THE ANALYTICAL SOLUTION FOR SEDIMENT REACTION AND DIFFUSION EQUATION WITH GENERALIZED INITIAL-BOUNDARY CONDITIONS

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Monte Carlo Simulations of Observation Time-Dependent Self-Diffusion in Porous Media Models

Observation time-dependent self-diffusion coefficients can be used to obtain microstructural information of porous media. This paper presents two different kinds of Monte Carlo simulations of the self diffusion process of fluids like water in porous systems, a lattice-free method and a lattice-based method. The results for simple porous media model geometries agree well with each other and with published analytical as well as semi-analytical equations. The use of these equations, which are important for the interpretation of Pulsed Field Gradient-Nuclear Magnetic Resonance (PFG-NMR) time-dependent diffusion data with respect to properties of porous media, is discussed.     

对流扩散方程的迎风变换及相应有限差分方法

本文提出所谓迎风变换,将对流扩散方程分解为对流迎风函数和扩散方程,并构造相应的有限差分格式。对流迎风函数以简明的指数解析形式反映对流扩散现象的迎风效应,原则上消除了源于不对称对流算子的困难,能够便利对流扩散方程的数值求解。有限差分格式具有二阶精度和无条件稳定性,算例表明其准确性、收敛速度及对边界层效应的适应能力均明显优于中心差分格式和迎风差分格式。     

Simulation of anisotropic diffusion processes in fluids with smoothed particle hydrodynamics

Anisotropic diffusion phenomenon in fluids is simulated using smoothed particle hydrodynamics (SPH). A new SPH approximation for diffusion operator, named anisotropic SPH approximation for anisotropic diffusion (ASPHAD), is derived. Basic idea of the derivation is that anisotropic diffusion operator is first approximated by an integral in a coordinate system in which it is isotropic. The coordinate transformation is a combination of a coordinate rotation and a scaling in accordance with diffusion tensor. Then, inverse coordinate transformation and particle discretization are applied to the integral to achieve ASPHAD. Noting that weight function used in the integral approximation has anisotropic smoothing length, which becomes isotropic under the inverse transformation. ASPHAD is general and unique for both isotropic and anisotropic diffusions with either constant or variable diffusing coefficients. ASPHAD was numerically examined in some cases of isotropic and anisotropic diffusions of a contaminant in fluid, and the simulation results are very consistent with corresponding analytical solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

Physicomathematical modeling of the processes of capillary impregnation of porous materials

The process of capillary impregnation of porous materials is studied numerically. A physicomathematical model of liquid diffusion in a porous sample is proposed. The model involves an analytical presentation of the diffusion coefficient, which describes available experimental data. A method of solving one-dimensional unsteady problems of impregnation is developed and tested on a self-similar solution of the corresponding boundary-value problem of impregnation. If the impregnation process is sufficiently long, the motion of the liquid in the sample is described by a stable self-similar solution. A classification of moisture diffusion on the basis of the initial humidity on the sample boundary is proposed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 42–51, January–February, 2009.     

On diffusion velocity and the mass conservation equation for components

The mass migration velocity(absolute velocity)of component i in a multicomponent flow is equal to the convection velocity(frame velocity)plus the diffusion velocity(relativevelocity).The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.In turbulent flow,the mass migration velocity of component i is(?)(mass-weighted time average velocity).The diffusion velocity(-a)consists of turbulent diffusionvelocity(?)and molecular diffusion velocity(?)(?is the simple time average velocity of component i and a is a certain convection velocity).So,the part of turbulent diffusion velocity is independent of what convection velocity is taken.In the mass conservation equation for component i,the expression for the diffusion term on its right-hand side will change when the convection velocity on its left-hand side changes.In turbulent flow,there could be no diffusion terms,or a turbulent diffusion term only,or both the turbulent and molecular diffusion     

Application of a n-Phase Model to the Diffusion Coefficient of Chloride in Mortar

The determination of the chloride diffusion coefficient of a concrete is needed to help the prediction of the service life of concrete structure. In this paper, we propose first a critical review of models for chloride diffusion coefficients already used in literature at different scales and then we develop an analytical model, which takes into account the characteristics of the different phases of concrete. These materials are treated as a three-phase composite, consisting of a cement continuous phase, of an aggregates dispersed phase and of an interface transition zone. Chloride diffusion coefficient using an n-layered inclusion-based micromechanical modeling is predicted. The details of calculations are summarized hereafter and experimental measurements obtained on mortars are compared with predicted results.     

粉末热压扩散与应力场耦合的力学模型

以弹性接触应力场为初始条件,建立了热压条件下球形颗粒表面扩散与应力场耦合的力学模型. 引入包含表面能项级数形式的应力函数,以描述随时间演化的表面扩散过程及扩散对应力场演化的影响. 而应力场通过改变化学势梯度,又会促进(或阻止)表面扩散结合的进程.利用该模型分析了压力、温度和界面区应力场演化对致密化参数的影响. 比较了满足粘着或非粘着对结合宽度和应力分布的影响,将考虑粘着的弹性接触应力场作为初始条件,分析了弹性变形和表面扩散共同驱动的粉末冶金热压烧结致密化规律.      

Triphasic FE Modeling of the Skin Water Barrier

A skin–air model is developed to model the water barrier function of skin. The skin model is a porous solid saturated with a monovalent salt solution. The air model is a vapor diffusion model in non-moving air. In vivo measurements of water loss from human skin under varying ambient conditions are used to validate the model.     

Coupled Water and Salt Transport in Porous Materials: Rapid Determination of a Varying Diffusion Coefficient from Experimental Data

A direct method for an accurate and rapid evaluation of a varying salt diffusion coefficient, \(D\) , from experimental data is proposed for a coupled water and salt transport in porous materials. The evaluation uses data on the moisture and salt concentration profiles and is based on a formula obtained from the Boltzmann-Matano method. The coupled transport is described by the diffusion-advection model of Bear and Bachmat. A simple expression for \(D\) in the center of the concentration interval is deduced from the formula to provide a rapid estimate on \(D\) . Possible extensions of this analytical approach are pointed out, suggesting that it can serve as a convenient general tool in engineering calculations. The theoretical results are applied to a laboratory experiment in which a coupled moisture and chloride transport had been investigated in a lime plaster, and the chloride diffusion coefficient had been obtained numerically in dependence on the chloride concentration. The agreement with the numerical results is shown to be rather good, except at low concentrations where our analytical results should be more reliable. It is also shown that the unusually high value of the calculated chloride diffusion coefficient—about three orders of magnitude higher than for free chloride ions in water—cannot be explained by possible inaccuracies in the measurements and/or numerical calculations. The reason is that changes in the measured profiles’ data could cause a change in \(D\) of just the same order of magnitude. This shows that, besides diffusion and advection, additional mechanisms take part in the considered chloride transport.     

Mixing dynamics of a vapor-condensate cloud with the ambient air

The mixing of a wet vapor with a gas is studied using analytical and numerical models. The one-dimensional problem of diffusion mixing accompanied by phase transitions is solved in a self-similar formulation. The versions of mixing of the vapor with a cold and warm gas and with a superheated vapor are analyzed. The atmospheric diffusion of immediate emissions containing water vapor and condensate is modeled numerically in a three-dimensional formulation. A study is made of the evolution of hydrodynamic, concentration, and temperature fields as a function of the initial emission parameters (temperature and humidity) and ambient air parameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 114–127, May–June, 2008.     

A coupled lattice Boltzmann model for the shallow water‐contamination system

A coupled numerical method for the direct simulation of shallow water dynamics and pollutant transport is formulated and implemented. The conservation equations of shallow water dynamics equations and the convection–diffusion equations are solved using the lattice Boltzmann (LB) method. The local equilibrium distribution of the pollutant has no terms of second order in flow velocity. And the relaxation time of the pollutant deviates from a constant for the flows with variable free surface water depth. The numerical tests show that this scheme strictly obeys the conservation law of mass and momentum. Excellent agreement is obtained between numerical predictions and analytical solutions in the pure diffusion problem and convection–diffusion problem. Furthermore, the influences on the accuracy of the lattice size and the diffusivity are also studied. The results indicate that the variation in the free surface water depth cannot affect the conservation of the model, and the model has the ability to simulate the complex topography problem. The comparison shows that the LB scheme has the capacity to solve the complex convection–diffusion problem in shallow water. Copyright © 2008 John Wiley & Sons, Ltd.     

一类三维随机动力系统的最大Lyapunov指数

基于一维扩散过程的奇异边界理论,使用摄动方法研究了白噪声参激的一类余维二分岔系统的最大Lyapunov指数渐近表达式和数值解,主要讨论了一维相扩散过程同时存在两类奇异边界以及FPK方程存在平稳解的一般性条件. 通过对参激噪声作用项系数矩阵的分析,给出了不变测度的解析解及其相应的Monte Carlo数值仿真结果,并导出了一维相扩散过程P分岔点的确定方法. 对于一类特殊情形,给出了最大Lyapunov指数的渐近表达式;对于参激噪声作用项系数矩阵的一般情形,则给出了系统最大Lyapunov指数的数值结果.      

The spatial evolution of velocity and density profiles in an arrested salt wedge

The spatial variation in the properties of an arrested salt wedge have been investigated, both analytically and in the laboratory. In the laboratory particle image velocimetry and laser induced fluorescence were used to obtain flow velocities and the height of the density interface. An analytical solution for the profile of interface height, in the absence of interfacial instabilities, has been developed from two-layer internal hydraulic theory. The evolution of the velocity profile is predicted using a momentum diffusion equation following a Lagrangian frame of reference along the interface of the salt wedge. The centre of the shear layer is predicted to lie above the density interface, with this offset decreasing in the downstream direction. Our theoretical predictions are in good agreement with our laboratory measurements.     

Capillary absorption in porous sheets and surfaces subject to evaporation

Capillary absorption by an initially dry porous sheet or surface is examined. The sheet absorbs moisture from one end while evaporation takes place across its surface. We are interested in the effect of evaporation on the progress and distribution of moisture in the sheet, including the equilibrium moisture profile. The process is modelled using a nonlinear diffusion equation with a linear sink. An algebraic analytical approximation is obtained relating the various physical parameters as well as an exact steady state solution for arbitrary properties. The complete problem is solved numerically. Good agreement is obtained between the analytical and numerical solutions.     

A note on two upwind strategies for RBF‐based grid‐free schemes to solve steady convection–diffusion equations

In this paper, two radial basis function (RBF)‐based local grid‐free upwind schemes have been discussed for convection–diffusion equations. The schemes have been validated over some convection–diffusion problems with sharp boundary layers. It is found that one of the upwind schemes realizes the boundary layers more accurately than the rest. Comparisons with the analytical solutions demonstrate that the local RBF grid‐free upwind schemes based on the exact velocity direction are stable and produce accurate results on domains discretized even with scattered distribution of nodal points. Copyright © 2009 John Wiley & Sons, Ltd.     

Moving Boundary Problem for Diffusion Release of Drug from a Cylinder Polymeric Matrix

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｄｉｆｆｕｓｉｏｎｒｅｌｅａｓｅｏｆｄｒｕｇｆｒｏｍａｐｏｌｙｍｅｒｉｃｍａｔｒｉｘｉｓａｎｉｍｐｏｒｔａｎｔｐｒｏｂｌｅｍｉｎｔｈｅｄｒｕｇｃｏｎｔｒｏｌｌｅｄｒｅｌｅａｓｅｓｙｓｔｅｍ .Ｉｔｉｓｏｎｅｏｆｔｈｅｍａｉｎｃｕｒｒｅｎｔｄｉｒｅｃｔｉｏｎｓｆｏｒｅｘｐｌｏｉｔｉｎｇｎｅｗｄｒｕｇｓｔｈａｔｔｈｅｃｏｎｔｒｏｌｌｅｄｒｅｌｅａｓｅｄｒｕｇｗａｓｍａｄｅｂｙｐｕｔｔｉｎｇｔｈｅｅｆｆｅｃｔｉｖｅｔｒｅａｔｍｅｎｔｄｒｕｇｉｎｔｏｐｏｌｙｍｅｒｉｃｍａｔｒ…     

Two-dimensional interactions due to moving load in generalized thermoelastic solid with diffusion

The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.     

Numerical Experiments in Scalar Diffusion under Stochastic Convection

We study scalar diffusion, both from Eulerian and Lagrangian perspectives, advected by two dimensional flows. Emphasis is devoted to the problem of scalar diffusion under a synthetic turbulent flow. We present numerical and analytical results for the turbulent diffusion coefficient either from the influence of the turbulent synthetic field and a periodic array of eddies. Preliminary results concerning Lagrangian dispersion are also reported.     

地球物理流体动力学的发展和室内实验研究的影响

系统介绍了大气、海洋与新兴的地质系统中的流体力学,尤其是通过室内实验的研究进展．详细描述了诸如羽流、湍流、卷挟、异重流、海洋环流、混合层、双扩散、盐指、锋面、岩浆库、地幔对流、板块运动、热斑等有趣的地球物理现象,它们对于了解因浮力引起的对流的机理是十分重要的．同时在气候、环境、灾害、成矿等领域有广泛的应用．论文反映了在 Ｇ．Ｉ． Ｔａｙｌｏｒ, Ｇ．Ｋ． Ｂａｔｃｈｅｌｏｒ领导下剑桥研究组的风格──通过小型室内实验了解机理,再用应用数学方法求解问题,他们对流体力学的发展作出了重大贡献．