Ultrasonic scattering cross sections of shell-encapsulated gas bubbles immersed in a viscoelastic liquid: first and second harmonics

The oscillations of gas bubbles, without shell, immersed in viscoelastic liquids and driven by an acoustic wave have been the subject of several investigations. They demonstrate that the viscosity coefficient and the spring constant of the liquid have significant influence on the scattering cross section of the gas bubble. For shell-encapsulated gas bubbles, the investigations have been concentrated to bubbles immersed in a pure viscous liquid. This present work computes the ultrasonic scattering cross section, first and second harmonics, of shell-encapsulated gas bubbles immersed in a viscoelastic liquid. The theoretical model of the bubble oscillation is based on the generalized Rayleigh-Plesset equation of motion of a spherical cavity immersed in a viscoelastic liquid represented by a three-parameter linear Oldroyd model. The scattering cross section is computed for Albunex type of bubble (shell thickness=15 nm, shell shear viscosity=1.77 Pas, shell modulus of rigidity=88.8 MPa) irradiated by a 3.5 MHz ultrasonic pressure wave with an amplitude of 30 kPa. The results demonstrate that encapsulated bubbles respond independently of the surrounding liquid being pure viscous or viscoelastic as long as the surrounding liquid shear viscosity is as low as 10(-3) Pas. Nevertheless, for higher shear viscosities, the bubble responds differently if the surrounding liquid is pure viscous or viscoelastic. In general, the scattering cross sections of first and second harmonics are larger for the viscoelastic liquid.     

Viscosity modeling of the ternary system 1-methylnaphthalene +n-tridecane+2,2,4,4,6,8,8-heptamethylnonane up to 100 MPa

Abstract

Viscosity measurements of well-defined mixtures can be used to evaluate existing viscosity models. Recently, an extensive experimental study of the viscosity up to 100 MPa have been carried out for the ternary system composed of 1-methylnaphthalene+n-tridecane+2,2,4,4,6,8,8-heptamethylnonane. This system is a very simple, representation of some petroleum distillation cuts at 510 K. Three recently proposed viscosity models with a physical and theoretical background have been evaluated on this ternary system. The evaluated models are based on the rough hard-sphere scheme, the free-volume, and the friction theory. For all models, the predicted viscosities for the three pure compounds, the three binaries and the ternary are within or close to the experimental uncertainty (±2%)). satisfactory for most industrial applications. This work shows the potential extension of these viscosity approaches to real petroleum fluids. For comparison purposes results obtained with the well-known mixing laws (Grunberg-Nissan and Katti-Chaudhri) are also presented. Further, it has been found that the widely used LBC model can not predict the viscosity of this ternary system satisfactorily.     

Production of Fine Particles from Melts of Metals or Highly Viscous Fluids by ultrasonic standing wave atomization

Ultrasonic standing wave atomization (USWA) is a new process capable of atomizing both high surface energy liquids and highly viscous liquids. Atomization is achieved through acoustic forces acting upon a liquid jet which is guided into the central pressure node of a standing wave field. Spherical metal powders with minimum mass median diameters of less than 15 μm have been produced from metal melts with surface tensions of about 0.5 N/m. Organic liquids with viscosities between 1 and 10 Pas have been atomized, yielding mass median diameters from 20 to 330 μm. The influence of different operating parameters on the mass median diameter of metal melts and highly viscous liquids was evaluated. Parameters which were varied were ambient gas pressure, vibration amplitude of the transducers, mass flow rate, density of liquid, viscosity of the liquid, surface tension and the outlet diameter. The powders and sprays were analyzed with laser diffraction particle sizers. The physical background of the atomization process is discussed and an equation for the prediction of the mass median diameter is derived.     

Field evaporation of impurity ions from a liquid gallium ion source

The charge states of ions emitted from a gallium liquid metal field ion (LMI) source contaminated with tin and copper have been measured. The results for tin show that the proportion of Sn²⁺ to Sn⁺ is much larger than is found for a LMI source of pure tin. A model in which Sn²⁺ is assumed to be produced by post-ionization of Sn⁺ is used to set an upper limit to the electric field at the point of emission. Its value is approximately equal to that predicted by field evaporation theory for a pure gallium source. Consequently the charge states of emitted impurity ions are determined by field strengths imposed by the main component.     

Investigation of an anisotropic tortuosity in a biot model of ultrasonic propagation in cancellous bone

The modeling of ultrasonic propagation in cancellous bone is relevant to the study of clinical bone assessment. Historical experiments revealed the importance of both the viscous effects of bone marrow and the anisotropy of the porous microstructure. Of those propagation models previously applied to cancellous bone, Biot's theory incorporates viscosity, but has only been applied in isotropic form, while Schoenberg's anisotropic model does not include viscosity. In this paper we present an approach that incorporates the merits of both models, by utilizing the tortuosity, a key parameter describing pore architecture. An angle-dependent tortuosity for a layered structure is used in Biot's theory to generate the "Stratified Biot Model" for cancellous bone, which is compared with published bone data. While the Stratified Biot model was inferior to Schoenberg's model for slow wave velocity prediction, the proposed model improved agreement fast wave velocity at high propagation angles, particularly when sorted for porosity. An attempt was made to improve the fast wave agreement at low angles by introducing an angle-dependent Young's Modulus, which, while improving the agreement of predicted fast wave velocity at low angles, degraded agreement at high angles. In this paper the utility of the tortuosity in characterizing the architecture of cancellous bone is highlighted.     

Towards a unified view of fluids

It has traditionally been believed that, unlike normal fluids whose structural properties are determined primarily by the intermolecular short-range repulsive interactions, the properties of polar and associating fluids are strongly affected by the long-range Coulombic interactions. In the course of investigations to determine the primary driving forces governing the behaviour of various (non-simple) fluids, and hence to gain a deeper understanding of the molecular mechanisms leading to the development of theoretically based simple models and theory, extensive and systematic computer simulations have been performed on typical quadrupolar (carbon dioxide), dipolar (acetone and acetonitrile), and associating (hydrogen fluoride, methanol, and water) fluids using the available realistic effective pair potentials and their variants involving forces of different ranges. In addition to the main structural characteristics (one- and two-dimensional site–site correlation functions, local g factors, and radial slices through the full pair correlation function), the dielectric constants and the thermodynamic properties (internal energy and pressure) of both the homogeneous liquid and supercritical fluid phases, and vapor–liquid equilibria have also been considered. Furthermore, in the case of water, the diffusion coefficient and viscosity have also been considered along with water at the interface. All the obtained results lead to the unambiguous conclusion that the structure, defined in terms of the complete set of site–site correlation functions, for both polar and associating pure fluids is governed by the same molecular mechanism as for normal fluids, i.e. by the short-range interactions (which, however, may be both repulsive and attractive), whereas the long-range part of the electrostatic forces, regardless of their strength, plays only a marginal role and may be treated as a perturbation only. The consequences of these findings for theory and applications are also discussed.     

A dislocation model for the viscosity of water

A dislocation model for the shear viscosity of water is proposed, based upon the dislocation theory of melting and liquid state. This model, studied extensively within the last years in relation to phase transitions in two-dimensional systems, makes rigorous use of the similarity between the structure of a liquid and that of a crystalline solid. Viscous flow in water due to slip of dislocation loops is proposed as an alternative point of view to the hole theories and the cluster models of hydrogen bonded molecules. The model correctly yields the temperature dependence of the viscosity at normal pressure between melting and boiling point.     

Three-dimensional immiscible lattice gas: Application to sheared phase separation

A new lattice-gas cellular automaton model for simulating binary fluids in three dimensions is introduced. It is particularly suitable for modeling slow flows of mixtures with complicated interface geometries or within complicated boundaries, such as in the interior of a porous rock. Phase separation is triggered spontaneously in the model by statistical fluctuations and phase domains are approximately isotropic. The measured surface tension is large compared to that in analogous two-dimensional models. The model is applied to a study of the time-dependent effective viscosity of a phase-separating mixture in a simple shear flow. Results qualitatively match both experiment and theory: the viscosity increases rapidly, then decays gradually to a steady-state value which is larger than the viscosity of the pure fluids. The effective viscosity increases with increasing concentration and decreases with increasing strain rate.     

Ultrasonic atomization: effect of liquid phase properties

Experiments have been conducted to understand the mechanism by which the ultrasonic vibration at the gas liquid interface causes the atomization of liquid. For this purpose, aqueous solutions having different viscosities and liquids showing Newtonian (aqueous solution of glycerin) and non-Newtonian behavior (aqueous solution of sodium salt of carboxy methyl cellulose) were employed. It has been found that the average droplet size produced by the pseudo-plastic liquid is less than that produced by the viscous Newtonian liquid having viscosity equal to zero-shear rate viscosity of the shear thinning liquid. The droplet size was found to increase initially with an increase in the viscosity up to a certain threshold viscosity after which the droplet size was found to decrease again. Also droplet size distribution is found to be more compact (uniform sizes) with an increasing viscosity of the atomizing liquid. The presence of the cavitation and its effect on the atomization has been semi quantitatively confirmed using energy balance and by the measurement of the droplet ejection velocities and validated on the basis of the decomposition of the aqueous KI solution. A correlation has been proposed for the prediction of droplet size for aqueous Newtonian fluids and fluids showing non-Newtonian behavior based on the dimensionless numbers incorporating the operating parameters of the ultrasonic atomizer and the liquid phase physico-chemical properties.     

Viscosity of liquid selenium and selenium-sulphur mixtures

The viscosity of selenium has been studied in the liquid state, and the effect of thallium and sulphur additives was investigated. The rotating cylinder method was used. Experimental measurements show that the viscosity of liquid selenium with sulphur admixtures is higher than that for pure selenium, and a complex molecular structure is formed. The results were explained on the basis of the free volume model and the data for liquid selenium were fitted to the model withE _act=0.6 eV.     

高温金属熔体黏度突变探索

高温金属熔体的黏度是衡量液态金属动力学性质的一个重要指标,是高温金属熔体的基本物理性能之一.熔体的黏度在表征脆性系数、金属玻璃形成能力的大小和液-液相变现象方面起关键性作用.本文在介绍高温金属熔体黏度测量方法的基础上,综合评述了单质、二元和多元合金黏度随温度的变化规律和黏度突变特征,分析了黏度突变研究的物理意义,并指出高温金属熔体黏度今后研究的发展方向。     

A three-dimensional model for T-shaped acoustic resonators with sound absorption materials

Recent development in noise control using T-shaped acoustic resonators calls for the development of more reliable and accurate models to predict their acoustic characteristics, which is unfortunately lacking in the literature. This paper attempts to establish such a model based on three-dimensional theory for T-shaped acoustic resonators containing sound absorption materials. The model is validated by experiments using various configurations. Predictions on fundamental and high-order resonance frequencies are compared with those obtained from the one-dimensional model and finite element analyses, and the effects of the physical and geometric parameters of the absorption materials on the resonance frequencies and Q-factor are also investigated numerically and experimentally. Limitations and applicability of existing one-dimensional models are assessed. The proposed general three-dimensional model proved to be able to provide an accurate and reliable prediction on the resonance frequencies for T-shaped acoustic resonators with or without absorption materials. This can eventually meet the requirement for resonator array design in terms of accuracy.     

The thermodynamics of symmetric two centre Lennard-Jones liquids

We have carried out molecular dynamic simulations for the thermodynamic properties of two centre Lennard-Jones fluids at lower densities and higher temperatures than have been studied previously, and have also made simulations for one additional shape. The results, together with results already given in the literature, are presented in a parameterized form which is very convenient to use in testing the simulation results against data for real liquids. Tables of second virial coefficients are also provided. We illustrate the use of our results by an analysis of pure liquid ethane, which is found to be well represented by such a model with L* = 0·67, ε/k = 137·5 K and σ = 3·506 Å. We also suggest that the experimental thermodynamic properties of suitable liquid mixtures can, with the aid of a theory for the equivalent pure liquid parameters (L _x *, ε _x , σ _x ), be satisfactorily interpreted using the general results given in this paper.     

Embedding atom-jellium model for metal surface

To describe metal surfaces efficiently and accurately, an embedding atom-jellium model is proposed. Within density functional theory, we consider a multiscale scheme that combines jellium and atomistic approaches. We use the former to model layers deep inside a metal surface to reduce the computational cost and the later to maintain the accuracy required for chemical bonding. Work functions of Al(111) and Cu(111) surfaces are studied using this model with comparisons to all-atom and pure jellium models. The much closer results of the embedding atom-jellium model to the all-atom results than to the pure jellium results show a good prospect for our approach in large-scale density functional calculations.     

Weakly nonlinear propagation of focused ultrasound in bubbly liquids with a thermal effect: Derivation of two cases of Khokolov–Zabolotskaya–Kuznetsoz equations

A physico-mathematical model composed of a single equation that consistently describes nonlinear focused ultrasound, bubble oscillations, and temperature fluctuations is theoretically proposed for microbubble-enhanced medical applications. The Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation that has been widely used as a simplified model for nonlinear propagation of focused ultrasound in pure liquid is extended to that in liquid containing many spherical microbubbles, by applying the method of multiple scales to the volumetric averaged basic equations for bubbly liquids. As a result, for two-dimensional and three-dimensional cases, KZK equations composed of the linear combination of nonlinear, dissipation, dispersion, and focusing terms are derived. Especially, the dissipation term depends on three factors, i.e., interfacial liquid viscosity, liquid compressibility, and thermal conductivity of gas inside bubbles; the thermal conduction is evaluated by using four types of temperature gradient models. Finally, we numerically solve the derived KZK equation and show a moderate temperature rise appropriate to medical applications.     

Gas flow characteristics in straight silicon microchannels

Experiments have been conducted to investigate nitrogen gas flow characteristics through four trapezoidal silicon microchannels with different hydraulic diameters. The volume flow rate and pressure ratio are measured in the experiments. It is found that the friction coefficient is no longer a constant, which is different from the conventional theory. The characteristics are first explained by the theoretical analysis. A simplified rectangular model (rectangular straight channel model) is then proposed. The experimental results are compared with the theoretical predictions based on the simplified rectangular model and the two-dimensional flow between the parallel-plate model which was usually used. The difference between the experimental data and the theoretical predictions is found in the high-pressure ratio cases. The influence of the gas compressibility effect based on the Boltzmann gas kinetic analysis method is studied to interpret the discrepancy. We discuss two important factors affecting the application extent of different prediction models.     

Light-scattering study of a supercooled epoxy resin

The dynamics of the fragile glass-forming liquid diglycidyl ether of bisphenol-A was studied by depolarized Rayleigh-Brillouin light-scattering and photon correlation spectroscopy above the glass transition, in the temperature range from 261 to 473 K and in the frequency range from 1 Hz to 300 GHz. The structural (alpha-) relaxation process was revealed and no signature of the secondary relaxation previously evidenced by dielectric spectroscopy at about 0.1 GHz was observed. The characteristic time of the alpha process differs from that determined by dielectric spectroscopy of an amount, which increases with increasing temperature. The relaxation times were compared with viscosity data to test the predictions of the classic Stokes-Einstein-Debye model. The tau proportional, variant eta behavior was verified for dielectric data, while a fractional power law of viscosity tau proportional, variant eta(0.89) was obtained for light-scattering relaxation times, extending over more than seven decades in viscosity and time. This deviation of light scattering from viscosity data could be interpreted in terms of cooperative motion in the supercooled liquid with a characteristic length xi(a) proportional, variant(T-T0)(-v) where T(0)=229 K is the Vogel temperature and v is close to 2 / 3 which is consistent with the prediction of the fluctuation theory of glass transition.     

Electrical conductivity and thermopower of metallic helium

The pair effective interionic interaction, electrical resistance, and thermopower of liquid metallic helium have been calculated over wide temperature and density ranges using the perturbation theory for the potential of electron-ion interaction. For conduction electrons, the random-phase approximation has been used taking into account the exchange interaction and correlations in the local-field approximation. The nuclear subsystem has been described by the hard-sphere model. The sphere diameter is the only parameter of the theory. The diameter and the system density at which helium is transformed from the singly ionized to doubly ionized state have been estimated based on an analysis of the pair effective interaction between helium nuclei. The case of doubly ionized helium atoms has been considered. The numerical calculations have been performed taking into account the perturbation theory in terms up to the third order. In all cases, the role of the third-order correction is significant. In the case of metallic helium, the values of the electrical resistance and its temperature dependence are characteristic of divalent simple liquid metals, as well as the dependences of the thermopower on the density and temperature.     

Piezoelectric transducer vibrations in a one-dimensional approximation

Summary The theory of piezoelectric transducer vibrations, which may be treated as onedimensional, is developed in detail for thin discs vibrating in a pure thickness extensional mode. An effort has been made to obtain relations of general validity, which include losses, and which are in a simple explicit form convenient for practical calculations. The behaviour of transducers is discussed with special attention to their characteristics at the two fundamental frequencies, the so-called parallel and series resonances. Several peculiarities occur when transducers are coupled to media with considerably different acoustic impedances. These peculiarities are discussed and illustrated by numerical results for quartz and PZT 4 piezoelectric discs radiating into water, air and liquid hydrogen. The application of the theory to different types of vibrations is briefly illustrated for thin bars vibrating longitudinally. Short discussions are included on compound transducer systems, and on the properties of thin discs as receivers.