Explicit results for wave scattering and transmission through a rough fluid-fluid interface

This paper describes an analysis of reflection and transmission of acoustic waves from an imperfectly reflecting, rough fluid-fluid interface within the Kirchhoff approximation. It presents the results of calculations of the coherent and diffuse field. This work is motivated by the fact that few explicit results of the characteristics of the scattered and transmitted wave field exist in the literature for this problem. For the problem of interest, the surface reflection coefficient depends at each point upon the local angle between the incident wave and the rough surface. For surfaces with statistically independent local surface position and gradient, coherent field calculations show that the correction to constant reflection coefficient analyses is simply a multiplicative factor that depends upon the statistical characteristics of the surface gradient, sound speed and density ratio across the surface. This multiplicative factor is interpreted as an average reflection or transmission coefficient, <R> and <T>, respectively. The principle differences between these results and constant reflection coefficient analyses occur when waves impinge upon regions with higher sound speeds, where total internal reflection may occur. While the wave characteristics of smooth or constant reflection coefficient surfaces change abruptly in the vicinity of the angle of total internal reflection, the average reflection coefficient exhibits a much smoother dependence upon angle of incidence or sound speed ratio for rough surfaces. It is also shown that the direction of maximum diffuse scattering moves relative to its value were the reflection coefficient constant.     

Numerical simulations of complex fluid-fluid interface dynamics

Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually deformable and their shapes are not known a priori. Since experiments do not provide access to all observables of interest, computer simulations pose attractive alternatives to gain insight into the physics of interfaces. In the present article, we restrict ourselves to systems with dimensions comparable to the lateral interface extensions. We provide a critical discussion of three numerical schemes coupled to the lattice Boltzmann method as a solver for the hydrodynamics of the problem: (a) the immersed boundary method for the simulation of vesicles and capsules, the Shan-Chen pseudopotential approach for multi-component fluids in combination with (b) an additional advection-diffusion component for surfactant modelling and (c) a molecular dynamics algorithm for the simulation of nanoparticles acting as emulsifiers.     

Acoustic X-wave reflection and transmission at a planar interface: spectral analysis

The spectral structure of a three-dimensional X-wave pulse incident on a planar surface of discontinuity is examined. Introducing a novel superposition of azimuthally dependent pulsed plane waves, it is shown for oblique incidence that the reflected pulse has a localized wave structure. On the other hand, the transmitted field maintains its localization up to a certain distance from the interface, beyond which it starts disintegrating. An estimate of the localization range of the transmitted pulse is established; also, the parameters affecting the localization range are identified. The reflected and transmitted fields are deduced for X-waves incident from either a slower medium or a faster one. For the former case the evanescent fields in the second medium are calculated and their explicit time dependence is deduced for a normally incident X-wave. Furthermore, at near-critical incidence the transmitted pulse exhibits significant pulse compression and focusing.     

Electric and magnetic susceptibilities for a fluid-fluid interface; The ellipsometric coefficient

Formulae for the electro-magnetic constitutive coefficients are derived in terms of the interfacial position autocorrelation function. Explicit expressions for these coefficients are then found in terms of e.g. the surface tension and the capillary length. The ellipsometric coefficient is expressed in these constitutive coefficients and a comparison with recent experiments by Beaglehole is made.     

Numerical simulation of continuum models for fluid-fluid interface dynamics

This paper is concerned with numerical methods for two-phase incompressible flows assuming a sharp interface model for interfacial stresses. Standard continuum models for the fluid dynamics in the bulk phases, for mass transport of a solute between the phases and for surfactant transport on the interface are given. We review some recently developed finite element methods for the appropriate discretization of such models, e.?g., a pressure extended finite element (XFE) space which is suitable to represent the pressure jump, a space-time extended finite element discretization for the mass transport equation of a solute and a surface finite element method (SurFEM) for surfactant transport. Numerical experiments based on level set interface capturing and adaptive multilevel finite element discretization are presented for rising droplets with a clean interface model and a spherical droplet in a Poisseuille flow with a Boussinesq-Scriven interface model.     

Electric and magnetic susceptibilities for a fluid-fluid interface: II. Critical behaviour

Formulae for the electromagnetic constitutive coefficients derived in a previous paper are used to analyse the critical behaviour of the reflectivities at normal and oblique incidence as well as the ellipsometric coefficient at the Brewster angle. Contributions due to correlations, which are neglected if one uses the average profile, are taken into account. Thus we e.g. calculate the energy losses due to scattering at the interface. We find that the ellipsometric coefficient contains the intrinsic thickness of the profile rather than the thickness of the average profile. For cyclohexane-aniline a comparison is made with recent experiments by Beaglehole.     

Scattering from a single bubble near a roughened air-water interface: laboratory measurements and modeling

The problem of scattering from a single bubble located close to a slightly roughened, air-water interface is studied both theoretically and experimentally. Two well-controlled laboratory experiments were performed to investigate the effects of surface roughness on the scattering response of the bubble. In the first experiment, a bubble of radius 1200 microm was placed on a fine thread at a variable distance, d, from the mean-still-water level of the surface, which was roughened using a wind source. In the second experiment, a bubble of radius 800 microm was utilized, while the water surface was roughened using a plunger wave-making source. The waveheights and important characteristic length scales associated with each experiment were quantified using digital photography. The wind source produced waveheights that were represented by a Gaussian distribution, while the plunger source produced waveheights that were represented by a bimodal distribution. To model the acoustic measurements, an expression describing the four scattering paths, from source to bubble to receiver, was used. A random phase shift due to the surface roughness was added to the paths that interacted with the surface, and expectations of this phase shift were computed based on the analytical representations for the waveheight distribution. The data show good agreement with the simulations and the sensitivity of scattering from a subsurface bubble to small changes in waveheight is illustrated. The experiments highlight important parametric dependencies, which are summarized here, and the relation between monostatic and bistatic scattering is also discussed.     

正交各向异性板液/固界面的声反射与声透射

采用Legendre正交多项式法,对液/固界面声波反射和透射系数进行求解。利用Legendre正交多项式对正交各向异性板中的位移解进行展开,推导出板中的应力和波动控制方程。联立液/固界面的边界条件和波动控制方程,建立线性无关方程组,用以计算液/固界面的反射和透射系数及Legendre多项式的展开系数,计算所得铝板液/固界面的反射和透射系数与传递矩阵法的计算结果吻合良好。以单向纤维增强复合材料板为例,在不同的方位角下,分析了反射和透射系数随斜入射角度、入射波频率的变化关系,以及板中声场的位移分布。所取Legendre正交多项式截止阶数越大,可用来计算的频厚积范围越大。研究拓展了Legendre正交多项式法的适用范围,为材料力学性能的声学测量提供了理论基础。     

正交各向异性板液/固界面的声反射与声透射

采用Legendre正交多项式法,对液/固界面声波反射和透射系数进行求解。利用Legendre正交多项式对正交各向异性板中的位移解进行展开,推导出板中的应力和波动控制方程。联立液/固界面的边界条件和波动控制方程,建立线性无关方程组,用以计算液/固界面的反射和透射系数及Legendre多项式的展开系数,计算所得铝板液/固界面的反射和透射系数与传递矩阵法的计算结果吻合良好。以单向纤维增强复合材料板为例,在不同的方位角下,分析了反射和透射系数随斜入射角度、入射波频率的变化关系,以及板中声场的位移分布。所取Legendre正交多项式截止阶数越大,可用来计算的频厚积范围越大。研究拓展了Legendre正交多项式法的适用范围,为材料力学性能的声学测量提供了理论基础。     

Confinement-enhanced electron transport across a metal-semiconductor interface

We present a combined scanning tunneling microscopy and ballistic electron emission microscopy study of electron transport across an epitaxial Pb/Si(111) interface. Experiments with a self-assembled Pb nanoscale wedge reveal the phenomenon of confinement-enhanced interfacial transport: a proportional increase of the electron injection rate into the semiconductor with the frequency of electron oscillations in the Pb quantum well.     

双相多孔锂离子电池液/固界面的声反射与声透射

采用传递矩阵法,同步联立改进的Biot理论,对含液固界面的双相多孔锂离子电池的超声反射与透射系数进行理论求解。考虑锂离子的摇摆特性对电极力学性能的影响,计算了对应状态下液/固界面的双相多孔锂离子电池声反射及透射系数的角度谱与频率谱。同时,构建了不同荷电状态时含单元锂离子电池的频域仿真模型,以萃取对应的超声反射及透射角度谱及频率谱,并与理论计算结果对比吻合良好。随后,以多单元锂离子电池为例,在不同的荷电状态下,分析了反射与透射系数随斜入射角度、入射波频率的变化关系,并分别指出了其角度谱及频率谱特征点随荷电状态的变化特征,为锂离子电池运行状态的超声无损测量提供了理论基础。     

Low-frequency sound transmission through a gas-liquid interface

Typically, sound speed in gases is smaller and mass density is much smaller than in liquids, resulting in a very strong acoustic impedance contrast at a gas-liquid interface. Sound transmission through a boundary with a strong impedance contrast is normally very weak. This paper studies the power output of localized sound sources and acoustic power fluxes through a plane gas-liquid interface in a layered medium. It is shown that, for low-frequency sound, a phenomenon of anomalous transparency can occur where most of the acoustic power generated by a source in a liquid half-space can be radiated into a gas half-space. The main physical mechanism responsible for anomalous transparency is found to be an acoustic power transfer by inhomogeneous (evanescent) waves in the plane-wave decomposition of the acoustic field in the liquid. The effects of a liquid's stratification and of guided sound propagation in the liquid on the anomalous transparency of the gas-liquid interface are considered. Geophysical and biological implications of anomalous transparency of water-air interface to infrasound are indicated.     

Low-frequency sound transmission through a gas-solid interface

Sound transmission through gas-solid interfaces is usually very weak because of the large contrast in wave impedances at the interface. Here, it is shown that diffraction effects can lead to a dramatic increase in the transparency of gas-solid interfaces at low frequencies, resulting in the bulk of energy emitted by compact sources within a solid being radiated into a gas. The anomalous transparency is made possible by power fluxes in evanescent body waves and by excitation of interface waves. Sound transmission into gas is found to be highly sensitive to absorption of elastic waves within a solid.     

Detonation propagation across a stratified layer with a diffuse interface

A study was conducted to examine detonation propagation in a stratified layer of hydrogen-oxygen-nitrogen above an inert gas in a horizontal narrow channel. The stratified layer was produced by a gravity current, generated by retracting a door initially separating a hydrogen-oxygen-nitrogen mixture in the predetonator and a heavier inert gas in the test-section. A steady detonation wave generated in the predetonator was transmitted into the stratified layer. The reactivity of the predetonator mixture was varied via the hydrogen-oxygen equivalence ratio and the amount of nitrogen dilution. Schlieren photography was used to visualize the detonation front in the test-section, and soot foils were used to obtain the cellular structure. Schlieren imaging showed a curved detonation front that decoupled at about mid channel height, into a shock wave and trailing contact surface. Both the hydrogen-oxygen-nitrogen reactivity and the type of inert gas initially in the test-section affected the distance travelled by the detonation wave in the stratified layer. The mixture composition distribution within the test-section before ignition was obtained via a three-dimensional CFD simulation. The lateral extent of the cellular structure captured on the soot foil, coincided with the calculated inert gas mole fraction contour that corresponds to a sharp increase in the ZND induction zone length, e.g., 70% argon dilution for a stoichiometric hydrogen-oxygen predetonator mixture.     

Quantum transmission across a low-dimensional nanoscale diffuse junction

The transmission across a nano-scale diffuse junction between two metals is studied numerically for 1D wires and 2D ribbons within a tight-binding model. In such a situation, a junction electric potential must appear to equilibrate the electrochemical potential on each side of the junction. We compute the transmission under two very different potential distributions and we find that the typical transmission does not depend on the details of this distribution. The transmission is found to follow a scaling law. The variations of the 1D transmission are explained in a semi-classical way by considering the multiple reflections caused by the barriers due to the on-site energy mismatch between the two metals. Both the 1D and 2D results can also be partly interpreted in the frame of the Anderson theory of localisation.     

Study of electric potentials across a moving solid-liquid interface

The electric potential across a melting sample of pure lead was measured as a function of time. A difference of the order of a few hundred microvolts was seen between the measured values of the potential and those calculated using the temperature gradients and the thermopowers of the solid and the liquid phases. This difference persists as long as the solid-liquid interface moves and is attributed to the Galvani potential present at the solid-liquid interface. It is suggested that such measurements can be used to obtain the value of the Fermi energy for liquids.     

Linear wave interaction at the charged fluid-fluid interface under tangential discontinuity of the velocity field

Capillary wave flow in a two-layer fluid with the upper layer moving parallel to the charged interface at a constant velocity is treated within a linear mathematical model. Interaction between waves excited on the free surface of the upper layer and at the interface results not only in classical Kelvin-Helmholtz instability (at low velocities of the upper layer) but also in oscillatory instability of the interface. The instability increment depends on the fluid density ratio, translational velocity, and charge density at the interface.     

Acoustic impedance at the interface between a plain and a perforated pipe

This paper considers the effective impedance that pertains as low frequency sound in a plain pipe radiates into a general perforated pipe of equal diameter. A previous theory that considered only the reactance is extended to also include resistance. Experimental measurements are made of the response of a Helmholtz resonator to an external sound field, where the neck of the Helmholtz resonator has both plain and perforated pipe sections. A complete theoretical model of this resonator allows for comparison between measured and predicted results of transfer functions from the external to internal sound fields of the resonator. The Nyquist plot of the admittance transfer function is extremely sensitive to the small resistance values, whereas the pressure transfer function gives more accurate results for resonant frequency and hence reactance than the usual method. In particular the results for resistance are so sensitive that it becomes possible to infer which of the current models for aperture resistance within the perforate is the most appropriate.