基于显微CT图像的岩芯孔隙分形特征

采用国内自主开发的高分辨率显微CT设备,对岩芯样本进行图像采集,运用数字图像分析方法获得图像中的岩芯孔隙目标,并以此为基础重建三维模型。然后基于分形理论,分别从二维图像和重建的三维模型角度计算孔隙的分形维数。最后,再采用基于多孔介质的分形模型对岩芯孔隙分形特征进行验证,得出岩芯的二维分形维数和三维分形维数之间的差值均值为1.000 3,最大偏差为0.004,很好地满足多孔介质分形模型中关于二维和三维分形维数的关系。     

裂缝-孔隙型双重介质油藏渗吸机理的分形分析

低渗透油藏常常伴随裂缝发育,形成裂缝-基质双重介质.自发渗吸是低渗裂缝性水驱油藏的重要采油机理,有顺向和逆向两种渗吸方式.基于基质孔隙结构的分形特征,引入分形几何对裂缝性双重介质渗吸机理的判据进行了改进,建立了渗吸机理的分形判据模型,并进一步推导了结构常数的解析表达式.结果表明,渗吸机理的判别参数是基质孔隙度、高度、孔隙分形维数、流动迂曲度、最大孔隙直径、界面张力、油水密度差以及接触角的函数.改进后的判据模型与现有结果一致.最后绘制了判别渗吸机理的图版,为利用表面活性剂提高低渗透油藏采收率提供理论依据.     

无格点基底表面的杂质分布对分枝状凝聚体的影响

根据含杂质熔融玻璃表面金原子凝聚的实验规律，在原子团簇具有随机的线扩散步长和刚性转动角的特征条件下，建立了含杂质无格点基底表面上改进的杂质限制团簇-团簇(IRCCA)凝聚模型.对团簇的扩散、刚性转动以及凝聚全过程进行了计算机模拟，系统地研究了杂质区域分布情况对分枝状凝聚体诸多特性的影响.结果表明规则分布的杂质对凝聚体生长的影响比随机分布的杂质大，导致杂质规则分布的基底表面上的分枝状凝聚体的数密度更大，分枝状凝聚体的回旋半径，凝聚体平均大小及分形维数更小. 关键词： 薄膜生长 Monte Carlo模拟 分形 杂质     

变化电压下扩散限制电解沉淀过程对铜的分形维数的影响

研究了铜的二维电解沉淀物在限制条件下的分形维数.拍摄了铜沉淀物随时间变化的照片,使用盒维法分析了各种条件下的豪斯多夫分形维数,并建立了计算机评估模型,以证明电压对豪斯多夫维数的重要影响.根据照片显示沉淀物的欧几里德几何形状也有着规则的变化.     

随机多孔介质的蒙特卡罗重构与渗流特性模拟

根据多孔介质微观结构的分形尺度标度特征,采用蒙特卡罗方法分别重构随机多孔介质的微观颗粒和孔隙结构,并基于分形毛管束模型研究多尺度多孔介质的气体渗流特性,建立多孔介质微观结构和宏观渗流特性的定量关系。结果表明：分形蒙特卡罗重构的多孔介质微细结构接近真实介质结构,气体渗流特性的计算结果与格子玻尔兹曼模拟数据较为吻合; 多孔介质气体渗透率随着克努森数的增加而增大,孔隙分形维数对于气体渗流的微尺度效应具有显著影响,而迂曲度分形维数对于表观渗透率和固有渗透率的比值影响可以忽略。提出的分形蒙特卡罗方法具有收敛速度快且计算误差与维数无关的优点,有利于深入理解多尺度多孔介质的渗流机理。     

空温式翅片管气化器结霜模型及数值模拟

以分形理论的DLA模型为基础,建立了空温式翅片管气化器深冷表面上霜晶生长的二维模型,模拟了深冷表面上的霜晶生长过程.采用计盒维数法对模拟出的霜晶生长图像进行了分形维数的计算,结果表明深冷表面上霜晶的分形维数较一般冷表面上的分形维数大,从而说明深冷表面上的霜晶具有更加复杂的结构,充满空间的能力更大.这对进一步理解空温式深...     

分形理论在碳化材料三维烧蚀热防护计算中的应用

烧蚀过程中的传热传质对烧蚀防护工程具有重要意义,准确的温度评估可以为高超声速飞行器的热防护结构和烧蚀材料的设计提供有效的支持.由于材料烧蚀形成的碳化物是一种典型的多孔介质,其结构具有自相似性,可以用分形理论来描述.在烧蚀计算中引入了分形渗透率张量模型进行计算.针对烧蚀过程中热解气体在碳化层中的扩散方程、温度、材料等参数对烧蚀过程的影响,对不同迂曲度分形维数和不同孔径分形维数材料三维球头进行了数值模拟.计算结果表明:材料的孔径分形维数越小,迂曲度分形维数越大,热防护效果越好.      

石墨泡沫新材料导热的分形模型

新型导热材料石墨泡沫具有很好的热物理性质。本文在实验获取这种新型多孔材料的基础上,建立了基于分形理论的材料结构和导热模型,采用热阻法给出了石墨泡沫材料的等效导热系数的关系式,计算了石墨泡沫的剖面孔隙面积分形维数和等效导热系数.     

分形结构对CO催化氧化非线性动力学行为影响的理论研究

在平均场近似下建立了包含分形上反常扩散在内的理论模型，描述了典型单分子－双分子反应：ＣＯ＋Ｏ２的非线性动力学规律，并着重考察了分形结构对振荡行为以及非平衡相变的影响，我们发现：①随分形维数ｄｆ的降低，振荡区向ＣＯ的低分压方向偏移并减小，甚至消失；同时，在相同的反应条件下，对二维规则表面不存在振荡行为的区域，有可能因分形上的受限扩散而诱导振荡。②在较高温度下，分形结构除了控制体系的非线性动力学行为，     

利用分形理论研究气液界面特性

利用分形理论对Lennard-Jones12-6流体气液界面性质进行了研究。得到了密度分布及温度分布,将表面张力 与气液界面的分形维数进行关联。分形维数是界面层所固有的,它与界面的其它特性有着本质的联系,因此,可以通过测 量界面层的分形维数,再利用此分形维数确定界面的其它特性。这种全新的测量界面特性的方法有望由此产生。     

Changes in pore size distribution inside sludge under various ultrasonic conditions

The pore size distribution is quite significant for determining the transport capacity of heat and moisture in sludge during the drying process. It is crucial to investigate the transformation of the pore size in sludge under sonication. In this paper, the microstructures of pores inside sludge before and after ultrasonic treatment with various ultrasonic conditions were observed using a microscope. Fractal geometry and image analysis were combined to quantitatively identify the evolution of pore size in sludge undergoing various acoustic energy densities and treatment times. The surface fractal dimension (d_f) was applied to characterize the pore size distribution of sludge. The results confirmed that sonication has a positive influence on the characteristics of pore structure inside the sludge and that the average pore size increases with increasing ultrasonic energy level, as determined by both acoustic energy density and treatment time. The d_f appropriately characterizes and quantifies the evolution of the pore size distribution of sludge under various ultrasonic conditions. This work is quite valuable for further investigating and evaluating moisture removal in the sludge drying process assisted by ultrasonic treatment.     

Surface fractal analysis of pore structure of high-volume fly-ash cement pastes

The surface fractal dimensions of high-volume fly-ash cement pastes are evaluated for their hardening processes on the basis of mercury intrusion porosimetry (MIP) data. Two surface fractal models are retained: Neimark's model with cylindrical pore hypothesis and Zhang's model without pore geometry assumption. From both models, the logarithm plots exhibit the scale-dependent fractal properties and three distinct fractal regions (I, II, III) are identified for the pore structures. For regions I and III, corresponding to the large (capillary) and small (C-S-H inter-granular) pore ranges respectively, the pore structure shows strong fractal property and the fractal dimensions are evaluated as 2.592-2.965 by Neimark's model and 2.487-2.695 by Zhang's model. The fractal dimension of region I increases with w/b ratio and hardening age but decreases with fly-ash content by its physical filling effect; the fractal dimension of region III does not evolve much with these factors. The region II of pore size range, corresponding to small capillary pores, turns out to be a transition region and show no clear fractal properties. The range of this region is much influenced by fly-ash content in the pastes. Finally, the correlation between the obtained fractal dimensions and pore structure evolution is discussed in depth.     

Scale-dependent nature of the surface fractal dimension for bi- and multi-disperse porous solids by mercury porosimetry

The surface fractal dimension was calculated by using a mathematical model and mercury intrusion data for a variety of bi- and multi-disperse porous solids including silica gels, alumina pellets, and building stones. The mathematical model was obtained by modifying the well-established scaling relation published previously [Ind. Eng. Chem. Res., 34 (1995) 1383-1386]. It was also verified by comparing with the theoretical surface fractal dimensions for regular fractal structures (Skerpinski tetrahedron and Menger sponge) and the calculated surface fractal dimensions for silica gel and alumina particles via the linear fitting method established previously. The calculation results for various bi- and multi-disperse porous solids have demonstrated that the scale-dependent nature of the surface fractal dimension is ubiquitous. The difference in the surface fractal dimension between pore size intervals usually exists. The estimation of the surface fractal dimension on an average stand may lead to erroneous results.     

Moisture diffusivity in structure of random fractal fiber bed

A theoretical expression related to effective moisture diffusivity to random fiber bed is derived by using fractal theory and considering both parallel and perpendicular channels to diffusion flow direction. In this Letter, macroporous structure of hydrophobic nonwoven material is investigated, and Knudsen diffusion and surface diffusion are neglected. The effective moisture diffusivity predicted by the present fractal model are compared with water vapor transfer rate (WVTR) experiment data and calculated values obtained from other theoretical models. This verifies the validity of the present fractal diffusivity of fibrous structural beds.     

Fractal properties of acoustic location responses

The fractal dimension of reflected ultrasonic signals in steel slabs with wittingly introduced defects is analyzed. The dependence of the fractal dimension on the defect size is demonstrated. The resolving power of a method used to estimate the fractal dimension of acoustic location responses and its applicability in practical flaw detection are considered.     

On the origin of slow processes of charge transport in porous media

Dielectric relaxation spectra in porous media reveal the importance of slow processes of charge transport with polarisation currents down at least to mHz. The spatial scale of the relaxation is frequency-dependent, potentially allowing information about the structure of the medium to be obtained from the AC conductivity. Many mechanisms of relaxation have been proposed, but we review only two in any depth. These two approaches relate long relaxation times on the one hand to diffusion limited relaxation, on the other, to geometrical limitations on conduction pathways. For equidimensional non-fractal particles, the first (second) generates a quadratic (linear) dependence of relaxation time on particle (or pore) size. In each a fractal model of the pore space generates a power-law AC conductivity with the power of the frequency a function of the fractal dimensionality, but the powers have different relationships with system parameters. Comparison with data does not support either interpretation generally, though some data sets agree with each. Since surface conduction yields a quadratic dependence for particles elongated in one dimension, but more complex dependences for fractal interfaces, it seems easier and more productive to start from the perspective that surface conduction processes are the basis for the relaxation.     

气体吸附法测定二氧化硅干凝胶的分形维数

提出了一种方便、科学有效的利用气体吸附法测定二氧化硅干凝胶等多孔材料分形维数（表面分形维数和孔分布分形维数）的方法，不需要进行一系列的吸附/脱附实验，只需要利用单一气体的一次吸附/脱附实验得出的样品孔分布、比表面数据，与不同的标尺进行关联，即可同时获得表面分形维数和孔分布分形维数.通过误差分析和校正，保证了结果的可靠性.用上述方法测定了二氧化硅干凝胶的分形维数，以FHH法和SAXS法对所得结果进行了比较和验证，并对吸附/脱附过程所得结果的差异进行了初步分析. 关键词： 分形维数 气体吸附 二氧化硅 干凝胶