The performance of all-solid-state battery (ASSB) cathodes strongly depends on their microstructure. Optimizing the cathode morphology can therefore enhance effective macroscopic properties such as ionic and electronic conductivity. The search for optimized microstructures can be facilitated by virtual materials testing, i.e., by integrating image analysis and stochastic microstructure modeling to generate a wide range of realistic 3D microstructures and evaluate their effective macroscopic properties by means of numerical simulations, thereby reducing the need for extensive physical experiments. This approach allows for the investigation of structure-property relationships through parametric regression models that incorporate relevant geometric descriptors of 3D microstructures such as volume fractions, mean geodesic tortuosities, specific surface areas, and constrictivities. By linking these geometric descriptors to effective macroscopic properties, virtual materials testing provides quantitative insight into how microstructure influences material performance. In this paper, this framework is applied to ASSB cathodes. In addition, by systematically varying model parameters, a broad range of 3D microstructures can be generated, which remain close to the original cathode morphology while inducing targeted changes in selected geometric descriptors. The resulting database enables the calibration of regression models whose predictive performance is assessed by comparing predicted and simulated effective properties such as the ionic and electronic conductivity, thereby quantifying how accurately combinations of geometric descriptors can explain and predict variations in effective macroscopic properties.

Accurate elastic property estimation is essential in rock physics modeling, geomechanical analysis, and reservoir characterization. Reliable predictions of seismic properties such as compressional wave velocity vp and shear wave velocity vs in digital rocks enable a precise relation between pore-scale rock properties and field-scale data for well placement and production monitoring. This improves understanding of reservoir behavior during production. This study focuses on enhancing the computation of elastic properties and seismic parameters, including vp/vs across diverse rock types, from clastic stones to calcareous grainstones. It addresses the common overestimation of effective stiffness caused by limited image resolution, a frequent issue in standard digital rock analysis workflows. The proposed approach improves the identification of local grain configurations using a watershed segmentation algorithm. Based on the segmented microstructure, it adjusts local contact stiffness according to the relative size of contact areas, accounting for stiffness reduction at these contact zones. The effective stiffness tensor of each rock sample is then calculated through a homogenization process using linear elasticity equations solved with a fast Fourier transformation (FFT)-based solver. Post-processing yields vp and vs wave velocities, allowing direct comparison with experimental data. The developed algorithm significantly reduces the overestimation of effective stiffness by integrating detailed microstructural information and accurately representing grain-scale mechanics. It explicitly models stiffness reduction at grain-grain contacts and uses improved grain segmentation to enhance predictions of elastic properties. Applying this digital rock physics workflow yields results that closely match laboratory measurements, confirming that the simulated vp and vs reliably capture rock-specific behavior. Computed findings are consistent with literature-reported values for saturated rock samples. The proposed workflow delivers more realistic estimates of rock properties, improving the reliability of elastic property upscaling from pore-scale simulations to seismic-scale predictions. This higher accuracy strengthens geophysical interpretations, including rock-physics modeling and seismic analysis in oil and gas applications. Validation against laboratory data confirms the method's accuracy. Overall, the method is robust, broadly applicable to similar lithologies, and provides a powerful tool for digital rock analysis. It enables better-informed decisions in reservoir characterization, well planning, and production monitoring.

Fibrous materials are essential in industries such as lightweight automotive materials [1] [2], filtration [3], and hygiene products [4]. The properties of these materials depend on microstructural geometric statistics, making the analysis of individual fibers a powerful tool in material engineering. Fiber length, for example, is a fundamental parameter influencing material properties in composites and nonwovens. Traditional methods for determining fiber length are labor-intensive, prone to user bias, and time-consuming. In contrast, CT-scan-based approaches offer a novel, non-destructive, and reproducible method to assess fiber length distribution. These digital techniques enable the easy analysis of freshly manufactured samples and their re-examination after use to investigate material aging, including changes in fiber length, the matrix, or other components. In this work, we present our method to measure fiber length in micro-CT-scans and compare it to an established experimental method.

Gas diffusion layers (GDLs) are vital parts for the performance of proton-exchange membrane fuel cells (PEMFCs). In many cases, they are made of Carbon-Carbon Composite Paper (CCCP), which consists of carbon fibers and a carbonized binder material. The distribution of the fibers and binder in the GDL strongly influences the performance of a PEMFC. Synchrotron scans are a great way to obtain information about the microstructural composition of carbon paper GDLs (Figure 2), there is one major obstacle. Binder and fibers tend to have the same attenuation and, consequently, the same gray values in the scans. To overcome this, we introduce a machine learning-based method that segments fibers and binder from the local morphology of a CCCP. The training data is generated using FiberGeo, a module the GeoDict software for fibrous microstructure generation. FiberGeo creates fibers based on stochastic geometry and adds binder using morphological opening closing operations. We applied the machine learning-based method to four Scans of samples of Toray Carbon Paper with varying amounts of binder in them. result is the quantification of individual voxels as fiber or binder material that can be used, for example, in performance simulations of property simulations PEMFCs [1-4]. Here, we focus on the differences in the spatial distribution of the binder both in the through-plane and in-plane directions.

This paper presents a computational method for generating virtual 3D morphologies of functional materials using low-parametric stochastic geometry models, i.e., digital twins, calibrated with 2D microscopy images. These digital twins allow systematic parameter variations to simulate various morphologies, that can be deployed for virtual materials testing by means of spatially resolved numerical simulations of macroscopic properties. Generative adversarial networks (GANs) have gained popularity for calibrating models to generate realistic 3D morphologies. However, GANs often comprise of numerous uninterpretable parameters make systematic variation of morphologies for virtual materials testing challenging. In contrast, low-parametric stochastic geometry models (e.g., based on Gaussian random fields) enable targeted variation but may struggle to mimic complex morphologies. Combining GANs with advanced stochastic geometry models (e.g., excursion sets of more general random fields) addresses these limitations, allowing model calibration solely from 2D image data. This approach is demonstrated by generating a digital twin of all-solid-state battery (ASSB) cathodes. Since the digital twins are parametric, they support systematic exploration of structural scenarios and their macroscopic properties. The proposed method facilitates simulation studies for optimizing 3D morphologies, benefiting not only ASSB cathodes but also other materials with similar structures.

This work presents a novel approach to investigating the slip effect in nanofiber filter media. Electrospun nanofiber media with high efficiency and low pressure drop were produced at different concentrations and durations. The surface and cross-sectional morphology of nanofiber media were studied using FE-SEM. Fiber orientation and diameter distributions were also examined. The 3D virtual nanofiber media was modeled using this information along with the experimentally measured porosity and thickness of the media. The effect of the slip phenomenon in nanofiber media was studied numerically, and the results were compared to experimental data. Excellent agreements were found between the measured and simulation results. Additionally, filtration simulations considering aerosols injected with airflow through the nanofibrous filter media were conducted by considering the slip effect, and the effect of filter structure on filtration performance (removal efficiency and pressure drop) was investigated.

Quantifying the relationship between geometric descriptors of microstructure and effective properties like permeability is essential for understanding and improving the behavior of porous materials. In this paper, we employ a previously developed stochastic model to investigate microstructure-property relationships of nonwovens. First, we show the capability of the model to generate a wide variety of realistic nonwovens by varying the model parameters. By computing various geometric descriptors, we investigate the relationship between model parameters and microstructure morphology and, in this way, assess the range of structures which may be described by our model. In a second step, we perform virtual materials testing based on the simulation of a wide range of nonwovens. For these 3D structures, we compute geometric descriptors and perform numerical simulations to obtain values for permeability as an effective material property. We then examine and quantify the relationship between microstructure morphology and permeability by fitting parametric regression formulas to the obtained data set, including but not limited to formulas from literature. We show that for structures which are captured by our model, predictive power may be improved by allowing for slightly more complex formulas.

Measuring the thickness of thin porous materials provides valuable insights into their structure, properties, and performance, including key properties such as porosity and permeability, and is highly beneficial for a range of industrial applications, particularly for ensuring effective quality control processes. A novel approach for estimating the thickness of porous media and their surfaces is proposed based on voxel sets of 3D images, such as 3D scans and segmented scan data. Initially, the solid volume fraction (SVF) is computed for each voxel layer perpendicular to the through direction. Then, fitting functions consisting of piecewise linear segments are chosen to ensure an accurate representation of the layer data. Each function is associated with various thickness regions of the medium, including the medium itself and its surface. An optimization problem is then solved to find the best-fitting function based on the squared area between the SVF and the fitting function. The thickness of the medium and its surfaces is determined based on the identified optimal fit. This robust, reliable, and fast approach aims to provide not only a non-intrusive method for thickness estimation of porous media represented by voxel sets but also a precise alternative to existing methodologies.

Fibrous materials play a significant role in many industries, such as lightweight automotive materials, filtration, or as constituents of hygiene products. The properties of fibrous materials are governed to a large extent by their microstructure. One way to access the microstructure is to use micro-Computed Tomography (micro-CT). Completely characterizing the microstructure requires geometrically characterizing each individual fiber. To make this possible, one must identify the individual fibers. Our method achieves this by finding in segmented mu CT scans the centerline of all individual fibers. It uses a convolutional neural network that was trained on automatically generated synthetic training data. From the centerlines, analytic descriptions of the individual fibers are constructed. These analytic representations allow detailed insights into the statistics of the geometric properties of the fibrous material, such as the fibers' orientation, length, or curvature. The method is validated on artificial data sets and its usefulness demonstrated on a very large micro-CT scan of a nonwoven composed of long fibers with random curvature.

AbstractMany different definitions of tortuosity can be found in literature. In addition, also many different methodologies are nowadays available to measure or to calculate tortuosity. This leads to confusion and misunderstanding in scientific discussions of the topic. In this chapter, a thorough review of all relevant tortuosity types is presented. Thereby, the underlying concepts, definitions and associated theories are discussed in detail and for each tortuosity type separately. In total, more than 20 different tortuosity types are distinguished in this chapter. In order to avoid misinterpretation of scientific data and misunderstandings in scientific discussions, we introduce a new classification scheme for tortuosity, as well as a systematic nomenclature, which helps to address the inherent differences in a clear and efficient way. Basically, all relevant tortuosity types can be grouped into three main categories, which are (a) the indirect physics-based tortuosities, (b) the direct geometric tortuosities and (c) the mixed tortuosities. Significant differences among these tortuosity types are detected, when applying the different methods and concepts to the same material or microstructure. The present review of the involved tortuosity concepts shall serve as a basis for a better understanding of the inherent differences. The proposed classification and nomenclature shall contribute to more precise and unequivocal descriptions of tortuosity.

This open access book provides a thorough review of tortuosity in porous materials and discusses the impact of the microstructure on materials properties

In this paper we lay the foundation for data-driven 3D analysis of virtual fiber systems with respect to their microstructure and functionality. In particular, we develop a stochastic 3D model for systems of curved fibers similar to nonwovens, which is fitted to tomographic image data. By systematic variations of model parameters, efficient computer-based scenario analyses can be performed to get a deeper insight how effective properties of this type of functional materials depend on their 3D microstructure. In a first step, we consider single fibers as polygonal tracks which can be modeled by a third-order Markov chain. For constructing the transition function of the Markov chain, we formalize the intuitive notions of intrinsic fiber properties and external effects and build a copula-based transition function such that both aspects can be varied independently. Using this single-fiber model, in a second step we derive a model for the entire fiber system observed in a bounded sampling window and fit it to two different 3D datasets of nonwovens measured by CT imaging. Considering various geometric descriptors of the 3D microstructure related to effective properties of the pore space, we evaluate the goodness of model fit by comparing geometric descriptors of the 3D morphology of model realizations with those of tomographic image data.

This paper presents, discusses, and compares three methods for measuring the water per-meability of metal woven meshes. Two pieces of equipment were designed for this purpose. The first uses declining pressure - falling head method (FHM). The other uses constant pressure - the constant head method (CHM). The results obtained with these two empirical methods were compared with the fluid flow simulation through the studied samples. The results showed that each studied technique provided valuable and unique information for the water permeability investigation. All three techniques were in good agreement when they all worked under turbulent flow conditions. These conditions were observed for the samples whose pore size was above 30 mu m. FHM worked only under turbulent flow. Therefore, it was recommended to work with high permeable samples. The samples whose pore size was below 30 mu m required laminar flow. CHM could provide these conditions. This method was also the fastest with the lowest standard deviation value. It is recommended as the basis for forming a standard for measuring the water permeability of woven filter media. Data Availability: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.(c) 2022 The Authors. Published by Elsevier Ltd on behalf of Institution of Chemical Engineers. This is an open access article under the CC BY license (http://creative-commons.org/licenses/by/4.0/).

AbstractIt is generally assumed that transport resistance in porous media, which can also be expressed as tortuosity, correlates somehow with the pore volume fraction. Hence, mathematical expressions such as the Bruggeman relation (i.e., τ2 = ε−1/2) are often used to describe tortuosity (τ)—porosity (ε) relationships in porous materials. In this chapter, the validity of such mathematical expressions is critically evaluated based on empirical data from literature. More than 2200 datapoints (i.e., τ – ε couples) are collected from 69 studies on porous media transport. When the empirical data is analysed separately for different material types (e.g., for battery electrodes, SOFC electrodes, sandstones, packed spheres etc.), the resulting τ versus ε—plots do not show clear trend lines, that could be expressed with a mathematical expression. Instead, the datapoints for different materials show strongly scattered distributions in rather ill-defined ‘characteristic’ fields. Overall, those characteristic fields are strongly overlapping, which means that the τ – ε characteristics of different materials cannot be separated clearly. When the empirical data is analysed for different tortuosity types, a much more consistent pattern becomes apparent. Hence, the observed τ − ε pattern indicates that the measured tortuosity values strongly depend on the involved type of tortuosity. A relative order of measured tortuosity values then becomes apparent. For example, the values observed for direct geometric and mixed tortuosities are concentrated in a relatively narrow band close to the Bruggeman trend line, with values that are typically < 2. In contrast, indirect tortuosities show higher values, and they scatter over a much larger range. Based on the analysis of empirical data, a detailed pattern with a very consistent relative order among the different tortuosity types can be established. The main conclusion from this chapter is thus that the tortuosity value that is measured for a specific material, is much more dependent on the type of tortuosity than it is dependent on the material and its microstructure. The empirical data also illustrates that tortuosity is not strictly bound to porosity. As the pore volume decreases, the more scattering of tortuosity values can be observed. Consequently, any mathematical expression that aims to provide a generalized description of τ − ε relationships in porous media must be questioned. A short section is thus provided with a discussion of the limitations of such mathematical expressions for τ − ε relationships. This discussion also includes a description of the rare and special cases, for which the use of such mathematical expressions can be justified.

Abstract100 years ago, the concept of tortuosity was introduced by Kozeny in order to express the limiting influence of the microstructure on porous media flow. It was also recognized that transport is hindered by other microstructure features such as pore volume fraction, narrow bottlenecks, and viscous drag at the pore surface. The ground-breaking work of Kozeny and Carman makes it possible to predict the macroscopic flow properties (i.e., permeability) based on the knowledge of the relevant microstructure characteristics. However, Kozeny and Carman did not have access to tomography and 3D image analysis techniques, as it is the case nowadays. So, their descriptions were developed by considering simplified models of porous media such as parallel tubes and sphere packings. This simplified setting clearly limits the prediction power of the Carman-Kozeny equations, especially for materials with complex microstructures. Since the ground-breaking work of Kozeny and Carman many attempts were undertaken to improve the prediction power of quantitative expressions that describe the relationship between microstructure characteristics (i.e., tortuosity τ, constrictivity β, porosity ε, hydraulic radius rh) and effective transport properties (i.e., conductivity σeff, diffusivity Deff, permeability к,). Due to the ongoing progress in tomography, 3D image-processing, stochastic geometry and numerical simulation, new possibilities arise for better descriptions of the relevant microstructure characteristics, which also leads to mathematical expressions with higher prediction power. In this chapter, the 100-years evolution of quantitative expressions describing the micro–macro relationships in porous media is carefully reviewed,—first, for the case of conduction and diffusion,—and second, for flow and permeability.The following expressions are the once with the highest prediction power:$$\sigma_{eff} \left( {or D_{eff} } \right) = \varepsilon^{1.15} \beta^{0.37} /\tau_{{dir_{geodesic} }}^{4.39} ,$$ σ eff o r D eff = ε 1.15 β 0.37 / τ d i r geodesic 4.39 , for conduction and diffusion, and$$\kappa_{I} = 0.54\left( {\frac{\varepsilon }{{S_{V} }}} \right)^{2} \frac{{\varepsilon^{3.56} \beta^{0.78} }}{{\tau_{dir\_geodesic}^{1.67} }},$$ κ I = 0.54 ε S V 2 ε 3.56 β 0.78 τ d i r _ g e o d e s i c 1.67 , $$\kappa_{II} = \frac{{\left( {0.94r_{min} + 0.06r_{max} } \right)^{2} }}{8} \frac{{\varepsilon^{2.14} }}{{\tau_{dir\_geodesic}^{2.44} }},$$ κ II = 0.94 r min + 0.06 r max 2 8 ε 2.14 τ d i r _ g e o d e s i c 2.44 , both, for permeability in porous media.

AbstractIn this chapter, modern methodologies for characterization of tortuosity are thoroughly reviewed. Thereby, 3D microstructure data is considered as the most relevant basis for characterization of all three tortuosity categories, i.e., direct geometric, indirect physics-based and mixed tortuosities. The workflows for tortuosity characterization consists of the following methodological steps, which are discussed in great detail: (a) 3D imaging (X-ray tomography, FIB-SEM tomography and serial sectioning, Electron tomography and atom probe tomography), (b) qualitative image processing (3D reconstruction, filtering, segmentation) and (c) quantitative image processing (e.g., morphological analysis for determination of direct geometric tortuosity). (d) Numerical simulations are used for the estimation of effective transport properties and associated indirect physics-based tortuosities. Mixed tortuosities are determined by geometrical analysis of flow fields from numerical transport simulation. (e) Microstructure simulation by means of stochastic geometry or discrete element modeling enables the efficient creation of numerous virtual 3D microstructure models, which can be used for parametric studies of micro–macro relationships (e.g., in context with digital materials design or with digital rock physics). For each of these methodologies, the underlying principles as well as the current trends in technical evolution and associated applications are reviewed. In addition, a list with 75 software packages is presented, and the corresponding options for image processing, numerical simulation and stochastic modeling are discussed. Overall, the information provided in this chapter shall help the reader to find suitable methodologies and tools that are necessary for efficient and reliable characterization of specific tortuosity types.

In the present paper, we propose a novel single-fiber model which exploits a description of fibers as a sequence of bond and torsion angles. Using the Frenet–Serret formulas, this representation can be translated into three-dimensional (3D) space and vice-versa. While the precise locations of points along a fiber do not directly convey information about the inner material properties of the fiber, the distribution of bond, and torsion angles may be related to various material characteristics and, thus, our model may form a direct link between inner material properties and emerging microstructure properties. More precisely, we model curved fibers in the 3D Euclidean space R3 as polygonal tracks that we represent by their local curvature and torsion at each sampling point. The 2D sequences of curvatures and torsions obtained in this way are then considered as realizations of a Markov chain with finite memory which takes its values in R2. The transition kernel of this Markov chain is given by a family of conditional multivariate probability distributions. They are constructed using so-called R-vine copulas, which are fitted and validated by means of experimental data.

The hydraulic permeability of sea ice is an important property that influences the role of sea ice in the environment in many ways. As it is difficult to measure, so far not many observations exist, and the quality of deduced empirical relationships between porosity and permeability is unknown. The present work presents a study of the permeability of young sea ice based on the combination of brine extraction in a centrifuge, X-ray micro-tomographic imaging and direct numerical simulations. The approach is new for sea ice. It allows us to relate the permeability and percolation properties explicitly to characteristic properties of the sea ice pore space, in particular to pore size and connectivity metrics. For the young sea ice from the present field study we obtain a brine volume of 2 % to 3 % as a threshold for the vertical permeability (transition to impermeable sea ice). We are able to relate this transition to the necking of brine pores at a critical pore throat diameter of ≈0.07 mm, being consistent with some limited pore analysis from earlier studies. Our optimal estimate of critical brine porosity is half the value of 5 % proposed in earlier work and frequently adopted in sea ice model studies and applications. By placing our results in the broader context of earlier studies, we conclude that the present threshold is more significant in that our centrifuge experiments and high-resolution 3D image analysis enable us to more accurately identify the threshold below which fluid connectivity ceases by examining the brine inclusion microstructure on finer scales than were previously possible. We also find some evidence that the sea ice pore space should be described by directed rather than isotropic percolation. Our revised porosity threshold is valid for the permeability of young columnar sea ice dominated by primary pores. For older sea ice containing wider secondary brine channels, for granular sea ice and for the full-thickness bulk permeability, other thresholds may apply.