Method to determine the equivalent thermal diffusion coefficient of the intumescent coating for cables

The thermal diffusion coefficient of the intumescent insulating layer, which forms when a fire-retardant coating is subjected to heat in a fire, is a key factor used in assessing the fire protection performance of the coating. However, because there are many factors influencing this coefficient, it is usually difficult to measure its value directly from tests. Based on the insulation failure experiment of a cable exposed to heat, the relationship between failure time, equivalent thermal diffusion coefficient, and thickness of expansion layer has been determined by means of numerical calculation from a heat transfer model built in this paper; a computing formula has been thus established. According to the formula, the equivalent thermal diffusion coefficient of the expansion layer can be determined after the diffusion coefficient and the thickness of the expansion layer are obtained from the insulation failure experiment of a cable.     

A method of determining the diffusion coefficient

Conclusions It is proposed to determine the diffusion coefficient by the moving boundary method, without using a solution of the diffusion equation, by studying the finishing stage of boundary movement in appropriate coordinates, which take account of the symmetry and characteristic dimensions of the system.The method is suitable for systems with the symmetry of a plate, a round cylinder, or a sphere, at an arbitrary dependence of the diffusion coefficient on concentration of the diffusing substance.In the case of spinning solutions, the studies may be carried out by observing the movement of the optical boundary in a round drop which is flattened out in the gap between two transparent plates, where, at a certain moment of time, a liquid containing the diffusing substance is introduced.Translated from Khimicheskie Volokna, No. 2, pp. 43–44, March–April, 1984.     

Determination of the trichloroethylene diffusion coefficient in water

Trichloroethylene (TCE) is a halogenated aliphatic organic compound frequently detected as pollutant in soils and ground water. To study the fate of TCE in water and to devise effective remediation strategies, a series of advection‐diffusion (dispersion) models, where the diffusion coefficient of TCE (D_TCE) is an important parameter, have been developed. However, D_TCE in water has never been experimentally determined and only theoretical values ( cm² s^?1 at 25°C) are present in the literature. A new method based on the Taylor dispersion technique, which allows to measure D_TCE in a broad range of temperature and, in principle, in any solvent is presented. At 25°C D_TCE = cm² s^?1 and the value increases almost linearly with the temperature, while, in the limit of the experimental error, is independent from [TCE] for dilute solutions. From the temperature dependence of D_TCE, it was possible to calculate the specific TCE fitting constant in the well‐known Wilke and Chang theoretical relation and the activation energy of the diffusion process through the Arrhenius plot. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3511–3515, 2015     

Estimation of the diffusion coefficient from sorption measurements

In this paper a procedure for the estimation of the diffusion coefficient for a sorption process from the measurements of the adsorbed amount is proposed. The experiments from which the data have been obtained are described and the numerical results are discussed.     

Using diffusion measurements to determine pore-size distributions in porous materials

A method for determining a type of pore-size distribution from diffusion measurements is presented. A Wicke-Kallenbach experiment, for measuring diffusion fluxes within porous materials, is carried out over a significant portion of the transition range between Knudsen flow and bulk diffusion. If the internal porous structure of the material is modeled as myriad nonintersecting cylindrical pores, an equation may be derived for the flux as a function of pressure, in which the flux is a functional of the pore-size distribution. The equation is a Fredholm integral equation of the first kind. This is an application of the general inversion problem, and solution of the equation for the pore-size distribution is possible. It is demonstrated from calculated fluxes using postulated ideal distributions that the method works very well for both unimodal and bimodal distributions. The method is not extraordinarily sensitive to experimental error. The pore-size distribution obtained using this method embodies not only the sizes of the pores, but includes other properties affecting diffusion rates, such as pore shapes, directions, and interconnectivities.     

Measurement of the diffusion coefficient of aluminum in mercury

The diffusion coefficient of aluminum in mercury was measured over a concentration of 0.9 to 14 mM. It was found to increase with increasing concentration from 1.2 × 10^?5 to 1.9 × 10^?5 cm² sec ^?1. This unusual dependence of D on C was attributed to the formation of aggregates of several aluminum atoms in the amalgam.     

盐种类和浓度对蛋白质疏水性吸附过程有效孔扩散系数的影响

研究了牛血清白蛋白在配基密度不同的两种疏水性吸附剂Phenyl Sepharose FF low sub和Phenyl Sepharose FF high sub上的吸附平衡和孔内传质动力学,重点考察了盐种类和浓度的影响.结果表明,Na2SO4溶液中盐浓度的增加导致蛋白质吸附容量的增大和解离常数的降低比(NH4)2SO4溶液更显著.利用孔扩散模型得到的有效扩散系数随盐浓度及配基密度的增大而提高,表明表面扩散作用对孔内传质的贡献随吸附容量提高而增大.     

A simplified method to determine the 3D orientation of an injection molded fiber‐filled polymer

In short‐fiber reinforced composites, it is widely accepted that the fiber orientation plays an important role on their overall physical and thermomechanical properties. To predict the properties of such composite materials, a full 3D fiber orientation characterization is required. A variety of destructive and nondestructive techniques have been developed, but all the methods have the same common point that they are very tedious and time consuming. Knowing that the fiber orientation induced by the flow remains mainly in the flow plane, an easier method has been performed for injection molded fiber‐filled polymers. It is based on the simple 2D SEM image analysis of a specific 45°‐oblique section plane. Then, the indetermination of fiber orientation from an ellipse mark analysis does not exist anymore. This novelty also turns out to be much more accurate. To achieve measurements over large composite samples, the method has been fully automated. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

A special case of spatial averaging of the diffusion coefficient

Steady-state mass transfer through a heterogeneous layer formed by coordinate planes of an orthogonal coordinate system is considered under the assumption that the boundary conditions at both layer boundaries are independent of coordinates. It is established that, if the coordinate dependence of the diffusion coefficient is described by the product of functions depending on different coordinates, then the surfaces of equal concentration (isohalines) coincide with the coordinate planes. It is shown that, in this case, the diffusion problem has an exact solution and the averaging of the diffusion coefficient is performed by elementary methods.Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 1, 2005, pp. 101–105.Original Russian Text Copyright © 2005 by Babenko.     

Measurement of diffusion coefficient and partition coefficient of sodium in nonionic polymer membranes

The difficulties involved in the measurement of the partition coefficient and diffusion coefficient of NaCl in hydrophilic polymer membranes are examined by the initial rate and late-time analysis of desorption data for three nonionic polymer systems. The late-time analysis, based on the plot of the logarithmic relative desorption versus time, was found to be useful when the diffusion is Fickian and the magnitude of D₂/l² is small. Depending on the magnitude of D₂/l², an accurate measurement of k₂ and determination of D₂ cannot be achieved without correction for the effect of surface salt solution, impossible with late-time analysis. The initial rate measurement was found more versatile for general non-Fickian diffusion and it gave a means of correction of the errors involved in estimating the partition coefficient. In general, the diffusion of NaCl in hydrophilic polymers is not ideal Fickian and the discrepancy between the two analyses is appreciable.     

On the formulation of the diffusion coefficient in isothermal binary systems

The diffusion of a component in a binary isothermal mixture can be regarded as arising either from its concentration gradient or from the gradient of its chemical potential. The ‘kinetic’ and the ‘thermodynamic’ approach can both be related to the simple, measurable, mutual diffusion coefficient D_m. When considering the concentration dependence of D_m the ‘thermodynamic’ approach leads naturally to the presence of the term (d ln a_i/d ln n_i), while the ‘kinetic’ approach does not. In systems showing marked non-ideality, of which two examples are discussed, allowance for this term greatly simplifies the concentration dependence of D_m. This lends support to the proposition that the gradient of chemical potential should be regarded as the ‘natural force for diffusion’. In ideal systems it does not matter which approach is used, but where non-ideality is marked, the ‘thermodynamic’ approach would appear to have advantage.     

Solubility and diffusion coefficient of antioxidants in polyethylene

As an aid in assessing the ability of antioxidant additives to persist in polymers and thus remain effective in protecting against oxidation, the solubility and diffusion coefficient of two antioxidants in branched polyethylene have been determined in this work. A method was developed for this purpose by which the diffusion coefficient and solubility could be determined simultaneously. The method consists of analyzing the concentration profile across a stack of polyethylene sheets through which the antioxidant was allowed to diffuse. The concentration of antioxidants in polyethylene was determined by a thermogravimetric technique which relies directly on the ability of the additives to suppress oxidation reaction. The diffusion coefficients determined showed excellent agreement with values in the literature which were obtained by a radiotracer method. The solubility of the antioxidants in three normal hydrocarbon solvents of varying molecular sizes was also determined by a conventional technique at various temperatures and found to correlate well with their solubility in polyethylene determined by the diffusion method. In particular, the dependence of the solubility on the size of solvent molecules and on temperature agrees well with an equation derived on the basis of the regular solution theory of liquid mixtures.     

Effective diffusion coefficient of chloride in porous concrete

A simplified diffusion model is given in the present paper to represent the chloride diffusion in porous concrete. The model with appropriate effective diffusion coefficient is shown to represent equally well as the more complex diffusion/reaction model proposed by Pereira and Hegedus.⁴ However the present model has the main advantages of being amenable to an analytic solution and ease of model parameter estimation.     

纸张干燥中湿分扩散系数的估算

纸张干燥过程涉及到多孔介质的热质传递,如何确定质量扩散系数是所建立的多孔物料湿分扩散模型能否进行数值计算的关键。按Liukov公式将湿分扩散系数视为含湿质量分数的非线性函数,在恒温下进行纸张干燥实验,通过比较湿分蒸发质量的测量值与理论计算值,采用多变量寻优的方法对多孔介质一维情况下的湿分扩散系数进行估算,得到了实验条件下的纸张湿分扩散系数的计算公式。并进一步确定了纸张中的湿分扩散系数与含湿质量分数和温度之间的函数关系式。     

氨基酸扩散系数的分子动力学模拟

采用分子动力学模拟的方法模拟了298. 15 K正则系综下甘氨酸、丙氨酸等12种氨基酸在水中的扩散过程，扩散系数的计算采用微分-区限变分法。计算结果表明：相同浓度下按不同分子数样本计算得到的扩散系数有较大差别，且分子数越多则模拟结果越接近于实验值。5种氨基酸在水中的扩散系数与文献值相对比，误差小于7%。还用同样的方法模拟了氧气在水中的扩散过程，模拟结果与实验结果吻合也较好。实验表明采用分子模拟手段可以获得具有工业应用价值的扩散系数，从而有助于计算传质学的发展。     

An approach to determine the second virial coefficient for calculation of phase equilibria in water-protein-neutral polymer systems

Summary A method to determine the apparent coordinates of critical points and effective values of the second virial coefficients in water-protein-neutral polymer systems enabling one to obtain the above values from data on the phase analysis within a restricted region of two-phase compositions has been proposed. The data obtained by this method for the coordinates of the critical points and binodals in water-bovine serum albumin-dextran (W-BSA-D) and waterbovine serum albumin-polyethylene glycol (W-BSA-PEG) systems are compared with experimentally determinated. Several peculiarities of the mechanism of the phase separation in above systems have been outlined in the course of this study.     

Stress dependence of the coefficient of moisture diffusion in composite materials

A model for the effect of external loading on diffusion into the bulk resin matrix of unidirectional composite materials is proposed. The model attributes the effect to a change in the free volume of the resin matrix, which is equal to its volume strain. The latter is calculated by substracting the volume strain of the fibers from that of the composite. The ratio of the diffusion coefficients in the stressed and unstressed states is expressed as a function of the stress level, the volume fraction of the fibers, and the angle between the applied stress and the fiber direction. Calculations for a glass-fiber-reinforced epoxy composites are presented.