Diffusion coefficient is determined by the combination of gas and solid properties. From the microscopic point of view, the inside of any solid material will at least part of the gas during the gas diffusion, and the diffusion mechanism of the gas in the solid and the gas alone The diffusion mechanism is the same. Therefore, by studying the diffusion behavior of the gas inside the nanopore material, we can understand the influence of different parameters inside the nanopore material on the gas diffusion within the material, and also understand the influence of the parameters that change the external environment of the material on the diffusion of the gas inside the material. Through these studies, we can gain a deeper understanding of the relevant properties of nanoporous materials, and study the effect of porosity, sample size, and boundary conditions on the diffusion of gases within nanoporous materials. The higher the porosity, the greater the pressure at which the sample reaches equilibrium and the initial The smaller the change from pressure to equilibrium pressure, the smaller the volume; the greater the volume change, the greater the pressure change at equilibrium pressure, the smaller the pressure at the time of reaching equilibrium, and the longer the time to reach equilibrium; the greater the pressure at the boundary, the greater the pressure at which the sample reaches equilibrium. The longer it takes to reach balance. Through these findings, the performance of nanomaterials can be better utilized in future experimental studies. For unknown solid materials, the diffusion coefficient of the research gas in its interior can be understood from the physical properties in terms of its structure and properties, which will affect the research and development of materials science and related engineering fields.

Keywords: nanomaterials；numerical simulation；gas diffusion；porous media；CFD

目  录

1  绪论 1

1.1 课题研究背景 1

1.2 CFD介绍 2

1.3 COMSOL Multiphysics 介绍 4

2  有限元方法解决问题流程 6

2.1有限元法介绍 6

2.2物理模型 9

2.3数学模型 10

3  模拟与分析讨论 11

3.1扩散系数的影响 11

3.2孔隙率的影响 15

3.3体积的影响 19

3.4边界条件的影响 23

4  结果与小结 34

论文致谢 35

参考文献 36

一、绪论

1.1 课题研究背景

纳米材料的独特性在于当材料的尺寸小至特定的大小的时候，传统的力学观点就不能用来解释其行为，这时候就要用的量子力学，例如当微粒的粒子直径由100微米减小到100纳米的时候，粒子直径虽然只减小了1000倍，但是换算体积的时候则减小了109之多，因此二者产生行为上的差别也是显而易见的。这是因为纳米材料的大小已经和电子相干的长度相似，所以纳米材料的性质也是由于这种强相干而发生了巨变。

  纳米多孔材料(Nanoporous materials)是指孔径在100纳米以下的多孔材料,分为有机纳米多孔材料和无机纳米多孔材料。也可以分为大块纳米多孔材料和薄膜纳米多孔材料。纳米多孔材料许多都是自然存在的，不过随着近年来纳米技术的发展现在的人工技术也可以制造一些高分子纳米多孔材料。[13][23][26]

细分：按照IUPAC,纳米多孔材料可细分为三类；

 1.微孔材料；0.2-2nm

 2.介孔材料；2-5nm

 3.大孔材料；50-1000nm

直径/nm

原子总数N

表面原子百分比

表1-1  粒子的大小与表面原子数的关系

  当材料的结构大小在纳米的层次范围内调控的时候，会产生特别的纳米效应。所以由于其比较大的比表面积与特别的孔结构，目前在许多领域都有着非常良好的发展前景，人们对其的关注度也非常高。在当今世界，无论是科技领域还是国防领域的发展都对材料提出了更多的要求，例如原件智能化与小型化，高度的集成化与储存高密度以及超高速数据传输等方面都对材料的尺寸方面提出了更高的标准。同时对材料的性能更是要求严格，军事装备与航空航天等先进制造技术的发展都依赖于材料科学的发展。所以说经济与科学的发展都离不开新材料产业的创新。[27][29]