Nonlinear analysis of the time evolution of an unstable flat charged fluid surface

Nonlinear second-and fourth-order corrections to the critical Tonks-Frenkel parameter (which characterizes the stability of the uniformly charged flat surface of an ideal conducting incompressible fluid) are found by asymptotic calculations of the fifth order of smallness in ratio of the wave amplitude to the capillary constant of the fluid. A nonlinear integral equation for the time evolution of the unstable wave amplitude is derived and solved. It turns out that the linear stage of instability development takes a major part of the total time, while the nonlinear stage is very short. It is shown that the characteristic time of instability development on the fluid surface is a rapidly decreasing function of the initial amplitude of a virtual wave and the overcritical surface charge (i.e., the excess of the charge over the critical value).     

The fluid phenomena in the crystallization of the protein crystal

This paper reports that an optical diagnostic system consisting of Mach-Zehnder interferometer with a phase shift device and image processor has been used for study of the kinetics of protein crystal growing process. The crystallization process of protein crystal by vapour diffusion is investigated. The interference fringes are observed in real time. The present experiment demonstrates that the diffusion and the sedimentation influence the crystallization of protein crystal which grows in solution, and the concentration capillary convection associated with surface tension occurs at the vicinity of free surface of the protein mother liquor, and directly affects on the outcome of protein crystallization. So far the detailed analysis and the important role of the fluid phenomena in protein crystallization have been discussed a little in both space- and ground-based crystal growth experiments. It is also found that these fluid phenomena affect the outcome of protein crystallization, regular growth, and crystal quality. This may explain the fact that many results of space-based investigation do not show overall improvement.     

Nonlinear dynamics of magnetohydrodynamic flows of a heavy fluid on slope in the shallow water approximation

Magnetohydrodynamic equations for a heavy fluid over an arbitrary surface are studied in the shallow water approximation. While solutions to the shallow water equations for a neutral fluid are well known, shallow water magnetohydrodynamic (SMHD) equations over a nonflat boundary have an additional dependence on the magnetic field, and the number of equations in the magnetic case exceeds that in the neutral case. As a consequence, the number of Riemann invariants defining SMHD equations is also greater. The classical simple wave solutions do not exist for hyperbolic SMHD equations over an arbitrary surface due to the appearance of a source term. In this paper, we suggest a more general definition of simple wave solutions that reduce to the classical ones in the case of zero source term. We show that simple wave solutions exist only for underlying surfaces that are slopes of constant inclination. All self-similar discontinuous and continuous solutions are found. Exact explicit solutions of the initial discontinuity decay problem over a slope are found. It is shown that the initial discontinuity decay solution is represented by one of four possible wave configurations. For each configuration, the necessary and sufficient conditions for its realization are found. The change of dependent and independent variables transforming the initial equations over a slope to those over a flat plane is found.     

Vector Green's function algorithm for radiative transfer in plane-parallel atmosphere

Green's function is a widely used approach for boundary value problems. In problems related to radiative transfer, Green's function has been found to be useful in land, ocean and atmosphere remote sensing. It is also a key element in higher order perturbation theory. This paper presents an explicit expression of the Green's function, in terms of the source and radiation field variables, for a plane-parallel atmosphere with either vacuum boundaries or a reflecting (BRDF) surface. Full polarization state is considered but the algorithm has been developed in such way that it can be easily reduced to solve scalar radiative transfer problems, which makes it possible to implement a single set of code for computing both the scalar and the vector Green's function.     

Ab initio investigation of the surface properties of Cu(111) and Li diffusion in Cu thin film

Ab initio density-functional calculations have been performed to investigate the surface properties of Cu(111) and lithium diffusion in copper thin film. The calculation results including lattice constant, cohesive energy, work function and surface energy are in fair agreement with that derived from corresponding experiments. The various diffusion pathways such as diffusion of lithium as a substitution atom and various mechanisms are investigated with ab initio molecular dynamics. The energy barrier has been calculated corresponding to each possible pathway. Theoretically, we have identified that lithium can diffuse through copper thin film by successive nearest neighbor vacancy-atom exchanges, therefore, the nearest neighbor vacancy assisted jumping is deduced to be the most probable by comparing the different mechanisms. It is found that more free diffusion may be observed by increasing the number of copper vacancies in the thin film. It is also confirmed that the diffusion is more obvious as temperature is increased.     

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric spherical shell and the associated radiation of sound

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric sphere, with radial polarization, submerged in a compressible viscous fluid medium are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. A theoretical formulation cast the piezoelectric shell problem into a corresponding problem of an elastic shell with the contribution of piezoelectricity confined to slightly modified in vacuum natural frequencies and their associated mode shapes. It is noted that the fluid inside the shell will have a dominating influence on the vibrational characteristics of the submerged shell. The circular components of the natural frequency spectra closely follow those of the fluid-filled shell in vacuo. Furthermore, the corresponding damping components of those natural frequencies are rather small, making acoustic radiation and under-damped oscillation possible for an infinite number of natural frequencies. The characteristics of natural frequencies are elucidated using a fluid-filled polyvinglindene fluoride (PVDF) shell submerged in both air and water as an example. It is found that the piezoelectric parameters that contribute to the shell's natural frequencies is of a small order for thin PVDF shells, and is thereby negligible. It is noted that, with the mechanical constant typically associated with piezoelectric materials, fluid viscosity could have a significant effect on some vibrations. In certain cases, a natural frequency associated with a minimum viscous damping and a maximum of total damping (indicating highly efficient acoustic radiation) is possible with such a frequency.The vibrational characteristics, fluid loading, and energy flow are evaluated for a fluid-filled PVDF shell submerged in air and water. The inclusion of fluid inside the shell is shown to produce various narrow band peaks responses, vibrational absorbing frequencies, and non-dissipating frequencies. Those vibrational characteristics could have many potential applications. For example, the interior fluid could offer the option of generating a desired narrow band near resonant sound radiation while keeping power dissipation due to fluid viscosity to a minimum. Those well-defined narrow band characteristics also open up possibilities of using a vibrating, fluid-filled shell as a micro scale sensor for sensing and detection applications.     

Contributions to the acoustic excitation of bubbles released from a nozzle

It has recently been demonstrated that air bubbles released from a nozzle are excited into volume mode oscillations by the collapse of the neck of air formed at the moment of bubble detachment. A pulse of sound is caused by these breathing mode oscillations, and the sound of air-entraining flows is made up of many such pulses emitted as bubbles are created. This paper is an elaboration on a JASA-EL paper, which examined the acoustical excitation of bubbles released from a nozzle. Here, further details of the collapse of a neck of air formed at the moment of bubble formation and its implications for the emission of sound by newly formed bubbles are presented. The role of fluid surface tension was studied using high-speed photography and found to be consistent with a simple model for neck collapse. A re-entrant fluid jet forms inside the bubble just after detachment, and its role in acoustic excitation is assessed. It is found that for slowly-grown bubbles the jet does make a noticeable difference to the total volume decrease during neck collapse, but that it is not a dominant effect in the overall acoustic excitation.     

Aspects of the reflexion and free wave properties of a composite panel under fluid loading

The response of a composite panel to external forcing, with inclusion of fluid loading effects, is considered. Of the two strata comprising the composite panel one, backed by a vacuum, is of the conventional thin elastic plate or membrane kind, while the other, in contact with the fluid, is more like an elastic solid and may suffer significant compression. The behaviour of the acoustic field close to grazing incidence is examined, this behaviour being determined by that of the plane wave reflexion coefficient. In the absence of the upper stratum it is well known that the reflexion coefficient has the value ?1 around grazing incidence, so that direct and reflected fields from an external source cancel and preclude the propagation of a genuine acoustic field over the surface (a situation known in optics as the “Lloyd's mirror” effect). It is shown that, at any given frequency, an impedance for the upper stratum can be prescribed which will lead to the value +1 for the grazing incidence reflexion coefficient, and will thus obviate the severe power loss which would otherwise occur in directions close to the surface. Next the free subsonic surface waves which can exist in the coupled three-part (two-layer panel plus fluid) system are examined. It is shown analytically that, if the upper layer has low impedance controlled by stiffness forces, a new surface wave can exist in the system. This wave essentially involves the stiffness of the upper layer and the mass of the fluid, and has a wavenumber much higher than that of the surface wave in a single conventional panel. It is also shown from numerical studies that two subsonic surface waves will exist over quite a wide range of parameters, though not necessarily with the wide wavenumber separation of the low impedance case. A discussion is given of the possible importance of the high wavenumber mode in the case of excitation by high wavenumber boundary layer turbulence, and of the significance of two free subsonic surface wave modes in calculations of energy transmission over composite panels of the kind modelled here.     

Field ion image qualities of Ga,In and Sn on W and work functions

It has been found previously that Ga, In and Sn form a pseudomorphic monolayer on W which maximizes the work function of the covered surface. In the present work the bright and sharp field ion images of the pseudomorphic monolayer are shown comparing the images of the substrate tungsten. The interesting finding is that the images of the covering layer are most distinct for Sn which gives rise to the largest increment in the work function, and are least for In which has the smallest work function increment. A simple calculation on the penetration probaility of an electron into the potential barrier between an imaging gas atom and a metal surface indicates that the probability increases significantly with the work function and consequently the covered area would be images brightly. The calculation also suggests that the work function, that is the surface charge distribution, is one of the key factors controlling the quality of the field ion images.     

Compressibility effects on steady streaming from a noncompact rigid sphere

The problem of steady streaming around a rigid isolated sphere in a plane standing acoustic field is considered. Existing results in the literature have been generalized to allow for noncompactness of the sphere, and the influence of fluid compressibility on the streaming behavior has been included. It is found that in the high-frequency limit of interest for which the streaming is strongest, the effective steady slip velocity at the edge of the inner boundary layer region that is responsible for driving the steady streaming in the bulk of the fluid in the outer region, has a complex variation over the surface of the sphere that depends on (i) the sphere position (with respect to the node/antinode of the acoustic field), (ii) the extent of sphere compactness, and (iii) on a well-defined function (representing compressibility effects) of the fluid Prandtl number and its ratio of specific heats. Not surprisingly, the contribution from this function is negligible when the host fluid is a liquid. The steady streaming behavior around the sphere is demonstrated with the help of flow streamlines for various cases in the diffusive limit of weak outer flow for low streaming Reynolds numbers.     

Tests of the empirical potential structure refinement method and a new method of application to neutron diffraction data on water

Empirical potential structure refinement (EPSR) is a method for developing a structural model of a liquid for which diffraction measurements are available. The EPSR technique involves refining a starting interatomic potential energy function in a way that produces the best possible agreement between the simulated and measured site-site partial structure factors. Here a series of test simulations are performed to establish how well the EPSR method can recover the interatomic potential for a single component fluid of Lennard-Jones particles, and for a binary fluid consisting of charged atoms interacting at short range by a Lennard-Jones potential. Special attention is given to the problem of developing an accurate interatomic potential for water using these procedures. An alternative method for perturbing the starting potential is used to obtain the best possible fit to the diffraction data. The resulting parametrization of the water potential is in contrast to many existing effective potentials for water, and indicates that water molecules in the liquid at ambient conditions are highly polarized, as has been suggested in recent ‘first-principles’ simulations of water. Three-body correlation functions and spatial density functions derived from the EPSR simulations show excellent agreement with those obtained with the model potential simulations. However, the potentials extracted by EPSR are found to depend on the constraints applied to the hardness of the core potential and the energy and pressure of the simulation, even when the fits to the data are equally good. It is concluded that performing EPSR on diffraction data can be used as a good test for interatomic potentials and to derive reliable many-body structures in the liquid state, but cannot on its own be used to derive a reliable set of site-site pair potentials for a particular system.     

流体黏性及表面张力对气泡运动特性的影响

基于气泡边界层理论,引入黏性修正,采用边界积分法,考虑黏性效应和表面张力在单气泡以及双气泡耦合作用过程中的影响.首先将建立的数值模型与Rayleigh-Plesset的解析解进行对比,发现二者符合良好,验证了数值模型的有效性;在此基础上,建立考虑流体弱黏性效应的双气泡耦合模型,研究流体黏性和表面张力作用下,气泡表面变形、射流速度、流场能量转换等物理量的变化规律;最后研究雷诺数和韦伯数对于气泡脉动特性的影响规律.结果表明,流体黏性会抑制气泡脉动和气泡射流发展,降低气泡半径和射流速度;表面张力不改变气泡脉动幅值,但缩短了脉动周期,提升气泡势能.     

Influence of Tb incorporation on the structural and the optical properties of ZnO nanoparticles

Structural and optical properties of the Tb doped ZnO nanoparticles are systematically studied as a function of the Tb mole-fraction. Our study suggests that the Tb incorporates mostly on the surface and affects the optical properties of the ZnO nanoparticles by influencing the attachment of certain adsorbed groups, which are found to be responsible for the appearance of a broad green luminescence (GL) band in the photoluminescence spectra recorded for these nanoparticles. It has been found that the accumulation of Tb on the surface of the nanoparticles not only enhances the band edge to green luminescence intensity ratio under the vacuum condition but also increases the band gap energy by introducing a hydrostatic compressive strain in individual nanoparticles, which provides a unique opportunity to study the pressure dependence of the optical properties of nanoparticles without applying any external pressure. The hydrostatic compressive strain is explained in terms of the increase of the surface strain energy as a result of the Tb accumulation on the surface of the nanoparticles. The average value of the surface energy density for the particles has been estimated as a function of Tb mole-fraction. The pressure coefficient of the band gap which is obtained from the variation of the band gap energy with the hydrostatic strain has been found to decrease significantly with the particle size for the ZnO nanoparticles.     

A self-consistent density-functional approach to the structure of electric double layer: charge-asymmetric electrolytes

A self-consistent density-functional approach has been employed to study the structure of an electric double layer formed from a charge-asymmetric (2:l) electrolyte within the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The particle correlation due to hard-core exclusions is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the diffuse layer potential drop, ionic density profile, and the mean electrostatic potential near the electrode surface at several surface charge densities are found to be in quantitative agreement with the available simulation data.     

NMR studies of the sedimentation of ferromagnetic nanoparticles in a magnetic fluid

A method has been proposed for studying the sedimentation of ferromagnetic nanoparticles in a magnetic fluid from the rate of decrease in its magnetization measured by the NMR technique. The dependence of the rate of variations in the magnetization of the magnetic fluid over time on the concentration of the stabilizer is investigated. A colloidal aqueous solution of magnetite nanoparticles with varying concentrations of the sodium oleate stabilizer was used as the magnetic fluid. It has been found that the ratio of the mass concentrations of the stabilizer and magnetite in a stable magnetic fluid must satisfy the condition C ≥ 0.7, which corresponds to the formation of a double layer of stabilizer on the surface of magnetite nanoparticles.

     

Dynamical chaos for a limited power supply for fluid oscillations in cylindrical tanks

Forced oscillations of the fluid surface in a cylindrical tank due to interaction with the excitation mechanism of a limited power supply (so-called “limited excitation” phenomena) are investigated in detail. On the basis of analysis of the largest Lyapunov exponents for a complex system—a tank with fluid and an excitation arrangement—the three types of steady-state regimes are found: equilibrium positions, periodic and chaotic regimes. Phase portraits, Poincaré sections and maps, distributions of spectral densities and invariant measures are constructed and thoroughly studied. Attention is concentrated mainly on the properties of chaotic attractors and schemes of transition from “order” to chaos. It is established that different scenarios of transition to chaos and various structures of chaotic attractors are possible in the same physical system. The new scenario transition to chaos which generalizes scenario of Pomeau-Manneville is revealed. It is shown that chaotic regimes with the single-mode fluid free surface oscillations can originate only due to interaction with the excitation mechanism.     

Entropy production in the flow over a swirling stretchable cylinder

In the present work, the entropy generation due to the heat transfer and fluid friction irreversibility is investigated numerically for a three-dimensional flow induced by rotating and stretching motion of a cylinder. The isothermal boundary conditions are taken into account for the heat transfer analysis. The similarity transformations are utilized to convert the governing partial differential equations to ordinary differential equations. Resulting nonlinear differential equations are solved using a numerical scheme. Expressions for the entropy generation number, the Nusselt number and the Bejan number are obtained and discussed through graphs for various physical parameters. An analysis has been made to compare the heat transfer irreversibility with fluid friction irreversibility using the expression of the Bejan number. It is found that the surface is a durable source of irreversibility and the curvature of cylinder is to enhance the fluid friction irreversibility.     

Features in atomic force microscopy studies of dielectric surfaces

To improve the accuracy of AFM measurements in air and the reproducibility of results, a clean room-based metrological facility has been designed and built. The main function of the facility is to control temperature and humidity in an operation zone in various combinations and to maintain them with high accuracy. Measurements under controlled conditions are particularly important for dielectric materials. It has been shown that special procedures allow one to avoid disturbances caused by static charges on the surface under study, i.e., to remove the already accumulated charge and prevent its appearance during experiments. The use of the proposed procedures makes it possible to adequately study the features of the dielectric surface relief at micro-and nanoscale levels.     

Numerical study of transitional brittle-to-ductile debonding of a capsule embedded in a matrix

This work presents a numerical study that addresses the role of the interfacial fracture energy on the debonding process of a capsule embedded in an elastic matrix, which undergoes a uniaxial far-field stress. The motivation of this work is to analyze and to understand the effects of this energy in the framework of the so-called encapsulation-based self-healing cementitious materials, where glass capsules filled with a fluid healing agent are embedded in a cement-based matrix. A two-dimensional plane strain model based on a combination of the classical finite element method and cohesive surface techniques implemented in the commercial code Abaqus^® has been used. It has been found that there exist three types of debonding regimes, ranging from a perfect brittle response up to a ductile-limited response, and whose range of validity is governed by a straightforward dimensionless number able to predict the type of debonding as a function of flexural properties of the capsule and the interface strength.     

Experimental Simulation of the Generation of a Vortex Flow on a Water Surface by a Wave Cascade

The generation of a vortex flow by waves on a water surface, which simulate an energy cascade in a system of gravity waves at frequencies of 3, 4, 5, and 6 Hz, has been studied experimentally. It has been found that pumping is accompanied by the propagation of waves on the surface at different angles to the fundamental mode and by a nonlinear interaction between waves resulting in the generation of new harmonics. It has been shown that large-scale flows are formed by modes of the lowest frequency of 3 Hz intersecting at acute angles. The energy distribution of the vortex motion can be described by a power-law function of the wavenumber and is independent of the energy distribution in a system of surface waves. The energy coming to large-scale vortex flows directly from the wave system is transferred to small scales. A direct rather than inverse energy flux is established in the system of vortices.