瓷釉涂层/金属基体界面分形维数的研究

研究瓷釉涂层和金属基体界面形貌的分形特征,建立了分形曲线的提取模型,用计盒维数法计算分形维数,并和落球冲击试验结果相比较,发现分形维数的变化和瓷层的密着性的好坏呈现相同的变化趋势.分形理论为研究喷瓷管道的密着性提供了一种新的方法,为深入研究瓷层的密着性奠定了基础.     

分形理论及其在无机材料研究中的应用

分形学是一门处于迅速发展的学科,是研究复杂性科学理论的重要组成部分,其影响范围和应用领域也在日益扩大.在材料科学领域,分形学是一种研究材料的数学工具.笔者介绍了分形学的基本理论,分形维数的测定方法以及其在材料的烧结、氧化,薄膜的生长,材料的磨损、断裂,陶瓷粉体和玻搪材料中的应用,并展望了分形学的发展前景.     

聚合物基复合材料断面轮廓曲线的测量技术及其分形维数的测算方法研究

聚合物基复合材料的断面具有限层次的分形结构。首先介绍了触针式轮廓仪测量技术、微型貌图仪测量技术、光干涉显微测量技术和SEM测量技术等常用的材料轮廓曲线的测量技术的工作原理及其适用范围;其次分析了包括垂直界面法、尺码法、盒维数法、方差法、结构函数法、协方差加权法、功率谱法和均方根法在内的现有轮廓曲线分形维数的测算方法的基本原理。最后,文章指出该研究领域的主要发展方向。     

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。     

分形理论在PVC／粉末NBR共混研究中的应用

采用分形理论研究了PVC／粉末NBR弹性体共混界面中粉末NBR用量、共混界面的分形维数、材料的力学性能之间的关系，提出用分形维数来定量描述共混界面的几何特征。并发现PVC／粉末NBR共混界面的分形维数与材料的力学性能间变化关系一致，当粉末NBR用量达到2份时，分形维数和材料的拉伸强度均达到最大值，分别为1．87和15．8mPa。当粉末NBR用量超过29份时，分形维数及材料的力学性能也随之降低。     

不同渗透率岩心一次进汞-退汞回路的分形特征

利用压汞法测得的毛细管压力曲线,比较分析了不同渗透率岩心的一次进汞-退汞回路的形态特征、变化规律及其孔隙分布特征。结合分形理论,分别用单分形段和多线性段拟合方法对中高渗透岩心和低渗透岩心的分形维数进行了拟合,阐述了分形维数作为量化指标与不同孔隙分布特征的关系。结果表明,中高渗透岩心水银以连续相退出岩心孔隙,进汞-退汞回路的分形特征曲线近于平行,计算的分形维数接近;而低渗透岩心退汞过程水银的连续性被破坏,大部分水银由于被孤立而形成残余饱和度,定量表现为分形特征曲线拟合的分形维数与岩心中较小孔隙的分形维数值接近。     

基于数字图像法的新老混凝土粘结面粗糙度表征

提出了一种制作新老混凝土粘结界面人造粗糙度的方法,并基于分形理论对用数字图像法获得的粗糙界面形貌进行处理,以分形维数表征界面的粗糙度;再利用自编的Matlab程序实现界面的三维重组,验证了数字图像法的准确性;最后,研究了界面粗糙度与新老混凝土粘结性能的相关性。结果表明:新老混凝土粘结性能与界面分形维数呈正相关,存在近似关系R=aD+b。     

中孔纯硅分子筛的表面分形结构表征

采用计盒维数方法对中孔纯硅分子筛的结构进行了分形研究.结果表明:所研究的多孔分子筛结构存在分形现象.根据计算,室温晶化(25℃)和水热晶化(125℃)工艺所得到的产物分形维数分别为2.56和2.61,高于典型活性炭的分形维数2.21;而且3个样品的分形维数与其BET低温氮吸附法测试的比表面积变化趋势一致.因此,对多孔材料表面进行分形表征可与其表面性质相联系.     

分形理论及其在炭素材料研究中的应用（2）：—炭素材料中的分形研究

炭素材料中广泛存在具有分形结构的体系。本文综述了有关石墨、炭黑、焦、玻璃炭及木炭等多种嵌素材料中气孔界面分形结构的研究,说明在这些材料中气孔界面均是分形结构,且分形维数可取2～3之间的任何数值。这些研究同时表明,对炭素材料由不同的吸附质进行吸附或采用不同的理论测得的比表面均可以产生很大差别,但所得分形维数的数值却是一致的,预示分形维数在某些场合下能更好地描述材料的结构。毫无疑问,此时讨论比表面随吸附质截面的变化率——分形维数较比较比表面的具体数值大小更有意义。     

不同水灰比、养护条件下混凝土孔结构、抗压强度与分形维数之间的关系

采用压汞法测试不同水灰比、不同养护条件下水泥砂浆的孔结构参数,计算它们的孔分形维数,并对分形维数与水泥砂浆的孔结构参数及所对应混凝土的抗压强度之间的关系进行了分析.试验结果表明:水泥砂浆孔结构具有明显的分形特征,孔分形维数在3.4～3.7之间,随着水灰比的增大,不同养护条件下,孔分形维数及孔结构的特征参数变化规律不同,但总体说来,随着分形维数的增大,孔结构劣化;分形维数与混凝土抗压强度之间呈负相关性,因此孔分形维数可作为评定材料孔结构的综合性指标,并在一定程度上反应混凝土宏观性能的相对优劣.     

基于分形理论的岩相图像识别与分析

基于分形理论 ,应用计算机数字图像处理技术 ,提出了一种岩相图像识别与分析的新方法。在对典型岩相图像进行图像处理的基础上 ,介绍了岩相轮廓的顺序跟踪识别方法 ,给出了岩相轮廓分形维数的具体计算公式和方法 ,最终得到不同岩相轮廓的分形维数。通过比较不同岩相的分形维数可知 ,同一种岩相轮廓具有比较接近的分形维数 ,而不同岩相分形维数相差较大 ,这说明分形理论可用于岩相图像识别与分析。     

非均匀多孔介质表面变压过程的分形特征研究

多孔物质的表面结构可以用分形维数D来表征,D与微孔结构存在对应的关系,不同的表面分形维数对应不同的微孔结构．详细讨论了分形维数和微孔结构随压力的变化规律．随着压力的增大,多孔介质表面形成更小的吸附微孔,孔径分布广．表面变得更粗糙,分形维数增大,至到趋于稳定值．分形维数表达表面结构简洁明了．     

非均匀多孔介质表面变压过程的分形特征

多孔物质的表面结构可以用分形维数D来表征,D与微孔结构存在对应的关系,不同的表面分形维数对应不同的微孔结构.详细讨论了分形维数和微孔结构随压力的变化规律.随着压力的增大,多孔介质表面形成更小的吸附微孔,孔径分布广,表面变得更粗糙,分形维数增大,至到趋于稳定值.分形维数表达表面结构简洁明了.     

Modeling of three-dimensional groundwater flow using the method to calculate fractal dimension

A three-dimensional finite-difference groundwater flow model was developed by the use of fractal theory. The model developed in this study can simulate the groundwater flow in fractured aquifers as well as in porous aquifers. The model was designed to be able to use other parameters, such as permeability, hydraulic conductivity, porosity and fractal dimension besides hydraulic parameters which are used in MODELOW. Methods which can calculate box fractal dimension used in the Baecher model and mass dimension used in Levy-Lee Fractal model were developed. The results of the model and MODFLOW agreed exactly in the case of the fractal dimension of 2.0 without regard to the use of a fractal equation. The fact that the drawdown along the distance from the well increases by increasing the fractal dimension shows the effect of fracture on groundwater flow.     

A quantitative study on the surface crack pattern of concrete with high content of steel fiber

The mechanical properties and digital image analysis of slurry-infiltrated fiber reinforced concrete (SIFCON) were investigated experimentally. Fractal dimension is used as a parameter to characterize the crack pattern on the surface of SIFCON. It is found that there exists fractal phenomenon for different fiber contents of SIFCON, fractal dimension can be a parameter to characterize crack pattern on the surface of SIFCON quantitatively, and there exists a good correlation between mechanical properties and fractal dimension.     

The use of fractal analysis in the textural characterization of coals

The materials studied were four bituminous coals as well as the corresponding coal samples oxidized in air at 543 K for different periods of time. The method proposed by Friesen and Mikula, the procedure of Neimark and the methodology of Zhang and Li were successfully employed to analyze mercury porosimetry data from a fractal perspective. Fractal dimensions as well as fractal profiles are sensitive to oxidation treatment, being useful to follow the changes undergone by the coal samples. The evolution of the fractal dimension of coals with oxidation is determined by a balance between two main mechanisms of pore development: the oxidation of the pore surface itself that tends to lower the fractal dimension and the access of mercury to previously non-accessible regions that tends to increase this dimension.     

Evolution of aggregate size and fractal dimension during Brownian coagulation

Fractal aggregate coagulation is described within a general framework of multivariate population dynamics. The effect of aggregate morphology on the coagulation rate, is taken into account explicitly, introducing in addition to aggregate particle size, the aggregate fractal dimension, as a second independent variable. A simple constitutive law is derived for determining the fractal dimension of an aggregate, resulting from a coagulation event between aggregates with different fractal dimensions. An efficient Monte Carlo method was implemented to solve the resulting bivariate Brownian coagulation equation, in the limits of continuum and free molecular flow regimes. The results indicate that as the population mean fractal dimension goes from its initial value towards its asymptotic value, the distribution of fractal dimension remains narrow for both flow regimes. The evolution of the mean aggregate size in the continuum regime is found to be nearly independent of aggregate morphology. In the free molecular regime however, the effects of aggregate morphology, as embodied in its fractal dimension, become more important. In this case the evolution of the aggregate size distribution cannot be described by the traditional approach, that employs a constant fractal dimension.     

Simulation of structure and mobility of aggregates formed by simultaneous coagulation,sintering and surface growth

In this work, a new model for the simulation of nanostructured aggregates by simultaneous coagulation, sintering and surface growth is presented. Coagulation is treated as cluster–cluster agglomeration along the line connecting the center of mass of both agglomerates and is implemented using a Monte Carlo algorithm. Sintering is modeled as successive overlapping of spheres which cause reduction in the surface area based on a rate law for surface reduction. Surface growth is modeled as an increase in primary particle diameter, e.g. as a result of surface reactions. The evolved aggregates are analyzed by calculating their fractal dimension, radius of gyration, mobility diameter and mobility shape factor. It is found that the aggregates structure tends to be more compact when introducing the surface growth in shorter time comparing to the coagulation-sintering step only. Fractal dimension and the mobility shape factor of the resulting aggregates are correlated to an effective dimensionless time that combines the characteristic times of these three fundamental mechanisms. It is shown that the mobility diameter in the free molecular regime is not proportional to the radius of gyration. A power law relation that correlates the aggregates projected area and the equivalent number of primary particles is found to be in a very good agreement with estimates published in literature.     

谷壳热解过程中颗粒孔隙结构分形特性

由于颗粒相本身的复杂特性,因此研究者多是对生物质颗粒定性或就某一方面进行描述。借助分形理论可以对颗粒物理结构进行全面而精确的表征。本文利用分形BET方程,基于非线性最小二乘法,提出一种新的分形维数计算途径。该方法是根据多层吸附理论,对氮气等温吸附/脱附法测定的数据分析,直接获得表征整个吸附范围的颗粒分形维数,同时回归得到吸附过程中的吸附层数。分析表明,该方法计算得到的分形维数在数学层面上可以很好地表征颗粒内部微孔特征,同时通过对计算得到的吸附层数分析发现该计算结论也能被多层吸附理论解释,表明该方法在物理层面上也符合实际情况。利用该方法计算得到谷壳在快速热解条件下焦颗粒分形维数的变化。     

Computer simulation of fractal dimensions of fat crystal networks

The rheological properties of fat-structured products are determined by the microstructure of their fat crystal networks, which can be quantified by using microscopical and rheological techniques. Of particular interest to this study is the quantification of the fractal dimension of the network using these two techniques. Fractal dimensions determined by polarized light microscopy include box-counting, particle-counting, and Fouriertransform fractal dimensions, whereas the fractal dimensions determined by small deformation dynamic rheology exploit the dependence of the storage modulus on the solids' volume fraction. This work reveals that different microscopy fractal dimensions are sensitive to different microstructural factors within the fat crystal network, and thus have different physical meanings. The boxcounting fractal dimension, D _b , increases with increases in crystal size and area fraction of the fat crystals, whereas the particlecounting fractal dimension, D _f , is sensitive to the radial distribution pattern of fat crystals; and the Fourier-transform fractal dimension, D _FT, decreases with increasing crystal size. In the studies on the macroscopic physical properties of fat crystal networks, it is necessary to find the determining structural characteristics and then use the fractal dimensions that are most closely related.