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。     

分形多孔材料的一种改进化气体扩散分形模型

基于分形理论与技术,提出了气体在由一簇弯弯曲曲、横截面积大小不等的椭圆形毛细管组成的多孔材料中的气体扩散率分形模型。研究结果表明:归一化气体扩散率是最大孔隙面积、最小与最大孔隙面积之比、多孔材料总横截面积、形状因子及分形维数等多孔材料微结构参数的函数;模型能清楚地揭示影响气体扩散率的物理机制。文中气体扩散率分形模型与已有的实验数据进行对比,结果显示它们之间吻合较好;提出的改进化气体扩散分形模型更具有一般性。     

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.     

附加空气层的多层墙体热湿耦合非稳态传递模型及验证

为准确预测附加空气层的多层墙体内的温湿度分布和动态变化,研究多孔介质墙体内的热湿耦合非稳态传递规律,基于Luikov、Fick定律等基础传递理论,推导出热湿空气在墙体内部的瞬态耦合传递控制方程。通过对控制方程驱动势、方程项系数的改进,以空气含湿量和温度为驱动势,建立了建筑多孔介质墙体热湿耦合传递非稳态模型。采用有限容积法隐式差分格式设计了MATLAB模拟计算程序,设置相应的初始条件和边界条件,计算附加空气层的多层墙体内温度、湿度、传热和传湿量随时间变化的分布规律。最后,通过对比新建模型模拟结果与WUFI软件的模拟计算结果,验证了模型的准确性和可行性。     

多孔介质内气泡熟化特性孔隙尺度研究

多孔介质内的气泡熟化行为广泛存在于CO₂封存等领域,为探究多孔介质内气泡的熟化特性,本文采用空气作为模拟气体,通过可视化实验和数值计算,对双孔隙和四孔隙气泡熟化过程进行了研究,阐释了多孔介质非均质性对熟化过程的影响规律。结果表明：在双孔隙气体饱和度较小情况下,虽然也发生正向熟化,但是孔隙结构的存在使熟化速率明显低于自由流体情况;四孔隙研究显示多孔介质非均质性对气泡熟化过程影响显著,由于孔隙的几何限制,气泡在某些情况下会发生逆Ostwald熟化,即生长的气泡在充满当前孔隙空间后会停止生长并反向熟化导致尺寸缩小;在非均质多孔介质中,由于熟化作用,气泡有传质到大孔隙区域趋势,导致大孔隙区域富集大气泡,存在泄漏风险,从而影响封存。     

基于REV的孔隙型多孔介质导热分析模型

多孔介质内部组成结构复杂，热质传递过程多变，如何针对多孔介质的微观孔隙分布特性，建立更加精准的分析模型，有待深入研究。基于表征单元体（representative elementary volume，REV）概念，提出了孔隙型多孔介质的两种微观物理模型，即空心骨架基元模型和实心颗粒基元模型，分别建立了相应的热导率计算公式。针对孔隙内的微观结构特征，采用分形方法，对两种基元模型进行了分形修正，更好地表征了微观孔隙结构。基于所建模型，进行了模拟计算，探讨了相关参数对多孔介质导热特性的影响。通过自主研发的实验装置进行了相关实验，验证了模型的准确性。     

多孔介质中的分数扩散方程

多孔介质复杂的几何结构可看作是随机分形。分形空间中的扩散与欧几里德空间中的扩散不同,为反常扩散,扩散方程不能用普通微分方程准确描述,需用分数微分方程。从微观和宏观相结合的角度讨论了三个比较有影响的分形介质中的扩散方程。     

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。     

多孔固体表面扩散问题中Fick定律交叉项扩散系数的确定

对多孔固体表面扩散二元系统给出Fick定律交叉项扩散系数矩阵形式的计算式,并将其推广到三元及多元扩散系统,得到Fick定律交叉项扩散系数普遍化的计算式。     

Multiple linear equation of pore structure and coal–oxygen diffusion on low temperature oxidation process of lignite

This work aimed at studying the feasibility of calculating the coal–oxygen diffusion properties during the low temperature oxidation process of lignite so as to predict its spontaneous combustion process. Coal samples were oxidized in air ambient under different temperatures. Scanning Electron Microscope was used to indicate the surface morphology changes of oxidization. Then, based on fractal theory and flow characteristics, the fractal dimension of gas diffusion in the pore ways was calculated under different temperature. Considering pore size distribution, connectivity distribution and Fick diffusion mechanisms, the relationship between the gas diffusivity change with pore area fractal dimension and porosity was investigated, and multiple linear equation of the coal–oxygen diffusion coefficients and pore parameters was obtained. Comparison between the experimental data and model prediction verifies the validity of the model. The research provides a theoretical basis for the prediction model of coal–oxygen diffusion law.     

Ibuprofen release from porous hydroxyapatite tablets

The present study investigated drug release profiles from porous hydroxyapatite [Ca₅(PO₄)₃OH, HAP] tablets. HAP tablets prepared synthetically and porous structure was generated via microemulsion after sintering at 700 °C. The influence of tablet's microemulsion concentration on drug release profiles from sintered porous tablets was investigated by using ibuprofen (C₁₃H₁₈O₂) as model drug.A numerical approach based on Fick's second diffusion law was used to investigate drug release kinetics from porous HAP tablets. Via this equation, diffusion coefficients were calculated for each tablet and compared. Drug release from the tablets was influenced by the porosity and tortuosity of the porous network. The drug release from porous HAP tablets was increased by microemulsion concentration. It is possible to obtain HAP based drug delivery system which has different drug release behavior by controlling microemulsion concentration in tablets before sintering.     

PARAMETER ESTIMATION OF FICK'S LAW DRYING EQUATION

Distributed parameter drying models such as the Fick's law diffusion model, unlike the lumped parameter model of van Meel whose parameters can be easily estimated by regression, suffer from the difficulty in estimating the parameters of the models quantitatively with accuracy. In the past they were estimated by visual inspection of the theoretical drying curves which fit the experimental drying curve best In this work, a quantitative parameter estimation technique originally suggested by Chavent, is developed by minimizing the integrated squares of error between theoretical and experimental curves over the drying lime (the criterion) subjected to the constraints that the theoretical curve is governed by the constant diffusivity Fick's taw diffusion equation (the constraint). Although the estimation of Fick's law constant diffusivity can be done by using the analytical solution developed by Crank, the use of the Fick's law model here is simply to demonstrate the utility of the proposed technique which can be used in more complex distributed models. The optimization problem is to solve for the adjoint equation for which the value of the Fick's law diffusivity minimizes the criterion. The Lagrangian derivative is solved by using a discrete derivative of the criterion. The theoretical curves are generated by using simple explicit (FSE) and modified Crank-Nicholson (FCR) algorithms The drying of oil palm kernels are used as a case study. Ii is found that the estimated diffusivities of moisture in oil palm kernels range from 0 5 to 5.0 × 10^-10 m²sol;s which are comparable with published data. It is also found that the estimated diffusivity is dependent on the initial moisture content.     

On the modified Stefan-Maxwell equation for isothermal multicomponent gaseous diffusion

Understanding multicomponent gaseous diffusion in porous media is crucial to describing the transport of fuel and reaction products in the anode of a solid oxide fuel cell, for which this work was originally pursued. The Stefan-Maxwell approach provides a general theoretical framework so that measured or predicted binary diffusion coefficients may be utilized for multicomponent diffusion (for which Fick's law is invalid). This approach has since been extended to account for a porous solid structure resulting in what is usually referred to as the “modified Stefan-Maxwell equation”, which is the subject of the present work. Using a virtual experiment involving ternary diffusion and the modified Stefan-Maxwell equation, it is shown that multicomponent diffusion in the Knudsen regime (in which wall drag is significant) produces a gradient in total pressure, which then drives the diffusion of gaseous components for which there are no mole fraction gradients. To the author's knowledge, this peculiar phenomenon has not been verified by a real experiment. The analysis also shows that bulk diffusion in the present virtual experiment is equimolar, which contradicts the common assertion that Graham's relation is valid even in conditions where bulk diffusion is dominant. Finally, the present work shows the importance of the term involving the total pressure gradient in the modified Stefan-Maxwell equation. In the literature, the gradient in total pressure is often mistakenly associated only with permeation. This paper demonstrates that it is an essential part of the driving force for diffusion and its omission leads to an erroneous prediction in the present virtual experiment. A detailed derivation of the modified Stefan-Maxwell equation is also provided, underscoring the relevance of the total pressure gradient term.     

逾渗多孔介质对固体颗粒吸附过程的影响

研究了悬浮液中的颗粒在通过逾渗多孔介质时的被吸附特性。采用数值计算的方法;通过求解描述低速流体流动的Stokes方程以及简化的颗粒运动方程;初步得到颗粒在逾渗多孔介质中的运动轨迹;并在此基础上;求得颗粒与多孔介质内表面的碰撞概率;进而研究颗粒的被吸附特性。数值结果表明均匀多孔介质和分形多孔介质对颗粒的吸附存在本质差异。颗粒流出概率（实际中常表示为出口悬浮液中的颗粒浓度）与多孔床深度间的指数关系仅对均匀多孔介质成立;而对分形多孔介质并不成立。