Sound propagation in saturated gas–vapor–droplet suspensions considering the effect of transpiration on droplet evaporation

The sound attenuation and dispersion in saturated gas–vapor–droplet mixtures with evaporation has been investigated theoretically. The theory is based on an extension of the work of Davidson (1975) to accommodate the effects of transpiration on the linear particle relaxation processes of mass, momentum and energy transfer. It is shown that the inclusion of transpiration in the presence of mass transfer improves the agreement between the theory and the experimental data of Cole and Dobbins (1971) for sound attenuation in air–water fogs at low droplet mass concentrations. The results suggest that transpiration has an appreciable effect on both sound absorption and dispersion for both low and high droplet mass concentrations.     

Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller's method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.     

Absorption and velocity dispersion due to crystallization and melting of emulsion droplets

The influence of droplet crystallization and melting on the ultrasonic properties of oil-in-water emulsions has been investigated. The ultrasonic velocity and attenuation were measured in a series of 3 wt% n-hexadecane-in-water emulsions as a function of frequency (0.3–4 MHz), droplet diameter (0.4 and 1 μm) and temperature (0–25°C). The emulsified n-hexadecane crystallized at about 5°C due to supercooling effects and melted at about 18°C. As solid and liquid n-hexadecane have significantly different ultrasonic properties, an appreciable change in the velocity and attenuation is observed during the phase transition. This behaviour is modified significantly in systems where the emulsion droplets are partially crystalline because the temperature fluctuations associated with the ultrasonic wave can perturb the phase equilibria solid liquid causing excess attenuation and velocity dispersion. The magnitude of this effect depends on the ultrasonic frequency and the average droplet size.     

Negative dispersion in bone: the role of interference in measurements of the apparent phase velocity of two temporally overlapping signals

In this study the attenuation coefficient and dispersion (frequency dependence of phase velocity) are measured using a phase sensitive (piezoelectric) receiver in a phantom in which two temporally overlapping signals are detected, analogous to the fast and slow waves typically found in measurements of cancellous bone. The phantom consisted of a flat and parallel Plexiglas plate into which a step discontinuity was milled. The phase velocity and attenuation coefficient of the plate were measured using both broadband and narrowband data and were calculated using standard magnitude and phase spectroscopy techniques. The observed frequency dependence of the phase velocity and attenuation coefficient exhibit significant changes in their frequency dependences as the interrogating ultrasonic field is translated across the step discontinuity of the plate. Negative dispersion is observed at specific spatial locations of the plate at which the attenuation coefficient rises linearly with frequency, a behavior analogous to that of bone measurements reported in the literature. For all sites investigated, broadband and narrowband data (3-7 MHz) demonstrate excellent consistency. Evidence suggests that the interference between the two signals simultaneously reaching the phase sensitive piezoelectric receiver is responsible for this negative dispersion.     

Observation of Diffusion Process of a Water Droplet Immersed in Protein Solution in Microgravity

Pure liquid-liquid diffusion driven by concentration gradients is hard to study in a normal gravity environment since convection and sedimentation also contribute to the mass transfer process. We employ a Math Zehnder interferometer to monitor the mass transfer process of a water droplet in EAFP protein solution under micro- gravity condition provided by the Satellite Shi Jian No 8, A series of the evolution charts of mass distribution during the diffusion process of the liquid droplet are presented and the relevant diffusion coefficient is determined.     

Dispersion characteristics of surface magnetostatic waves with dissipation

It is shown that unlike undamped waves, the dispersion characteristics of spin surface waves with dissipation have a maximum wave number at which there is a downward reversal in the dispersion curve of a wave number. This forms the upper branch of a dispersion curve with inverse dispersion and high attenuation, leading to an unclear frequency dependence of the wave vector. The lower primary dispersion branch corresponds to waves with forward dispersion, and attenuation is proportional to the small parameter of dissipation. However, the coefficient of wave attenuation grows sharply near the maximum wave number. Some angular and frequency limits of surface wave propagation change as well.     

Spectral transparency and microstructure of artificial mists

The results of the final stage of comprehensive investigations of the spectral transparency of artifical mists are reported. Preliminary results had been published by us earlier in [1, 2]. On the basis of a mass of experimental statistical data, a final comparison is made between the results of calculating the attenuation coefficients of the aerosol component of clouds and mists according to the method proposed in [2], with the results of obtaining the same coefficients by experimental determination in an artificial cloud chamber. Satisfactory agreement was obtained between calculated and measured values of the relative attenuation coefficients. It is suggested that the considerable divergence between calculated and experimental data on absolute attenuation coefficients is due to a systematic understatement of the droplet concentration value which was determined by means of a flow collector.     

Interrelation of optical and microstructural characteristics of mists

This work was undertaken to explain a discrepancy between values of the absolute attenuation coefficient calculated using the microstructure data from a flow collector, and those from measurements by a photometer.On the basis of a great many experiments, it has been demonstrated that these discrepancies were caused by a systematic understating of the value of absolute droplet concentration determined by the flow collector. It was also shown that the flow collector, while distorting the absolute droplet concentration data under the given conditions, determines quite accurately the drop size distribution function.     

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.     

Wave propagation in 2D elastic composites with partially debonded fibres by the null field approach

Time-harmonic plane wave propagation in a two-dimensional (2D) elastic matrix with partially debonded elastic fibres of nonclassical cross-section is investigated. The modified null field approach, taking into account the asymptotic behaviour of the solution at the interface crack-tips, is exploited to obtain the numerical results for a single scatterer. The effective medium approach based on Foldy's approximation is applied to estimate the average dynamic parameters of the composites containing randomly distributed partially debonded fibres of dilute concentration. Numerical results concern the longitudinal wave dispersion and attenuation owing to scattering by both randomly oriented and aligned fibres. The effects of the fibre shape, debonding (interface crack) size and direction of wave incidence on the effective P-wave velocity and attenuation coefficient are analysed.     

Finite-bandwidth effects on the causal prediction of ultrasonic attenuation of the power-law form

Kramers-Kronig (K-K) relations exist as a consequence of causality, placing nonlocal constraints on the relationship between dispersion and absorption. The finite-bandwidth method of applying these relations is examined where the K-K integrals are restricted to the spectrum of the experimental data. These finite-bandwidth K-K relations are known to work with resonant-type data and here are applied to dispersion data consistent with a power-law attenuation coefficient (exponent from 1 to 2). Bandwidth-restricted forms of the zero and once-subtracted K-K relations are used to determine the attenuation coefficient from phase velocity. Analytically, it is shown that these transforms produce the proper power-law form of the attenuation coefficient as a stand-alone term summed with artifacts that are dependent on the integration limits. Calculations are performed to demonstrate how these finite-bandwidth artifacts affect the K-K predictions under a variety of conditions. The predictions are studied in a local context as a function of subtraction frequency, bandwidth, and power-law exponent. The K-K predictions of the power-law exponent within various decades of the spectrum are also examined. In general, the agreement between finite-bandwidth K-K predictions and exact values grows as the power-law exponent approaches 1 and with increasing bandwidth.     

The theory of droplet diffusiophoresis for concentrated solutions

The theoretical diffusiophoresis velocity is obtained for a droplet of a concentrated solution suspended in a binary gaseous mixture. The droplet is characterized by a high thermal conductivity. The droplet radius is assumed to be much greater than the mean free path for gaseous-mixture molecules. One of the gaseous-mixture molecular components is the vapor of the droplet solvent. According to the formula obtained in this study, the droplet is driven toward lower concentration of the volatile gaseous-mixture component by diffusive slip and in the opposite direction by phase transition. An increase in the relative mass concentration of the volatile solvent in the droplet enhances effects associated with the dependence of surface tension on the volatile-component concentration and the reactive transport due to the surface nonuniformity of phase transition. As the relative mass concentration of the volatile solvent in the droplet approaches unity, the effect of diffusive slip tends to vanish.     

Spectral dispersion of cloud droplet size distributions and radar threshold reflectivity for drizzle

From first principles, we find that the radar threshold reflectivity between nonprecipitating clouds and precipitating clouds is strongly related to not only the cloud droplet number concentration but also the spectral dispersion of cloud droplet size distributions. The further investigation indicates that the threshold value is an increasing function of spectral dispersion and cloud droplet number concentration. These results may improve our understanding of the cloud-precipitation interaction and the aerosol indirect effect.     

A modified warping operator based on BDRM theory in homogeneous shallow water

In this paper, a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode (BDRM) theory is presented. According to the BDRM theory, the contribution of the beam displacement and the time delay to the group velocity can be easily considered in a shallow water waveguide. A more accurate dispersion formula is derived by using the cycle distance formula to calculate the group velocity of normal modes. The derived dispersion formula can be applied to the homogeneous shallow water waveguide. Theoretically, the formula is related to the phase of the reflection coefficient and suitable for various bottom models. Furthermore, based on the derived dispersion relation, the modified warping operator is developed to obtain linear modal structures. For the Pekeris model, the formulae for the phase of the reflection coefficient are derived in this work. By taking account of the effect of the bottom attenuation on the reflection coefficient, the formula for the phase of the reflection coefficient including the bottom attenuation is obtained for the Pekeris model with a lossy bottom. Performance and accuracy of different formulae are evaluated and compared. The numerical simulations indicate that the derived dispersion formulae and the modified warping operator are more accurate.     

Propagation of SH-wave in a corrugated viscous sandy layer sandwiched between two elastic half-spaces

The present paper attempts to investigate the effect of sandiness, corrugated boundary surfaces, heterogeneity, and gravity on phase velocity and attenuation of SH-wave propagating in a viscous sandy layer with corrugated upper and lower boundary surfaces sandwiched between an upper heterogeneous elastic half-space and lower viscoelastic half-space under gravity. Heterogeneity associated with the upper half-space is due to exponentially varying density which is a function of depth; but the rigidity is constant. The closed form of dispersion relation is established and found to be in complex form. Real part and imaginary part of the dispersion relation correspond to dispersion curve and attenuation curve, respectively. One of the salient points of present study is the use of DEBYE asymptotic expansion to establish that the obtained dispersion relation is in well-agreement with the classical Love wave equation in isotropic case. The effect of presence and absence of corrugated boundary surfaces, measured by initial flatness parameter, on dispersion and attenuation curves have been meticulously examined. Moreover, the substantial effect of heterogeneity, sandiness, internal friction, and Biot’s gravity parameter on phase velocity and attenuation coefficient of SH-wave has been studied and demonstrated by means of graphical illustration and numerical computations.     

Ultrasonic waves in diluted and densified suspensions

A theory of propagation of stress waves in diluted and densified suspensions is developed to make the theoretical basis for analysis of ultrasonic waves through these media. The formulae for the phase velocity and the attenuation coefficient are determined as the function of wave frequency and the suspension structure parameter, which is the volume or mass fraction of the solid phase. These formulae can be use, after suitable calibration, for determination of the solid volume fraction in diluted suspensions, and the solid mass fraction or the water content in densified suspensions, that is, parameters that characterize the structure of a suspension. These structure parameters can be determined by measuring the transition time of ultrasonic wave through a given distance of suspension. The phase velocity dispersion curves and the attenuation coefficients determined theoretically and experimentally are plotted as a function of the volume fraction of the solid phase for dilute suspension, or the solid mass fraction for densified suspension.     

Ultrasonic waves in diluted and densified suspensions

A theory of propagation of stress waves in diluted and densified suspensions is developed to make the theoretical basis for analysis of ultrasonic waves through these media. The formulae for the phase velocity and the attenuation coefficient are determined as the function of wave frequency and the suspension structure parameter, which is the volume or mass fraction of the solid phase. These formulae can be use, after suitable calibration, for determination of the solid volume fraction in diluted suspensions, and the solid mass fraction or the water content in densified suspensions, that is, parameters that characterize the structure of a suspension. These structure parameters can be determined by measuring the transition time of ultrasonic wave through a given distance of suspension. The phase velocity dispersion curves and the attenuation coefficients determined theoretically and experimentally are plotted as a function of the volume fraction of the solid phase for dilute suspension, or the solid mass fraction for densified suspension.     

The dependence of time-domain speed-of-sound measurements on center frequency, bandwidth, and transit-time marker in human calcaneus in vitro

Time-domain speed-of-sound (SOS) measurements in calcaneus are effective predictors of osteoporotic fracture risk. High attenuation and dispersion in bone, however, produce severe distortion of transmitted pulses that leads to ambiguity of time-domain SOS measurements. An equation to predict the effects of system parameters (center frequency and bandwidth), algorithm parameters (pulse arrival-time marker), and bone properties (attenuation coefficient and thickness) on time-domain SOS estimates is derived for media with attenuation that varies linearly with frequency. The equation is validated using data from a bone-mimicking phantom and from 30 human calcaneus samples in vitro. The data suggest that the effects of dispersion are small compared with the effects of frequency-dependent attenuation. The equation can be used to retroactively compensate data. System-related variations in SOS are shown to decrease as the pulse-arrival-time marker is moved toward the pulse center. Therefore, compared with other time-domain measures of SOS, group velocity exhibits the minimum system dependence.     

Sound attenuation in a liquid containing suspended particles of micron and nanometer dimensions

The coefficient of sound attenuation in a liquid is calculated for attenuation due to both viscosity of the liquid and particles suspended in it. On the basis of analyzing the dispersion relations, a nonlinear integro-differential equation is reconstructed for describing the additional attenuation at high intensities of sound.     

Bubbles effect on sound dispersion in thin-walled tube with polymeric liquid and elastic central rod

The present study is devoted to the investigation of fine air bubbles effect on sound propagation in thin-walled elastic tube with compressible polymeric liquid and cylindrical elastic rod in the central part of the tube. The problem formulation and solution method follow the previous paper of the authors (S.P. Levitsky, R.M. Bergman, J. Haddad, Sound dispersion in deformable tube with polymeric liquid and elastic central rod, Journal of Sound and Vibration 275 (1-2) (2004) 267-281). In order to account for the bubbles' influence on sound dispersion and attenuation, dynamic equation of state of the mixture, formulated within homogeneous approximation, is used. It is assumed that the volume gas concentration is small. The resulting dispersion equation for the waveguide with viscoelastic liquid-gas mixture is studied in a long-wave range. Results of simulations illustrate the influence of free gas concentration, bubble radius and rheological properties of the liquid on sound dispersion and attenuation in the system.