Tortuosity and Microstructure Effects in Porous Media Classical Theories, Empirical Data and Modern Methods

• Main Authors: Holzer, Lorenz, Marmet, Philip, Fingerle, Mathias, Wiegmann, Andreas, Neumann, Matthias, Schmidt, Volker
• Format: eBook
• Language: English
• Published: Cham Springer Nature 2023; Springer International Publishing AG
• Edition: 1
• Series: Springer Series in Materials Science
• Subjects: 3D Imaging; Chemistry; Diffusion in Porous Materials; Digital Materials Design; Effective Transport Properties of Porous Media; Engineered Porous Materials; Engineering thermodynamics; Integrated Computational Materials Engineering; Materials science; Mathematical physics; Mathematics and Science; Mechanical engineering and materials; Microstructure-Property Relationships; Nonfiction; Physics; Science; Simulation of Transport Properties; Technology; Technology, Engineering, Agriculture, Industrial processes; Tortuosity of Materials; Tortuosity-Porosity Relationships; Virtual Materials Testing; X-Ray Tomography for Materials
• ISBN: 3031304772; 9783031304767; 3031304764; 9783031304774
• DOI: 10.1007/978-3-031-30477-4

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 m...

Table of Contents:

• 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
• 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
• Intro -- 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