气体有效扩散系数的分形模型

多孔介质中杂乱无序的孔分布结构特性显示了多孔介质具有孔分形结构。气体扩散在孔道中的分形模型是建立在分形理论和气体扩散特点的基础上。在考虑孔的大小分布、连通性分布和2种气体扩散机理的影响下,推导出了气体有效扩散系数和结构参数的关系。从参数分析中,可以得出有效扩散系数与孔的面积分形维数、孔隙率、联通数、气体自由扩散路径、孔最大最小直径比值成正比,与孔道迂曲度、迂曲分形维数成反比。通过实验数据与模型预测值对比验证了分形模型的正确性。     

分形多孔介质中气体的非稳态扩散

通过引入平均修正系数修正Fick第二扩散定律得到了描述分形多孔介质气体非稳态扩散的理论方程。基于“塞状流”扩散实验法建立了分形多孔介质非稳态扩散实验系统,对3个孔隙结构不同的分形多孔介质样品进行了非稳态扩散实验,通过实验对理论方程进行验证和修正。结果表明,Fick第二扩散定律不适用于分形多孔介质中气体非稳态扩散,分形多孔介质中气体非稳态扩散存在一定规律,且多孔介质孔隙结构不同其扩散规律不同。     

分形多孔介质的孔隙特性对气体扩散的影响

采用随机行走方法建立了分形多孔介质生成模型,生成的颗粒在形貌上与真实多孔颗粒接近,且能够反映其固有分形特征。在此模型基础上,根据经典分子动理论建立扩散控制方程,对气体在多孔介质中的扩散进行数值模拟。分析了比表面积、平均孔径、孔隙率等孔隙特性参数对扩散的影响,获得了分形多孔介质中气体扩散系数与平均孔径的函数关系。结果表明,扩散系数随平均孔径的增大以幂函数形式增大,相应的指数表征扩散系数对平均孔径的敏感度,其值随孔隙率的增大呈线性减小。     

基于分形理论的纳米颗粒多孔介质真空导热特性

采用分形理论,描述了纳米颗粒多孔介质材料的微尺度空间结构,建立了分形等效单元体模型,分析了影响其真空下有效热导率关键因素为固体基质热导率、填充率、分形维数、分形直径、残余气体压力及热导率等,并导出了气相、固相热传导计算公式和热辐射等效热导率计算公式及多孔介质材料总有效热导率计算公式。研究表明,纳米颗粒有效热导率随着分形直径、残余气体压力的增大而增大,并给出了纳米颗粒多孔介质材料作为真空材料的最佳直径。同时,模型计算值与实验测量值比较,具有较好的一致性。该理论分析方法对新型真空绝热材料的研制和绝热性能的提高具有实用价值。     

由吸附等温线分析膨润土的分形孔隙

膨润土是一种多孔的粘土材料，对气相和液相中的污染物均有很好的净化效果。为了了解其对气体的吸附性能，用氮气吸附等温线分析了2种膨润土和1种活性白土的BET比表面积和孔隙分布，并应用基于FHH模型的方法计算了它们的分形维数。结果表明，普通膨润土的分形维数接近2，而活性白土的达到了2．59。讨论了孔隙度、比表面积以及分形维数等参数与吸附量的关系，表明分形维数更能反映膨润土对气体的吸附性能。     

基于分形理论的油页岩有效扩散系数研究

以直径为1.6—2 mm柳树河油页岩为原料,采用扫描电镜法与氮吸附法得出油页岩吸附-脱附等温线,孔径分布曲线等;分析了油页岩内部孔隙结构,计算出孔道弯曲分形维数与孔隙面积分形维数,并研究油页岩内部的有效扩散系数。结果表明:油页岩吸附-脱附曲线属于Ⅲ型等温线,是一种典型的二端都开放的管状毛细孔型结构的多孔物质;其含有较发达孔隙,孔径分布为0.4—40 nm;油页岩孔道弯曲分形维数越小,孔道越平坦,孔隙面积分形维数为2.464;油页岩有效扩散系数与其内部结构和操作温度有关,温度越高,粒径越小,有效扩散系数越大。     

石墨基浸金属多孔材料微观孔隙结构及其分形特征

为定量描述石墨基浸渍金属材料的孔隙结构特征并研究其对浸渍过程的影响规律,在石墨基多孔材料孔隙形成机理研究的基础上,分析形成浸不透孔洞的原因,并运用分形理论对孔隙结构特征进行了描述. 研究表明,石墨基浸渍金属多孔材料的孔隙结构具有典型的分形特征,其基体、孔隙、浸渍金属分形维数分别为1.80~1.85, 1.55~1.65, 1.50~1.55,未浸渍区域的分形维数为1.42~1.60,孔隙率为17.25%~24.85%. 分形维数反映了孔隙结构的非均质性,与采用压汞实验获得的孔隙率变化规律有较好的一致性,证明可用分形维数表征石墨基浸金属材料的孔隙率.     

在多孔介质内气体扩散的分形表征

将多孔介质内孔抽象为分形曲线,并以该曲线的维数作为多孔介质的结构参数—谱维数d,藉此建立了气体在介质内的扩散通量计算式,并给出了测量分形结构码尺的计算方程和多孔介质谱维数的测定方法.由双组分气体在Ni/r- Al_2O_3催化剂上的扩散实验数据,计算出该催化剂的谱维数d=1.10.     

分形多孔介质传热传质过程的格子Boltzmann模拟

针对自然界中实际多孔介质具有的分形特性和随机性,利用中点替代算法和二值化处理构造统计上具有分形特性的随机多孔介质。分析了所构造的多孔介质盒维数与Hurst指数之间的关系。基于随机分形构造的原理,对二维实际多孔介质图像进行了重构。利用两点相关函数,分析了重构图像的结构相关性, 并与实际目标多孔介质的结构特征进行比较。在与解析解对比验证的基础上,将基于二元混合理论的格子Boltzmann模型（LBM）用于模拟多孔介质内流体扩散过程。通过计算不同分形特性的二维多孔介质的有效扩散系数,研究了重构多孔介质的分形维数与有效扩散系数的关系。利用热耦合LBM模型计算多孔介质内传热过程,分析了不同的分形特性对多孔介质蓄热过程的影响。     

分形多孔介质传热传质过程的格子Boltzmann模拟

针对自然界中实际多孔介质具有的分形特性和随机性,利用中点替代算法和二值化处理构造统计上具有分形特性的随机多孔介质。分析了所构造的多孔介质盒维数与Hurst指数之间的关系。基于随机分形构造的原理,对二维实际多孔介质图像进行了重构。利用两点相关函数,分析了重构图像的结构相关性,并与实际目标多孔介质的结构特征进行比较。在与解析解对比验证的基础上,将基于二元混合理论的格子Boltzmann模型(LBM)用于模拟多孔介质内流体扩散过程。通过计算不同分形特性的二维多孔介质的有效扩散系数,研究了重构多孔介质的分形维数与有效扩散系数的关系。利用热耦合LBM模型计算多孔介质内传热过程,分析了不同的分形特性对多孔介质蓄热过程的影响。     

基于显微边界形貌分形特征的耐火材料侵蚀维数研究

通过对侵蚀残砖的显微边界形貌研究发现 :耐火材料的抗侵蚀性能和基于显微边界形貌分形特征的分形维数存在良好的线性关系。根据分形维数的定义和含义 ,作者提出了一种基于分形理论的耐火材料侵蚀维数Rf (Refractoryfractal)的概念和抗侵蚀分类建议。根据耐火材料的使用经验和实绩而定义的Rf =[1.0 ,1.0～ 1.15 ,1.15～ 1.2 0 ,≥ 1.2 ]数值范围 ,可以用于耐火材料抗侵蚀性能的评判、分类 ,并且可用于设计选型和编制相对应的耐火材料的残余安全厚度的日常维护规程等     

Polymersomes mimic biofilms fractal growth

We have mimicked the biofilm formation with highly stable biocompatible poly(2-methyl-2-oxazoline)-based polymersomes by simple spreading-drying of a droplet of the sample solution onto a glass support. The diffusion-limited aggregation process of polymersomes onto the surface was analyzed within a fractal framework. The different examples analyzed and presented together indicate one means by which the aggregation process can be controlled and predicted. The anti-bacterial adhesion properties of poly(2-methyl-2-oxazoline) allow potential uses in surface modification for biofouling prevention improving stability and response time.

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The fractal analysis of copolymerization processes

The results obtained in the present article show that the fractal analysis and irreversible aggregation models application allow to obtain a clear physical picture of copolycondensation process and estimate its quantitative characteristics. The basic characteristic, controlling this process, is fractal dimension D_f of macromolecular coil in solution. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Radial density distribution of fractal clusters

The radial density distributions of fractal clusters generated in both DLCA and RLCA conditions by Monte-Carlo off-lattice cluster-cluster aggregation have been investigated. It has been computed by averaging a large number of clusters of same mass to form an average cluster, which is then considered as spherically symmetric. It is found that the radial density distribution, calculated using the mass center of the cluster as the center point, does not follow the fractal scaling, as sometimes assumed in the literature. An empirical model has been proposed to describe the dependence of the radial density distribution on the number of particles in the cluster. The obtained radial density distribution is used to compute permeability profile of the fractal cluster using several literature models, which is then applied to estimate the cluster hydrodynamic radius, R_h, by considering the cluster as a porous permeable object and using the solution of Brinkman equations for the fluid flow inside the cluster. The so obtained R_h values are compared to those in the literature, computed using the Kirkwood-Riseman (KR) theory. It has been found that, among the five permeability models examined, only the model proposed by Davis (Proceedings of the Institution of Mechanical Engineers Part B 1, 185) provides results in good agreement with those obtained using the KR model. Furthermore, it has been verified that the R_h values are insensitive to the model used for the density distribution.     

One-step creation of hierarchical fractal structures

Relatively recently, we advanced a route to create, in a controlled fashion, combined horizontal and vertical stratified structures by simple and energy-efficient processing operations employing static mixing elements. While in state-of-the-art static mixing the focus is on layer multiplication, here the aim is to create hierarchical fractal structures. Therefore, the main question addressed in this article is how structures, rather than layers, can be multiplied. The key aspect is the addition of layers on the sides or in the midplane of the flow during the process; every addition step increases the hierarchy by one level. This article derives the general formalism for forming fractal structures with controlled hierarchy, and we develop the language required to design and construct the dies. The main part of the article addresses this main topic and is based on the splitting serpentine static mixer geometry that can be easily made on the parting surfaces of a mold on both the micro- and the macroscale. The second part of the article addresses the strategy to minimize the number of mirroring steps, eventually avoiding mirroring completely, and is based on the rotation-free multiflux static mixer geometry. With the design language derived, complex hierarchical fractal structures can be generated simply by changing the number and sequence of operators within extrusion dies or molds, providing a one-step solution to produce material structures for potential use in diverse applications ranging from advanced mechanical systems to photovoltaic devices, where controlled assembly of dissimilar materials, and the realization of huge interfaces and genuine cocontinuity throughout the cross section, is critical.     

A comprehensive fractal char combustion model☆

The char combustion mechanisms were analyzed and a comprehensive fractal char combustion model was developed to give a better understanding and better predictions of the char combustion characteristics. Most of the complex factors affecting the char combustion were included, such as the coupling effects between the pore diffusion and the chemical reactions, the evolution of the char pore structures and the variation of the apparent reaction order during combustion, the CO/CO2 ratio in the combustion products and the correction for oxy-char combustion. Eleven different chars were then combusted in two drop tube furnaces with the conversions of the partly burned char samples measured by thermogravimetric analysis. The combustion processes of these chars were simulated with the predicted char conversions matching very well with the measured data which shows that this char combustion model has good accuracy. The apparent reaction order of the char combustion decreases, stabilizes and then increases during the combustion process. The combustion rates in the oxy-mode are general y slower than in the air-mode and the effect of the char-CO2 gasification reac-tion becomes obvious only when the temperature is relatively high and the O2 concentration is relatively low.     

分形理论在高技术陶瓷材料研究中的应用

分形方法是研究材料科学的一种数学工具。本文以Mo／β＇－Sialon系梯度功能材料为例，探讨了分形在材料科学研究中的应用。     

分数维几何在非均相催化中的应用

80年代以来,分数维几何已用于非均相催化研究。介绍了分数维几何在定量评估催化反应的结构敏感性、鉴别活性位、催化材料的性能测试、计算机模拟催化剂表面形貌设计及催化反应工程等方面的研究动向。     

The fractal dimension of corroded aluminium surfaces

The nature of surface features produced during the corrosion of a metallic surface is an important parameter that can affect both the corrosion kinetics and the response of the interface to electrochemical probing. These features are so visibly present, when the surface properties are studied over a certain frequency range, that scientists have recognized and attempted to model them for almost seventy years. But while the evidence is high that many of these features are probably related to the fractal nature of the surface, actual experimental evidence is still quite scarce. In this paper an attempt is made to correlate the fractal dimension of surface profiles measured with a commercial instrument on corroded aluminium specimens with results obtained with electrochemical impedance spectroscopy (EIS).