable PNP, the amplitudes of the harmonics reached by PWs are always higher, over extended regions, than those achieved with FW. For example, at MI = 0.2 the PW second harmonic turns out to be 9 dB higher at 25 mm depth (i.e. in the focal region), and 20 dB higher at 40 mm depth. Simulations additionally show that when ultrasound waves propagate through blood or muscle, the situation is in general reversed but, at low MI, the second harmonic amplitude can still be higher in PW than in FW. Furthermore, it is shown that increasing the array aperture size yields higher harmonic growth in PW compared to FW.

Superharmonic Imaging for Medical Ultrasound: a Review

Ultrasound with harmonics has emerged as an exceptional alternative to competitively low resolution fundamental ultrasound imaging. The use of second harmonic is already a trend now but higher harmonics are also being seen as even better option due to its improved resolution. The resolution improved with frequency but achieves penetration of reduced energy. The cumulative addition of higher harmonics during propagation yields higher harmonics giving better resolution with adequate penetration. This paper summarizes the progress of such similar decade old harmonic ultrasound imaging technique i.e., superharmonic imaging (SHI) geared towards medical field. It comprises of harmonics higher than second harmonic preferably up to 5th harmonic. We conclude that SHI can be an advanced ultrasound imaging with comprehensive high resolution and adequate penetration depth on sole and coded modes.

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

We investigate the acoustic wave propagation in bubbly liquid inside a pilot sonochemical reactor which aims to produce antibacterial medical textile fabrics by coating the textile with ZnO or CuO nanoparticles. Computational models on acoustic propagation are developed in order to aid the design procedures. The acoustic pressure wave propagation in the sonoreactor is simulated by solving the Helmholtz equation using a meshless numerical method. The paper implements both the state-of-the-art linear model and a nonlinear wave propagation model recently introduced by Louisnard (2012), and presents a novel iterative solution procedure for the nonlinear propagation model which can be implemented using any numerical method and/or programming tool. Comparative results regarding both the linear and the nonlinear wave propagation are shown. Effects of bubble size distribution and bubble volume fraction on the acoustic wave propagation are discussed in detail. The simulations demonstrate that the nonlinear model successfully captures the realistic spatial distribution of the cavitation zones and the associated acoustic pressure amplitudes.