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介绍了分形理论的主要内容,包括分形定义、特性和测定分形维数的方法,概括和评述了近年来分形理论在高分子链结构、结晶过程、溶液中、高分子材料断裂、磨损以及其他方面的研究和应用,并展望了分形理论今后的发展趋势。 相似文献
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本文从分形理论基础出发,总结了分形理论的发展历程和其核心内容。在论证了分形理论在渗流力学中应用的可行性后,总结了渗流力学和分形理论结合所产生的成果和研究现状。并进一步指出了分形理论在渗流力学中应用所存在的问题和未来的研究趋势。 相似文献
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Effects of surface topography of material on nucleation site density of dropwise condensation 总被引:1,自引:0,他引:1
Chunfeng Mu 《Chemical engineering science》2008,63(4):874-880
Heterogeneous nucleation is very important for the initial droplet formation of dropwise condensation, and it is directly related with the surface properties of materials. In this paper, the relationship of nucleation site density with surface topography in nanometer scale for dropwise condensation was experimentally studied on surfaces of magnesium in view of that magnesium can react with hot water (condensate) and make the chemical compositions of the surface changed, and thus leave the nucleation sites in nanometer on the surface. The differential box-counting was used to calculate the fractal dimension of these magnesium surfaces. And condensation experiments were carried out on the magnesium surfaces with different topography under same subcoolings and condensation time. The results showed that surface topography has a great influence on nucleation site density. The larger the fractal dimensions the more the nucleation sites. A new formula to calculate the nucleation site density was proposed based on the modification of Rose's formula with the experimental data. And this new formula can reflect the effect of surface fractal dimension on the nucleation sites. 相似文献
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Dongming Tang Alejandro G. Marangoni 《Journal of the American Oil Chemists' Society》2006,83(4):309-314
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. 相似文献
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利用氮气等温吸附脱附法和电镜扫描研究了印尼油砂干馏热解过程中半焦表面特性的变化,并利用分形维数来定量描述半焦表面形态的复杂程度。结果表明,半焦BET比表面积与孔容积随干馏终温的变化趋势相近,均呈现先增大后减小的趋势。通过FHH方程回归得到的分形维数能够较好地反映半焦内部孔隙结构的分形特性,挥发分的吸出、塑性变形、气体产物的逸出以及油蒸汽的再凝结造成的闭孔效应的多种作用的交替影响,使分形维数在不同的温度区间有不同的变化趋势。电镜扫描能够直观地观察到半焦表面的孔结构特征,利用Matlab编程分析电镜图片得到的盒子维数与氮吸附数据拟合得到的FHH分形维数变化趋势基本一致。 相似文献
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Direct image-based fractal characterization of micromorphology of calcium carbonate fouling crystals
Researches on macroscopic fouling behavior and micromorphology are usually conducted separately. In this paper, the relationship between the macroscopic fouling behavior and micromorphology on different materials is established. A direct fractal-characterization approach based on the micrographs of calcium carbonate fouling crystals is presented. The box-counting method is used to characterize the fouling crystals. For fractal measurements, t-distribution tests of linear regression hypothesis are performed at the significance level of 0.01. If all listed absolute t-statistics with the minimum of 164 are higher than the corresponding t value, the fouling crystals are determined as fractal, with a confidence level of 99%. The fractal dimensions obtained from the micrographs of different visual fields of a specimen are demonstrated to be almost identical, with maximum and minimum relative values of 4.42% and 0.75%, respectively, and standard deviations ranging from 0.0062 to 0.0266. The irregularity of the crystal morphology indicates larger fractal dimensions. Comparison and analysis of the relationship between macroscopic fouling behavior and micromorphology show that the larger fractal dimension of crystal morphology suggests a small amount of surface fouling. Thus, the reasons for the differences in the macroscopic fouling behaviors of different materials are revealed geometrically. 相似文献
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《分离科学与技术》2012,47(18):2713-2723
2D fractal dimension analysis of inline-coagulation (IC) flocs in microfiltration of NOM using power-law relationship and box-counting was done. Different process conditions represented by two types of coagulants (PIX and PAX) at four different hydraulic gradients (G-values of 4, 31, 98, and 300 s?1) were tested. Fractal dimensions of the flocs formed under the varying process conditions were found to be different. Overall NOM removal was found to be similar for all cases; however, the membrane filtration and fouling phenomenon observed were affected by the process conditions. This study has investigated the relationships between fractal dimensions, aggregate properties, and membrane fouling behavior observed. In general, PIX resulted in higher particle concentrations and the more irregular floc shapes resulted in high irreversible fouling, lower specific cake resistance, and a more compressible cake layer. In contrast, PAX resulted in lower particle concentrations and the more regular floc shapes resulted in a more reversible fouling, higher specific cake resistance and a less compressible cake layer. The fractal dimensions properties were found to be complementary for the analysis of membrane and cake resistances and can be useful tools in membrane fouling elucidation and minimization. 相似文献
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A coagulation coefficient of agglomerates with different fractal dimensions has not been considered in the past, even though there is a possibility of variations in the fractal dimension of agglomerates at any instant. In this study, a Brownian dynamics simulation was performed with simultaneous collision and sintering, and variations in the fractal dimension of agglomerates were observed. A coagulation coefficient expression for agglomerates with two different fractal dimensions was proposed. The coagulation coefficient based on the different fractal dimensions was at most 140% higher than that based on the average fractal dimension. To determine an accurate coagulation coefficient of agglomerates, the fractal dimension of each agglomerate has to be considered. 相似文献
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中低负荷下脉动热管壁温信号的分形特性分析 总被引:1,自引:0,他引:1
运用功率谱、小波分解、相空间重构、关联维数计算等非线性分析方法对脉动热管壁面温度波动信号分析。表明:功率谱呈现连续谱线,时间序列存在自相似性,展现温度波动信号的混沌行为;小波分解表现出温度波动的分形特性;重构吸引子展现出4种不同的空间分形结构,说明温度信号波动属于分形下的混沌行为。计算分形维数与传热性能的关系,发现系统存在3~6个分形维;随嵌入维数的增加,分形速度关系为R134a大于丙酮大于去离子水,基本表现为分形维数越大,传热性能越好。并发现关联维和热阻成负相关关系。 相似文献
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不同秸秆生物炭的孔隙结构及其差异 总被引:1,自引:0,他引:1
基于低温氮气吸附的研究方法,对水稻秸秆、玉米秸秆、小麦秸秆制备的生物炭进行了孔结构研究,用BET方程、BJH方程和t-plot方法分别计算得到生物炭的比表面积、孔径分布和微孔数据,利用FHH模型计算了孔隙分形维数。研究表明:不同温度不同材料都对生物炭的孔结构有较大影响,随着热解温度的升高水稻秸秆生物炭和小麦秸秆生物炭的BET比表面积和总孔容呈先增加后降低的趋势,而玉米秸秆生物炭的孔隙度随着热解温度升高持续增加;3种秸秆生物炭的孔径分布均以中孔为主,孔隙内部以Ⅱ型孔为主;水稻秸秆、玉米秸秆、小麦秸秆制备的生物炭都具有很好的分形特征,分形维数(D)分别为2.545 4~2.669 3、2.629 7~2.689 5、2.577 3~2.597 2,表明这3种生物炭孔隙结构比较复杂,非均质性强,其中水稻秸秆生物炭和小麦秸秆生物炭均在500 ℃条件下有较高的分形维数,分别是2.669 3和2.597 2,玉米秸秆生物炭则在700 ℃条件下有较高的分形维数,为2.689 5。 相似文献