Acoustic Waves In Bubbly Liquids Research Articles

Numerical modelling and theoretical analysis of the acoustic attenuation in bubbly liquids

The propagations of acoustic waves in bubbly liquids have been extensively investigated through experimental and theoretical methods, a computational fluid dynamics (CFD) method was introduced to investigate the acoustic attenuation through bubbles in this study. Numerical ‘measurements’ of attenuation coefficient (α) and phase velocity (V) were conducted using a homogeneous cavitation model, which were modeled from experimental schemes and compared with the theoretical results. At extremely small bubble volume fraction (β around 10−11), new formulas of the theoretical α (αtheo) were proposed respectively for linear and transient oscillations, and a new formula of the numerical α (αnum) was proposed for transient oscillations. Results showed that αnum matched precisely with αtheo for linear, nonlinear and transient oscillations. At medium β (around 10−4), the relative difference of αnum between the VOF and present methods was less than 1.6%, while it reached 15.4% after replacing the bounded Keller-Miksis equation (KME) in the present method with the KME. However, the traditional theoretical α and V matched precisely with the predictions by the present method with the KME. Thus new theoretical α and V were proposed based on the bounded KME, and the relative differences between αtheo and αnum were less than 1%. It can be concluded that the bounded KME should be used in both numerical and theoretical predictions.

Derivation of Nonlinear Schrödinger Equation for Long-Range Propagation of Acoustic Waves in Bubbly Liquids with a Polydispersity of Bubble Size

Derivation of Nonlinear Schrödinger Equation for Long-Range Propagation of Acoustic Waves in Bubbly Liquids with a Polydispersity of Bubble Size

Influence of bubble distributions on the propagation of linear waves in polydisperse bubbly liquids.

The influence of the spatial distributions of bubbles on the propagation of linear acoustic waves in polydisperse bubbly liquids is studied. Using the diagrammatic approach, the effective wavenumber, which includes both spatial information and higher orders of multiple scattering, is presented. The phase speed and attenuation coefficient of acoustic waves in bubbly liquids are calculated from the effective wavenumber. A three-dimensional random model, the Generalized Matérn's hard-core point process, is used to close the model. Numerical simulations reveal that as the bubble volume fraction becomes larger so does the effect of the bubble distributions on the attenuation and phase speed. The irregular discrepancy between previously reported experimental results and the classical theory is attributed to the influence of bubble clustering on the propagation of linear waves. The comparison between the present model and the experimental measurements [Leroy, Strybulevych, Page, and Scanlon. (2011). Phys. Rev. E 83, 046605] reveals that the proposed correction term significantly improves the theoretical predictions.

Influences of non-uniform pressure field outside bubbles on the propagation of acoustic waves in dilute bubbly liquids

Predictions of the propagation of the acoustic waves in bubbly liquids is of great importance for bubble dynamics and related applications (e.g. sonochemistry, sonochemical reactor design, biomedical engineering). In the present paper, an approach for modeling the propagation of the acoustic waves in dilute bubbly liquids is proposed through considering the non-uniform pressure field outside the bubbles. This approach is validated through comparing with available experimental data in the literature. Comparing with the previous models, our approach mainly improves the predictions of the attenuation of acoustic waves in the regions with large kR0 (k is the wave number and R0 is the equilibrium bubble radius). Stability of the oscillating bubbles under acoustic excitation are also quantitatively discussed based on the analytical solution.

Effect of direct bubble-bubble interactions on linear-wave propagation in bubbly liquids.

We study the influence of bubble-bubble interactions on the propagation of linear acoustic waves in bubbly liquids. Using the full model proposed by Fuster and Colonius [J. Fluid Mech. 688, 253 (2011)], numerical simulations reveal that direct bubble-bubble interactions have an appreciable effect for frequencies above the natural resonance frequency of the average size bubble. Based on the new results, a modification of the classical wave propagation theory is proposed. The results obtained are in good agreement with previously reported experimental data where the classical linear theory systematically overpredicts the effective attenuation and phase velocity.

Acoustic waves in bubbly liquids for two kinds of gas bubbles with phase transitions

The propagation of acoustic waves in a mixture of liquid with vapor-gas bubbles is studied. The dispersed phase consists of two fractions of the bubbles differing on gas structure and radii (a two-fractional mixture). The phase transitions take place at each of the fractions. The volume content of the bubbles is the low (about 1%). The dispersion relation, unified for plane, cylindrical and spherical waves is obtained. It is shown that a presence of the second fraction in the structure of a disperse phase of the bubbles changes significantly a dispersion and a dissipation of acoustic waves.

Numerical simulations of three-dimensional nonlinear acoustic waves in bubbly liquids

This paper presents three-dimensional simulations of nonlinear propagation of ultrasonic waves through bubbly liquids, which represent the continuity of our previous works included in the numerical tool SNOW-BL. The behavior of three-dimensional nonlinear acoustic waves in bubbly liquids is analyzed by means of numerical predictions. Nonlinearity, attenuation, and dispersion due to the presence of bubbles in the liquid are taken into account. The numerical solution to the differential problem is obtained by means of a finite-difference scheme. The simulations we present here consider a homogeneous distribution of bubbles in the liquid. Results compare high and low-amplitude waves to detect the nonlinear effects of the bubbles. Results are shown for radiation and enclosure problems.

Some qualitative properties of solutions of the system governing acoustic waves in bubbly liquids

In this note we analyze some qualitative aspects of the solutions of the system of acoustic waves in bubbly liquids. In this sense we show uniqueness and continuous dependence of solutions for the general case. We also prove the exponential decay of solutions of the one-dimensional problem and a spatial decay estimate for the general three-dimensional case. We show how to extend the arguments and results to the case of the one-dimensional non-classical heat conduction in periodic heterogeneous materials.

On the propagation of harmonic acoustic waves in bubbly liquids

The propagation of harmonic acoustic waves in a half-space (i.e., x>0) filled with a viscous, isothermal bubbly liquid is studied. The exact solution to this problem, which corresponds to the compressible Stokes' second problem for the van Wijngaarden–Eringen equation, is obtained and an in-depth analytical and numerical investigation is carried out. Specifically, high- and low-frequency asymptotic results are given for the attenuation coefficient, the wave number, as well as several other propagation parameters, and special/limiting cases are noted. In addition, general features of the solution are illustrated via numerical computations. Most significantly, the analysis shows the following: (i) the attenuation coefficient and wave number are equal at the natural bubble frequency; (ii) the bubbly liquid exhibits anomalous dispersion; (iii) for high-frequencies, there exists a layer adjacent to x=0 that oscillates virtually in phase with the boundary (driving) motion; (iv) for low-frequencies, there exists a layer adjacent to x=0 that is essentially transparent to harmonic waves; (v) the penetration depth exhibits an absolute minimum.

Spatial trapping of acoustic waves in bubbly liquids

The propagation of acoustic waves in fluids containing low-density bubbles is investigated, using a plane wave approach. Band structures, densities of modes and density of energy maps are computed in order to understand the mechanisms responsible for the generation of complete frequency gaps in these three-dimensional structures. The dependence of the band gap on different parameters such as the mass density and the sound velocity for different symmetries is discussed. A large unit cell containing randomly placed bubbles shows, for optimized values of the parameters, a strong level of wave confinement and the appearance of wide gaps.

The effects of interfacial viscosity on the attenuation and phase speed of acoustic waves in bubbly liquids

The attenuation and phase speed of bubbly fluids have been shown to be highly dispersive due in part to the resonance response of individual bubbles. Surface-active materials, or surfactants, are known to dramatically alter the viscoelastic dynamics of an interface without affecting the bulk fluid properties. In this theoretical model the effects of surface viscosity on the propagation of linear pressure waves through a bubbly fluid are examined. The attenuation and phase speed are calculated for varying radii, void fraction, and interfacial viscosity for air bubbles in water. The results show an increase in attenuation for frequencies far removed from the bubble resonance for radii less than 100 microns. There is no significant increase in attenuation for larger bubbles (order 1 mm). Interestingly, near resonance, the interfacial viscous case has a lower attenuation than the clean interface, most likely due to the reduced radiation damping associated with smaller radial excursions. Likewise, resonance effects on the phase speed dispersion curve are also significantly diminished due to the interfacial viscosity. These results could be important for understanding propagation near the surface of the ocean, where surface-active materials can dramatically affect the dynamics of micron-sized bubbles and bubble distributions. [Work supported by ONR.]

Bulk viscidity model in acoustics of bubbly water-saturated soil

Recent experimental studies of acoustic wave propagation in water-saturated soil showed that the shock wave structure in the medium is similar to acoustic waves in bubbly liquids; namely, shock waves in the medium have an oscillating profile and strong attenuation of amplitude. The main physical reasons preventing the generalization of bubbly liquid acoustics in this case are that bubble expansion in unlimited space differs from bubble expansion in porous media, and the most delicate moment of this generalization is how to define the mixture pressure, what the mixture pressure is, and how it corresponds to pressure in the bubbles and relates to bubble dynamics. The goal of this communication is to show how to generalize the bubbly liquid acoustics in the water–bubbles–sand case with the help of the cell-model approach. The cell model is used for the Rayleigh equation derivation for a single bubble dynamics in a porous medium, and the governing equations for nonlinear acoustic waves are derived. The obtained canonical equations can explain some experimental data of three-phase media acoustics.

Stop bands in periodic and random media

In periodic media, frequency regions may exist at which no bounded at infinity solution of the wave equation exists. In random systems frequency regions may appear at which all bounded solutions are localized, i.e., decay exponentially at infinity. Both regions give rise to stop bands. Such stop bands appear easily for acoustic waves in bubbly liquids. They are also predicted to exist for elastic waves in binary composites consisting of gold or lead spherical inclusions periodically placed in a Si, Be, or SiO2 (for gold inclusions only) matrix and occupying about 10% of the volume. The midfrequency ωg of the stop band was found to satisfy the relation ωg=ycil/Ri, where cil is the longitudinal velocity in the inclusion material, Ri is the radius of each inclusion, and y is a number between 1 and 2.

Acoustic waves in bubbly liquids: (1) Can strong localization of waves be attained by internal resonances? (2) Acoustic wave propagation in one-dimensional stratified gas–liquid media: The different regimes

An inhomogeneous medium with scatterers presenting internalresonances has been suggested to be an efficient system to localize classical waves. Within a mean-field approach describing the internal degrees of freedom of the scatterers and their strong interactions in the near field regime, the existence of two longitudinal modes associated with the scatterers and embedding medium degrees of freedom is found. Anderson localization is shown to be reached in a rather large frequency interval for the ‘‘slow’’ mode, above the single scatterer resonant frequency, whereas the ‘‘fast’’ mode is never localized. An experimental situation is discussed where the localization of the ‘‘slow’’ mode could be observed. This work appeared in J. Phys. I France 2, 1861–1867 (1992). Also considered is the problem of the propagation of acoustic waves in a one-dimensional bubbly liquid, either periodic or random. The response of the bubbly liquid to an incident wave in any range of concentrations, bubble size polydispersity, and frequency range has been computed exactly. Three main regimes are found, depending on the average value of the bubble radius R, average distance d between bubbles, and wavelength λ in the liquid: (1) ‘‘phonon’’ or ‘‘mass-spring’’ regime; (2) ‘‘bubble’’ regime; and (3) ‘‘stratified’’ regime. In the random systems, the Anderson localization length is computed both numerically and analytically in the limit of uncorrelated disorder, for various system realizations.