Tortuosity and Microstructure Effects in Porous Media: Classical Theories, Empirical Data and Modern Methods (Springer Series in Materials Science, 333)

This open access book presents a thorough look at tortuosity and microstructure effects in porous materials. The book delivers a comprehensive review of the subject, summarizing all key results in the field with respect to the underlying theories, empirical data available in the literature, modern methodologies and calculation approaches, and quantitative relationships between microscopic and macroscopic properties. It thoroughly discusses up to 20 different types of tortuosity and introduces a new classification scheme and nomenclature based on direct geometric tortuosities, indirect physics-based tortuosities, and mixed tortuosities (geometric and physics-based). The book also covers recent progress in 3D imaging and image modeling for studying novel aspects of tortuosity and associated transport properties in materials, while providing a comprehensive list of available software packages for practitioners in the community. This book is a must-read for researchers and students in materials science and engineering interested in a deeper understanding of microstructure–property relationships in porous materials. For energy materials in particular, such as lithium-ion batteries, tortuosity is a key microstructural parameter that can greatly impact long-term material performance. Thus, the information laid out in this book will also greatly benefit researchers interested in computational modeling and design of next-generation materials, especially those for sustainability and energy applications. Preface Acknowledgements Contents 1 Introduction References 2 Review of Theories and a New Classification of Tortuosity Types 2.1 Introduction 2.1.1 Basic Concept of Tortuosity 2.1.2 Basic Challenges 2.1.3 Criteria for Classification 2.1.4 Content and Structure of This Chapter 2.2 Hydraulic Tortuosity 2.2.1 Classical Carman-Kozeny Theory 2.2.2 From Classical Carman-Kozeny Theory to Modern Characterization of Microstructure Effects 2.3 Electrical Tortuosity 2.3.1 Indirect Electrical Tortuosity 2.3.2 Mixed Electrical Tortuosities 2.4 Diffusional Tortuosity 2.4.1 Knudsen Number 2.4.2 Bulk Diffusion 2.4.3 Knudsen Diffusion 2.4.4 Limitations to the Concept of Diffusional Tortuosity 2.5 Direct Geometric Tortuosity 2.5.1 Skeleton and Medial Axis Tortuosity 2.5.2 Path Tracking Method (PTM) Tortuosity 2.5.3 Geodesic Tortuosity 2.5.4 Fast Marching Method (FMM) Tortuosity 2.5.5 Percolation Path Tortuosity 2.5.6 Pore Centroid Tortuosity 2.6 Tortuosity Types: Classification Scheme and Nomenclature 2.6.1 Classification Scheme 2.6.2 Nomenclature 2.7 Summary References 3 Tortuosity-Porosity Relationships: Review of Empirical Data from Literature 3.1 Introduction 3.2 Empirical Data for Different Materials and Microstructure Types 3.3 Empirical Data for Different Tortuosity Types 3.4 Direct Comparison of Tortuosity Types Based on Selected Data Sets 3.4.1 Example 1: Indirect Versus Direct Pore Centroid Tortuosity 3.4.2 Example 2: Indirect Versus Direct Medial Axis Tortuosity 3.4.3 Example 3: Indirect Versus Direct Geodesic Tortuosity 3.4.4 Example 4: Indirect Versus Medial Axis Versus Geodesic Tortuosity 3.4.5 Example 5: Direct Medial Axis Versus Direct Geodesic Tortuosity 3.4.6 Example 6: Mixed Streamline Versus Mixed Volume Averaged Tortuosity 3.5 Relative Order of Tortuosity Types 3.5.1 Summary of Empirical Data: Global Pattern of Tortuosity Types 3.5.2 Interpretation of Different Tortuosity Categories 3.6 Tortuosity–Porosity Relationships in Literature 3.6.1 Mathematical Expressions for τ–ε Relationships and Their Limitations 3.6.2 Mathematical Expressions for τ–ε Relationships and Their Justification 3.7 Summary References 4 Image Based Methodologies, Workflows, and Calculation Approaches for Tortuosity 4.1 Introduction 4.2 Tomography and 3D Imaging 4.2.1 Overview and Introduction to 3D Imaging Methods 4.2.2 X-ray Computed Tomography 4.2.3 FIB-SEM Tomography and Serial Sectioning 4.2.4 Electron Tomography 4.2.5 Atom Probe Tomography 4.2.6 Correlative Tomography 4.3 Available Software Packages for 3D Image Processing and Computation of Tortuosity 4.3.1 Methodological Modules 4.3.2 Different Types of SW Packages 4.4 From Tomography Raw Data to Segmented 3D Microstructures: Step by Step Example of Qualitative Image Processing 4.5 Calculation Approaches for Tortuosity 4.5.1 Calculation Approaches and SW for Direct Geometric Tortuosities (τdir_geom) 4.5.2 Calculation Approaches and SW for Indirect Physics-Based Tortuosities (τindir_phys) 4.5.3 Calculation Approaches for Mixed Tortuosities 4.6 Pore Scale Modeling for Tortuosity Characterization: Examples from Literature 4.6.1 Examples of Pore Scale Modeling in Geoscience 4.6.2 Examples of Pore Scale Modeling for Energy and Electrochemistry Applications 4.7 Stochastic Microstructure Modeling 4.7.1 Stochastic Modeling for Digital Materials Design (DMD) of Electrochemical Devices 4.7.2 Stochastic Modeling for Digital Rock Physics and Virtual Materials Testing of Porous Media 4.8 Summary References 5 Towards a Quantitative Understanding of Microstructure-Property Relationships 5.1 Introduction 5.2 Quantitative Micro–Macro Relationships for the Prediction of Conductivity and Diffusivity 5.3 Quantitative Micro–Macro Relationships for the Prediction of Permeability 5.3.1 Bundle of Tubes Model 5.3.2 Sphere Packing Model 5.3.3 Determination of Characteristic Length and M-factor by Laboratory Experiments 5.3.4 Determination of Characteristic Length and M-factor by 3D Image Analysis 5.3.5 Determination of Characteristic Length and M-factor by Virtual Materials Testing 5.4 Summary References 6 Summary and Conclusions