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 transmission across a roughened fluid-fluid interface

A set of tank experiments was performed to investigate acoustic transmission across a roughened fluid-fluid interface with the intention to test heuristic Bragg scattering predictions used to explain observations of anomalous transmission in field experiments. In the tank experiments, two immiscible fluids (vegetable oil floating on glycerin) formed the layers. Small polystyrene beads were floated at the interface to simulate roughness. An array of hydrophones placed in the bottom layer (glycerin) was used to measure the acoustic levels transmitted across the interface. This array was also employed as a beamformer to determine the apparent angle and sound speed of the scattered signals. Data were acquired at subcritical grazing angles in the frequency range of 100-200 kHz for three different bead diameters and for various configurations in which the locations of the beads floating on the interface were varied. Results of these measurements demonstrated that a significant amount of acoustic energy can be scattered into the bottom layer by beads floating at the interface. The scattered levels increased with increasing bead diameter. However, discrepancies occurred between observed propagation properties and the Bragg predictions. By comparing the processed tank data to a computer simulation of the same it was determined that these discrepancies are a consequence of near-field reception of the scattering by the bead array and ignoring the directionality of the scattering by the beads. Consequences to observations made in field experiments are discussed.     

Numerical simulation of non-Abelian particle-field dynamics

Numerical 1D-3V solutions of the Wong-Yang-Mills equations with anisotropic particle momentum distributions are presented. They confirm the existence of plasma instabilities for weak initial fields and of their saturation at a level where the particle motion is affected, similar to Abelian plasmas. The isotropization of the particle momenta by strong random fields is shown explicitly, as well as their nearly exponential distribution up to a typical hard scale, which arises from scattering off field fluctuations. By variation of the lattice spacing we show that the effects described here are independent of the UV field modes near the end of the Brioullin zone.     

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.     

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.     

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.     

Numerical simulation of the intramolecular dynamics of photoisomerization

The results of mixed quantum-classical and quantum-mechanical numerical calculations of the intramolecular dynamics of photoisomerization under conditions similar to ordinary natural conditions, i.e., for irradiation of the molecule by a light pulse not shorter than the lifetime of the resonant excited electronic state of the molecule and with an intensity comparable to that of solar light at the Earth’s surface, are presented. It was concluded that the dynamics of such photoisomerization should be modeled using quantum-mechanical methods. The simplest approach to modeling the photoisomerization of a molecule with two isomeric forms can be based on the density matrix formalism for describing the interaction of a light pulse with a three-level system of Λ configuration.     

Numerical simulation of intramolecular dynamics during dual fluorescence

The dynamics of transformation of a light pulse by a five-level model molecule whose secondary emission spectrum can contain two fluorescence bands is simulated. The system of equations that determine the time behavior of the matrix elements of the statistical operator of the molecule interacting with the light pulse is numerically solved. From this solution, the time dependences of the populations of the molecular states are determined for different values of the parameters of the irradiation pulse, which is described in terms of the classical theory, and of the parameters that characterize the rates of radiative and nonradiative spontaneous transitions of the molecule. Based on particular examples of the choice of these parameters, it is demonstrated that the mechanism by which dual fluorescence occurs in molecules with intramolecular hydrogen bonds can be efficiently established from the numerically simulated intramolecular dynamics.     

一种描述金属界面原子扩散的加速分子动力学方法

传统分子动力学(MD)的纳秒级时间尺度限制了对固体界面原子的深层扩散、渗透以及相形成等长时动力学性质的模拟研究.在Voter的超动力学框架内,提出了一种更为简单的偏移势的构建方法.该方法通过在偏移势中引入一个加速因子,抬高了原势阱,从而加速了原子的跃迁,将MD模拟的时间尺度提高了若干个数量级.更为重要的是,该方法不需要预知体系势能的势阱及鞍点分布,还能够将原势能曲面的特性完全保留.以Mg/Zn界面扩散为例,选取简单的Lennard-Jones双体势,考察了不同加速因子对界面原子扩散速度的影响.结果显示,该 关键词： 超动力学 加速因子 原子扩散 金属界面     

激光非均匀性对内界面变形影响的数值模拟

使用LARED-S程序,参照NIF直接驱动DT点火靶,模拟研究了激光非均匀性对高收缩比球内爆内界面变形的影响。2维数值模拟计算表明：直接驱动高收缩比内爆对驱动激光非均匀性非常敏感,内界面流体不稳定性的发展严重破坏靶丸的对称压缩,使中心热斑的体积显著减小。以最大压缩时扰动增长幅度不超过热斑半径的1/3为限,模拟给出不同模数的低阶扰动模(模数小于等于12)对驱动激光均匀性的要求在2.5%～0.25%之间,其中模数在8～10之间的扰动模对激光功率均匀性的要求最严格,约为0.25%。     

激光非均匀性对内界面变形影响的数值模拟

 使用LARED-S程序,参照NIF直接驱动DT点火靶,模拟研究了激光非均匀性对高收缩比球内爆内界面变形的影响。2维数值模拟计算表明：直接驱动高收缩比内爆对驱动激光非均匀性非常敏感,内界面流体不稳定性的发展严重破坏靶丸的对称压缩,使中心热斑的体积显著减小。以最大压缩时扰动增长幅度不超过热斑半径的1/3为限,模拟给出不同模数的低阶扰动模(模数小于等于12)对驱动激光均匀性的要求在2.5%～0.25%之间,其中模数在8～10之间的扰动模对激光功率均匀性的要求最严格,约为0.25%。     

First-principles molecular dynamics simulation of biased electrode/solution interface

First-principles molecular dynamics simulations have been carried out for water in contact with Pt(1 1 1) surface. To apply negative bias potential to the water/Pt interface, excess electrons were added to our slab model using the recently developed computational scheme called “effective screening medium (ESM)”. Water molecules located away from the surface reoriented themselves to screen the electric field, but they responded differently near the surface. Water molecules nearest to the surface, forming a distinct layered structure with the hydrogen atom directed to the surface, increased the density with increasing field. On these bases, we discuss microscopic aspects of the electric double layer.     

Numerical renormalization group for continuum one-dimensional systems

We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Wilson's numerical renormalization group with Zamolodchikov's truncated conformal spectrum approach. The key to the method is that such theories provide a set of completely understood eigenstates for which matrix elements can be exactly computed. In this procedure the RG flow of physical observables can be studied both numerically and analytically. To demonstrate the approach, we study the spectrum of a pair of coupled quantum Ising chains and correlation functions in a single quantum Ising chain in the presence of a magnetic field.     

Numerical simulation of space-charge dynamics in a gyrotron trap

The particle-in-cell (PIC) method is used to simulate the self-consistent accumulation and bunching of space charge in the trap of a gyrotron electron-optical system. It is shown that it is possible to generate charge bunches that oscillate along the direction of the magnetic field. The dependence of the characteristics of these oscillations on the magnitude of the electron current into the trap is determined, along with the effect of the accumulated charge on the velocity distribution of electrons in the current passing through the magnetic mirror. Satisfactory agreement with the experimental data is obtained. Zh. Tekh. Fiz. 67, 98–101 (September 1997)     

CBMT测井数值模拟及水泥环第二界面成像

目前针对第一界面的固井质量评价技术已经很成熟,但第二界面固井质量评价仍存在很多问题.该文在中海油服自主研发的扇区水泥胶结成像测井仪器CBMT基础上,采用反褶积等算法,对数值模拟的CBMT仪器贴井壁测量的全波波形进行水泥环第二界面成像处理,并分析第一界面、第二界面不同胶结情况下的成像效果.通过成像分析得出,在水泥环第一界...     

Well-posedness of continuum models for weakly ionized plasmas

Continuum fluid models of weakly ionized plasmas are useful in the design and control of plasma-assisted deposition and etching processes. The equations in these models are numerically stiff. Their stiffness is affected by the imposed boundary conditions. In this work, a DC discharge model is studied and the effect of the boundary conditions on the model solution is investigated. It is established, both analytically and numerically, that depending on the choice of boundary conditions the model may range from being ill-posed to being solvable with standard software. It is also established that excessive truncation error maybe present in numerical simulations which appear to qualitatively capture plasma structure. Accurate numerical simulations of the considered model, with alternate boundary conditions, are shown to capture many characteristics of a DC discharge, albeit at lower values of applied voltage than those reported in the literature. Finally, model shortcomings are discussed     

Numerical simulation of underwater explosion bubble with a refined interface treatment

With the intermediate flow states predicted by local two phase Riemann problem,the modified ghost fluid method(MGFM)and its variant(r GFM)have been widely employed to resolve the interface condition in the simulation of compressible multi-medium flows.In this work,the drawback of the construction procedure of local two phase Riemann problem in r GFM was investigated in detail,and a refined version of the construction procedure was specially developed to make the simulation of underwater explosion bubbles more accurate and robust.Beside the refined r GFM,the fast and accurate particle level set method was also adopted to achieve a more effective and computationally efficient capture of the evolving multi-medium interfaces during the simulation.To demonstrate the improvement brought by current refinement,several typical numerical examples of underwater explosion bubbles were performed with original r GFM and refined r GFM,respectively.The results indicate that,when compared with original r GFM,numerical oscillations were effectively removed with the proposed refinement.Accordingly,with present refined treatment of interface condition,a more accurate and robust simulation of underwater explosion bubbles was accomplished in this work.     

On the validity of an einstein relation in models of interface dynamics

We consider models of interface dynamics derived from Ising systems with Kac interactions and we prove the validity of the Einstein relation=, where is the proportionality coefficient in the motion by curvature, is the interface mobility, and is the surface tension.     

Molecular dynamics simulation of a glissile dislocation interface propagating a martensitic transformation

The method of Parrinello and Rahman is generalized to include slip in addition to deformation of the simulation cell. Equations of motion are derived, and a microscopic expression for traction is introduced. Lagrangian constraints are imposed so that the combination of deformation and slip conform to the invariant plane shear characteristic of martensites. Simulation of a model transformation demonstrates the nucleation and propagation of a glissile dislocation interface.