A micromechanics model for molecular diffusion in materials with complex pore structure
A micromechanics model for molecular diffusion in materials with complex pore structure
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DOI：
10.1002/nag.2423
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发表时间：
2016-04
影响因子：
4
通讯作者：
J. Timothy;G. Meschke
中科院分区：
文献类型：
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作者：
J. Timothy;G. Meschke
分子在完全饱和多孔材料中的扩散受到孔隙空间的强烈影响，而孔隙空间通常具有复杂的拓扑结构。因此，关于宏观扩散特性的信息需要在多个空间尺度上对纳米孔和微孔内的输运过程进行放大。提出了一种在连续微观力学框架下预测多孔材料中有效分子扩散率的新模型。考虑具有代表性的体积元，表征多孔材料的孔隙空间微观结构复杂性，通过递归嵌入ESHELBY矩阵-包裹体形态的形式对均匀通量进行扰动，得到有效扩散率与孔隙率的递归函数关系。该模型预测了孔隙率的阈值，低于该阈值，由于存在未连接且无法运输的孤立孔隙团，因此不会发生分子扩散。球形夹杂物的最大孔隙度为1 / 3，低于此孔隙度不可能发生分子输运。该模型允许扩展到更复杂的内含物形态。我们还发现，微观结构对分子运输的影响以孔隙度依赖的远程和短程相互作用为特征。开发的框架被扩展到包括现实的孔径分布跨越几个空间尺度，通过在分层均质方案中的分布函数。现有的实验结果证实了模型的预测。版权所有©2015 John Wiley & Sons， Ltd
Molecular diffusion in fully saturated porous materials is strongly influenced by the pore space, which, in general, is characterized by a complex topological structure. Hence, information on macroscopic diffusion properties requires up‐scaling of transport processes within nano‐pores and micro‐pores over several spatial scales. A new model in the framework of continuum micromechanics is proposed for predicting the effective molecular diffusivity in porous materials. Considering a representative volume element, characterizing a porous material without any information about the pore space microstructure complexity, the uniform flux is perturbed by recursively embedding shape information hierarchically in the form of the ESHELBY matrix‐inclusion morphology to obtain the effective diffusivity as a function of the recurrence level and the porosity. The model predicts a threshold value for the porosity, below which no molecular diffusion can occur because of the presence of isolated pore clusters that are not connected and unavailable for transport. The maximum porosity, below which no molecular transport is possible, is predicted as one‐third for spherical inclusions. The model allows for extensions to more complex morphologies of the inclusions. We also identify, that the effects of the micro‐structure on molecular transport are characterized by porosity dependent long‐range and short‐range interactions. The developed framework is extended to incorporate realistic pore size distributions across several spatial scales by means of a distribution function within the hierarchical homogenization scheme. Available experimental results assert the model predictions. Copyright © 2015 John Wiley & Sons, Ltd.