Corrections to the classical continuity boundary conditions at the interface of a composite medium

Using the multiple-scales homogenization method, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the interface between two media, one of which is free-space and the other a certain type of composite material. The parameters in these new boundary conditions are interpreted as effective electric and magnetic surface susceptibilities, which themselves are related to the geometry of the scatterers that constitute the composite. We show that the effective tangential E and H fields are not continuous across the interface except in the limit when the lattice constant (the spacing between the scatterers—atoms, molecules or inclusions in the case of a composite material) of the composite medium is very small compared to a wavelength. We derive first-order corrections to the classical continuity conditions. For naturally occurring materials whose lattice constants are on an atomic scale, these effects are shown to be negligible for waves at optical frequencies or lower. However, once the lattice constant becomes a significant fraction of a wavelength (which is the case for many artificial dielectrics and metamaterials), the corrections can be important. In previous work we have alluded to the fact that such a GSTC is needed to correctly account for the surface effects when extracting the effective material properties of a metamaterial. The results of this current paper justify the assumptions made in that previous work. In general, these GSTCs will result in corrections to the classical Fresnel reflection and transmission coefficients (which are themselves merely zeroth-order approximations to the actual reflection and transmission coefficients), and in a separate publication we will use these GSTCs to address this issue.     

Nonlinear corrections to critical conditions for instability of liquid-liquid charged interface

It is shown that nonlinear corrections to the frequencies of waves arising on a charged interface appear in calculation of the third order of smallness. Because of them, the Tonks-Frenkel critical parameter and wavenumber of the most unstable mode vary in proportion to a small parameter squared. When going through resonance positions, the amplitude coefficients of the corrections change sign. Depending on the wavelength, nonlinear interaction between waves may decrease or increase the critical values of the parameters governing the stability of waves at the interface.     

Derivation of Slip boundary conditions for the Navier-Stokes system from the Boltzmann equation

Rarefied gas flow behavior is usually described by the Boltzmann equation, the Navier-Stokes system being valid when the gas is less rarefied. Slip boundary conditions for the Navier-Stokes equations are derived in a rigorous and systematic way from the boundary condition at the kinetic level (Boltzmann equation). These slip conditions are explicitly written in terms of asymptotic behavior of some linear half-space problems. The validity of this analysis is established in the simple case of the Couette flow, for which it is proved that the right boundary conditions are obtained.     

On the boundary conditions to the Ginzburg-Landau equations at the interface of two superconductors with different transition temperatures

The generalized Wiener-Hopf method was used to derive, on the basis of the microscopic BCS theory of superconductivity, the effective boundary conditions to the Ginzburg-Landau equations at the interface of two (including uncommon) superconductors with different transition temperatures in the absence of reflection from the boundary. According to these conditions, the order parameter and its derivative undergo jumps at the interface.     

Kinetic boundary condition at a vapor-liquid interface

By molecular dynamics simulations, the boundary condition for the Boltzmann equation at a vapor-liquid interface is found to be the product of three one-dimensional Maxwellian distributions for the three velocity components of vapor molecules and a factor including a well-defined condensation coefficient. The Maxwellian distribution for the velocity component normal to the interface is characterized by the liquid temperature, as in a conventional model boundary condition, while those for the tangential components are prescribed by a different temperature, which is a linear function of energy flux across the interface. The condensation coefficient is found to be constant and equal to the evaporation coefficient determined by the liquid temperature only.     

Boundary conditions at a fluid-solid interface

We study the boundary conditions at a fluid-solid interface using molecular dynamics simulations covering a broad range of fluid-solid interactions and fluid densities and both simple and chain-molecule fluids. The slip length is shown to be independent of the type of flow, but rather is related to the fluid organization near the solid, as governed by the fluid-solid molecular interactions.     

Understanding liquid-liquid immiscibility and LCST behaviour in polymer solutions with a Wertheim TPT1 description

The aim of the work presented in this paper is to help in the understanding of the lower critical solution temperature (LCST) fluid phase behaviour exhibited by polymer solutions. It is well recognized that the LCST in polymer solutions is a consequence of density (compressibility) effects; the solvent is much more compressible than the polymer and the increasing difference in compressibility when the temperature is increased leads to a negative volume of mixing. The separate roles that the repulsive and attractive intermolecular interactions play in this regard are less well understood. In this study we use the Wertheim first-order thermodynamic perturbation theory (TPT1) [Wertheim, M. S., 1987, J. chem. Phys., 87, 7323; Chapman, W. G., Jackson, G., and Gubbins, K. E., 1988, Molec. Phys., 65, 1057] to describe the phase equilibria of model polymer solutions of hard spheres and hard-sphere chains where the diameter of the solvent and the polymeric segments are the same (symmetrical system). The thermodynamic functions (volume, enthalpy, entropy and Gibbs function) of mixing are determined to assess the possibility of a demixing instability in such a system. No fluid-fluid phase separation is found for the purely repulsive (athermal) system, regardless of the chain length of the polymer. The role of the attractive interactions is then investigated by incorporating attractive interactions at the mean-field level; the simplest system with equivalent (symmetric) solvent-solvent, solvent-polymer segment, and polymer segment-polymer segment interaction energies is examined. The attractive interactions are found to be essential in describing the liquid-liquid phase separation; LCST behaviour is found for mixtures with ‘polymer’ chains of seven segments or more. In this case we show that the phase behaviour is driven by an unfavourable (negative) entropy of mixing due to an increase in the density of the solvent on addition of small amounts of polymer. We also determine the thermodynamic properties of mixing for a system of spherical molecules of the same size with directional interactions that give rise to LCST and closed-loop behaviour. As expected the mechanism for phase separation in such systems is very different to that in polymer solutions.     

Slip dynamics at a patterned rubber/glass interface during stick-slip motions

We report on an experimental study of heterogeneous slip instabilities generated during stick-slip motions at a contact interface between a smooth rubber substrate and a patterned glass lens. Using a sol-gel process, the glass lens is patterned with a lattice of parallel ridges (wavelength, 1.6 μm, amplitude 0.35 μm). Friction experiments using this patterned surface result in the systematic occurrence of stick-slip motions over three orders of magnitude in the imposed driving velocity while stable friction is achieved with a smooth surface. Using a contact imaging method, real-time displacement fields are measured at the surface of the rubber substrate. Stick-slip motions are found to involve the localized propagation of transverse interface shear cracks whose velocity is observed to be remarkably independent on the driving velocity.     

Diffusion and segregation along grain boundary at the electrolyte-anode interface in IT-SOFC

The atomic level chemical and microstructural features of grain boundaries in gadolinium-doped ceria (GDC) electrolyte thin film supported by Ni-GDC cermet anode were characterized by high resolution transmission electron microscope (HR-TEM) and scanning TEM (STEM). It was found that metallic Ni can diffuse from the anode into the thin film electrolyte along grain boundaries. In addition, Ce and Gd can also diffuse and segregate at grain boundaries between Ni grains in the anode substrate. HR-TEM observations revealed that Ni diffusion and segregation at grain boundaries between GDC grains enhanced the inhomogeneity and led to microstructural changes at grain boundary regions, i.e. the formation of superstructure. The observations also indicated that enhanced inhomogeneity at grain boundaries might play a significant role in the conductivity of GDC electrolyte film in solid oxide fuel cells.     

On the use of Fresnel boundary and interface conditions in radiative-transfer calculations for multilayered media

The ADO (analytical discrete ordinates) method is used to establish a concise and accurate solution for a multi-layer radiative-transfer problem with Fresnel boundary and interface conditions. A finite plane-parallel medium composed of a number (K) of sub-strata with different material properties is considered to be illuminated by isotropically incident radiation. While a general result is obtained, emphasis in the numerical work is given to computing accurately the currents and the intensities that exit each of the two exterior surfaces. Monochromatic forms (with anisotropic scattering) of the radiative-transfer equation are used, and numerical results are given for several specific cases. The complications introduced by the Fresnel boundary and interface conditions are well resolved, so that the numerical results obtained are thought to define a very high standard.     

Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium

In many applications of the theory of radiative transfer, it is important to consider the changes in the index of refraction that occur when the physical domain being studied consists of material regions with distinct optical properties. When polarization effects are taken into account, the radiation field is described by a vector of four components known as the Stokes vector. At an interface between two different material regions, the reflected and transmitted Stokes vectors are related to the incident Stokes vector by means of reflection and transmission matrices, which are derived from the Fresnel formulas for the amplitude coefficients of reflection and transmission. Having seen that many works on polarized radiative transfer that allow for changes in the index of refraction exhibit discrepancies in their expressions for the transmission matrix, we present in this work a careful derivation of the relations between the reflected and transmitted Stokes vectors and the Stokes vector incident on an interface. We obtain a general form of a transmission factor that is required to ensure conservation of energy and we show that most of the discrepancies encountered in existing works are associated with the use of improper forms of this factor. In addition, we derive explicit and compact expressions for the Fresnel boundary and interface conditions appropriate to the study of polarized radiative transfer in a multilayer medium.     

Optical properties of cadmium sulfide nanocrystal film prepared by electrochemical synthesis at liquid-liquid interface

Dendritic nanocrystalline CdS film was deposited at liquid-liquid interface of surfactants and an electrolyte containing 4 mmol L⁻¹ cadmium chloride (CdCl₂) and 16 mmol L⁻¹ thioacetamide (CH₃CSNH₂) with an initial pH value of 5 at 15 °C by electrochemical synthesis. The nanofilm was characterized by transmission electron microscopy (TEM), field emission scanning electron microscope (FE-SEM), atomic force microscopy (AFM), ultraviolet visible (UV-vis) absorption spectroscopy and fluorescence spectroscopy. The surface morphology and particle size of the nanofilm were investigated by AFM, SEM and TEM, and the crystalline size was 30-50 nm. The thickness of the nanofilm calculated by optical absorption spectrum was 80 nm. The microstructure and composition of the nanofilm was investigated by X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS), showing its polycrystalline structure consisting of CdS and Cd. Optical properties of the nanofilm were investigated systematically by UV-vis absorption and fluorescence spectroscopy. A λ_onset blue shift compared with bulk CdS was observed in the absorption spectra. Fluorescence spectra of the nanofilm indicated that the CdS nanofilm emitted blue and green light. The nanocomposites film electrode will bring about anodic photocurrent during illumination, showing that the transfer of cavities produces photocurrent.     

Thermal boundary resistance at the interface between a crystal and a disordered solid

The thermal boundary resistance at the interface between a crystalline and a disordered solid with large scattering mismatch but negligible acoustic mismatch is calculated. Under the assumption that phonon scattering in the disordered material is predominantly elastic and strongly frequency dependent, the thermal boundary resistance derives from the spectral redistribution of the heat current by inelastic processes in the vicinity of the interface.     

Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar–Parisi–Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ$XXZ$-type Hamiltonians.     

Slip boundary conditions and through flow effects on double-diffusive convection in internally heated heterogeneous Brinkman porous media

A model for double-diffusive convection in a heterogeneous porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source using the Brinkman model. In particular, we analyse the effect of slip boundary conditions on the stability of the model. Because of the many applications in micro-electro-mechanical systems (MEMS) and other microfluidic devices, a study of this problem is necessary. Both linear instability analysis and nonlinear stability analysis are employed. We accurately analyse when stability and instability will commence and determine the critical Rayleigh number as a function of the slip coefficient.     

尺寸效应对微通道内固液界面温度边界的影响

采用非平衡分子动力学方法模拟不同浸润性微通道内液体的传热过程,分析了尺寸效应对固液界面热阻及温度阶跃的影响.研究结果表明,界面热阻随微通道尺寸的变化可分为两个阶段,即小尺寸微通道的单调递增阶段和大尺寸微通道的恒定值阶段.随着微通道尺寸的增加,近壁区液体原子受对侧固体原子的约束程度降低,微通道中央的液体原子自由移动,固液原子振动态密度近似不变,使得尺寸效应的影响忽略不计.上述两种阶段的微通道尺寸过渡阈值受固液作用强度与壁面温度的共同作用:减弱壁面浸润性,过渡阈值向大尺寸区域迁移;相较于低温壁面,高温壁面处的过渡阈值更大.增加微通道尺寸,固液界面温度阶跃呈单调递减趋势,致使壁面温度边界和宏观尺度下逐渐符合.探讨尺寸效应有助于深刻理解固液界面能量输运及传递机制.     

Quasiclassical boundary conditions for Fermi liquids at surfaces

The general boundary conditions at surfaces are derived within the quasiclassical theory of superfluidity in Fermi liquids (superconductors, superfluid³He). These conditions supplement the transport-like equations first introduced into the theory of superconductivity by G. Eilenberger, and allow a quantitative analysis of superfluids near a wall.     

Junction conditions at the boundary of a charged viscous-fluid sphere

Junction conditions are studied at the boundary of a sphere consisting of a charged viscous fluid with outgoing heat and radiation flux. The motion is anisotropic and the matching is done with the exterior Reissner-Nordström-Vaidya metric. A general relation in terms of the energy-momentum tensor componentsT ₁ ¹ andT ₄ ¹ is satisfied at the boundary hypersurface and this relation gives appropriate physical conditions in different special cases, some of which were obtained previously.