基于分形理论的多孔介质导热系数研究

本文根据分形理论,对多孔介质几何结构进行了描述,计算出了不同孔隙率多孔介质简化模型的剖面面积分布分形维数d,并利用分形维数结合土壤导热模型推出了土壤的有效导热系数表达式,计算结果表明,该方法是符合客观实际的．     

使用条件生成对抗网络生成预定导热率多孔介质

多孔介质在工程领域中的应用非常广泛,其中有效导热率和孔隙率为多孔介质材料非常重要的性质,得到一个符合需要的有效导热率和孔隙率的多孔介质材料具有重要意义.本文使用四参数随机生成方法制作了训练数据集,搭建了一个条件生成对抗网络(CGAN),使用预定的有效导热率和孔隙率作为输入,生成一个满足输入条件的多孔介质结构.特别地,由于多孔介质的孔隙结构分布对材料的有效导热率影响巨大,提出局部结构损失函数参与网络训练,使得网络更好地学习到孔隙分布与导热率之前的关系.通过使用格子Boltzmann方法验证神经网络生成的多孔介质结构的有效导热率,结果表明该方法能够快速且准确地生成预定参数的多孔介质结构.     

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.     

Dielectric constant of porous ultra low-k dielectrics by fractal-Monte Carlo simulations

The effective dielectric constant of porous ultra low-k dielectrics is simulated by applying the fractal geometry and Monte Carlo technique in this work. Based on the fractal character of pore size distribution in porous media, the probability models for pore diameter and for effective dielectric constant are derived. The proposed model for the effective dielectric constant is expressed as a function of the dielectric coefficient of base medium and the volume fractions of pores and base medium, fractal dimension for pores, the pore size, as well as random number. The Monte Carlo simulations combined with the fractal geometry are performed. The predictions by the present simulations are shown in good accord with the available experimental data. The proposed technique may have the potential in analyzing other properties such as electrical conductivity and thermal conductivity in porous ultra low-k dielectrics.     

A Particle Resistance Model for Flow through Porous Media

A particle model for resistance of flow in isotropic porous media is developed based on the fractal geometry theory and on the drag force flowing around sphere. The proposed model is expressed as a function of porosity, fluid property, particle size, fluid velocity （or Reynolds number） and fractal characters D f of particles in porous media. The model predictions are in good agreement with the experimental data. The validity of the proposed model is thus verified.     

两相复合材料有效热导率的理论推导

复合材料有效热导率的解析表达式一直是传热问题中人们想要解决的问题.本文选用合适的单元体,采用热阻模型和积分平均方法,分别对分散相为球体和圆柱体的两相复合材料的有效热导率进行了推导.对于多孔复合材料,当孔隙率较大或温度较高时辐射换热的影响不能忽略,本文分析了气孔为球体或圆柱体时辐射换热对其有效热导率的影响.将计算所得有效热导率与相关实验数据进行了比较,结果表明两者吻合较好,证明了公式的准确性.     

The effective thermal conductivity of porous media based on statistical self-similarity

A fractal model is presented based on the thermal-electrical analogy technique and statistical self-similarity of fractal saturated porous media. A dimensionless effective thermal conductivity of saturated fractal porous media is studied by the relationship between the dimensionless effective thermal conductivity and the geometrical parameters of porous media with no empirical constant. Through this study, it is shown that the dimensionless effective thermal conductivity decreases with the increase of porosity (?) and pore area fractal dimension (Df) when ks/kg>1. The opposite trends is observed when ks/kg<1. In addition, the dimensionless effective thermal conductivity decreases with increasing tortuous fractal dimension (Dt). The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data.     

考虑接触热阻的纳米颗粒堆积热导率的分析

本文首先使用Callaway热导率模型对SiO₂纳米颗粒的热导率进行了近似计算,然后耦合堆积纳米孔隙内的导热和辐射、颗粒接触热阻,基于颗粒堆积单元结构模型的一维传热分析,最终推导得到了颗粒堆积有效热导率关于颗粒直径和温度、堆积孔隙率、颗粒热导率、气相热导率、辐射传热和接触热阻的关系式,并用该式进行了相关讨论。研究结果表明,对于纳米颗粒堆积,界面接触热阻不容忽略;在低孔隙率和颗粒不参与辐射的条件下,由于受到接触热阻的影响,存在最佳孔隙率（或密度）使得堆积热导率存在最大值。     

Positronium diffusion in porous methylsilsesquioxanethin films

Depth profiled positronium (Ps) annihilation lifetime spectroscopy (PALS) is an extremely useful probe of the pore characteristics in nanoporous low-dielectric (low-k) constant thin films. PALS has also been considered as a potential probe to investigate diffusion barrier integrity and the structural changes of porous low-k films during their integration with Cu. Hence, it is essential to understand the diffusion behaviour of positronium/Cu atoms in the films. In this work, based on the fact that porous materials possess characteristics of statistical self-similarity, a fractal model, the Menger sponge model, has been applied to simulate the structure of a promising dielectric, porous methylsilsesquioxane (MSQ) films. The diffusion behaviour of Ps out of the fractal model and into the surrounding vacuum is studied by means of the diffusion equation and traditional advective-diffusive theory. Predictive results from our model show good agreement with measurement data.     

Thermal conductivity of a kind of mesoporous silica SBA-15

Mesoporous silica SBA-15 consists of uniform hexagonal, unconnected cylindrical channels with diameters that can be tuned within a range of 1.5 nm-30 nm, and is thought to have a special thermal conductivity. The theoretical investigation of the shell thermal conductivity of the mesoporous silica is performed in the relaxation time approximation in this paper and an available one-dimensional heat transfer model is used to predict the effective thermal conductivity （ETC） of the mesoporous silica. The experimental result of the ETC is also presented for comparison. The shell thermal conductivity of the mesoporous silica decreases with mesochannel radius increasing or wall thickness decreasing, but does not strictly decrease with porosity increasing. The thermal radiation possibly plays a primary role in heat transfer at the large porosity scale. The predicted ETC of SBA-15 with only conduction considered is quite low at the large porosity, even lower than the thermal conductivity of the silica aerogels. To realize it, doping carbon or other matters which can strongly absorb infrared light into SBA-15 is a possible way.     

多孔介质热导率的数值计算

通过数值模拟得出面积分形维数和孔隙率相同,而孔隙结构不同的分形多孔介质的导热特性是不相同的.说明仅仅依靠孔隙率和分形维数两个参数无法有效确定多孔介质的热物理性质,寻找新的表征孔隙结构的参数是必要的.同时也说明了前人所得出的关于多孔介质的热物性的解析表达式具有一定的局限性和不确定性.     

二维多孔热密封材料的有效导热系数模拟

本文对于二维多孔热密封材料的有效导热系数模拟提出一种简单有效的方法,它可以模拟介于固相连续和固相不连续之间的任何形式的孔隙分布结构,通过类比多孔渗流模型得出一种相关系数,再根据热阻串并联的关系计算四种可计算模型的有效导热系数,通过相关系数得到具体模型的有效导热系数。本文的模拟方法可以控制孔隙率、孔径、孔隙分布、温度等影响有效导热系数的重要参数,考虑了辐射的影响,而且模拟简单,计算快速,模拟结果与文献中实验的结果相比较能很好的吻合,验证了本文方法的正确性。     

纳米多孔氩薄膜热导率的分子动力学模拟

利用经典的Lennard-Jones势能模型,采用分子动力学模拟方法研究纳米多孔氩薄膜热导率.结果表明,纳米多孔氩薄膜热导率明显小于同温度下纯纳米氩薄膜热导率,并且孔隙率越大热导率减小越多.借助基于并联方法的有效热导率模型,对纳米多孔氩薄膜的热导率随孔隙率的变化进行解释.模拟结果还发现,薄膜内的多孔分布对薄膜的热导率有影响.     

The Thermal Conductivity Theory of Non-uniform Granular Flow and the Mechanism Analysis

According to the fractal characteristics appearing in non-uniform granular system, we found the fractal model to study the effective thermal conductivity in the mixed system. Considering the quasi-equilibrium, we bring forward the fractal velocity probability distribution function. The equipartition of energy is employed to the non-uniform granular system, and the granular temperature is derived. We investigate the thermal conductivity in granular flow due to the movement of the particles, namely the heat transfer induced by the streaming mode only. The thermal conductivity in the mixed system changes with the fractal parameters such as the solid fraction v, structural character parameter η, and fractal dimension D of size distribution. These parameters depict the characteristics of the thermal conductivity in the actual complex granular system. Comparing our conclusion with the correlative experimental data and the theoretical conclusion of binary mixture of granular materials, the results can qualitatively confirm the generality of our prediction on the granular system.     

Investigation of self-assembled fractal porous-silica over a wide range of length scales using a combined small-angle scattering method

The unique structure of a set of self-assembled porous silica materials was characterized through a combined small-angle scattering (CSAS) method using small- and ultra-small angle neutron scattering as well as small-angle X-ray scattering. The porous silica specimens investigated were prepared by a sol-gel method under the presence of alkylketene dimer (AKD) template particles and through calcination, which leads to the development of porous silica having a mass-fractal structure over length scales from ~ 100 nm to ~ 10 μm. Furthermore, the specimens posses a hierarchical structure, which consist of a fractal porous structure, and also contain primary silica particles less than 10 nm in size, which form a continuous silica matrix. To characterize these complex structures, observation over a broad range of length scales is indispensable. We propose a CSAS technique that serves this purpose well.     

The Fractal Characteristic of Particles in Granular Material Flows and Its Effect on Effective Thermal Conductivity

According to the fact that many pulverized particles possess fractal characteristic, a fractal model for studying fine particles in granular material flows is first proposed. An expression of particles' fractal distribution is derived to describe the relationship between the particle fractal dimensions and particle velocity distribution function. In accordance with this model, the theoretical particle effective thermal conductivity is derived. The analytical results show that for the small Biot-Fourier number, the effective thermal conductivity increases with the square root of the granular temperature. For very large Biot-Fourier number, the effective thermal conductivity linearly increases with the granular temperature. Numerically calculated results show that the thermal conductivity increases with the particle size fractal dimensions and decreases with the particle surface fractal dimensions.     

基于微结构参数建模的多孔硅绝热层热导率研究

多孔硅由于具有较低的热导率,因而可以将其作为半导体器件中的绝热层.与其他从边界散射等复杂微观热传导机制出发建模研究多孔硅的热导率不同,将多孔硅热导率影响机制更表观地归结到孔洞的存在和分布等结构因素上,把整个多孔硅视为由硅连续材料介质和孔洞连续介质通过串联和并联组合成的复合微结构,给予其低热导率一个更为易于理解和简化的解释.进一步把孔隙率对等效热导率的影响分解为两个不同的部分,即纵向部分和横向部分,半定量地给出不同的孔洞结构和分布下孔隙率与等效热导率的关系.与实验数据进行对比后验证了模型的有效性.继而从结构的角度说明了多孔硅热导率较低的原因.     

Heat Conduction and Characteristic Size of Fractal Porous Media

Based on fractal theory, two types of random Sierpinski carpets （RSCs） and their periodic structures are generated to model the structures of natural porous media, and the heat conduction in these structures is simulated by the finite volume method. The calculated results indicate that in a certain range of length scales, the size and spatial arrangement of pores have significant influence on the effective thermal conductivity, and the heat conduction presents the aeolotropic characteristic. Above the length scale, however, the influence of size and spatial arrangement of pores on the effective thermal conductivity reduces gradually with the increasing characteristic size of porous media, the aeolotropic characteristic is weakened gradually. It is concluded that the periodicity in structures of porous media is not equal to the periodicity in heat conduction.     

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.