Microstructure Clustering in Multiphase Materials: Effect of Initial Configuration

In disperse multiphase systems, the dispersion/distribution of particles (microstructure) is regarded as a key factor, both affected by processing and in its turn determining performance. Among many miscrostructural features, clustering, that is, the tendency of dispersed particles to agglomerate forming clusters of differnt size, is considered of primary significance. Our purpose in this study is both, to understand the evolution of clustering generated by Monte-Carlo procedure with the change of the initial configuration of the particles...

A multi-scale model for Transport and Reaction in Heterogeneous Porous Media

Many practical problems in engineering occur over time and length scales that differ by many orders of magnitude. This makes the application of direct numerical approaches for the prediction of their response impractical. One such class of systems involves heterogeneous porous media in which small spherical porous particles are dispersed within a larger porous domain. We are interested in investigating such systems in which diffusional and convective transport in the continuous phase are coupled with diffusion and reaction/immobilization within the micro-scale inclusions; we develop multi-scale models which enable the prediction of the transient response of such systems taking into account, in a rigorous manner, the transport and reaction at the micro-scale. Immobilized bioreactors [1], ground-water or hydrocarbon flow in fractured rock [2] and ion diffusion in Li-ion batteries [3] are all potential systems of interest

Microstructure Clustering in Multiphase Materials: The role of dimensionless temperature and surface fraction

The significant development and intensified use of composite materials (reinforced plastics, extruded materials and mechanically blended thermoplastics) over the last 30 years has provided the impetus for intense research on their processability as well as on the durability and properties of the final products. In disperse multiphase systems, the dispersion/distribution of particles (microstructure) is regarded as a key factor, both affected by processing and in its turn determining performance

Microstructure Clustering in Multiphase Materials: Particle size effect

The significant development and intensified use of composite materials (reinforced plastics, extruded materials and mechanically blended thermoplastics) over the last 30 years has provided the impetus for intense research on their processability as well as on the durability and properties of the final products. In disperse multiphase systems, the dispersion/distribution of particles (microstructure) is regarded as a key factor, both affected by processing and in its turn determining performance..

A Multi-Scale, Semi-Analytical Model for Transient Heat Transfer in a Nano-Composite Containing Spherical Inclusions

http://ect-journal.kz/index.php/ectj/article/view/819This paper presents a semi-analytical model for transient heat conduction in a composite material reinforced with small spherical inclusions. Essential to the derivation of the model is the assumption that the size of the inclusions is much smaller than the length scale characterizing the macroscopic problem. An interfacial thermal resistance is also present between the two phases. During heating, the inclusions are treated as heat sinks within the matrix, with the coupling provided by the boundary conditions at the surface of the embedded particles. Application of Duhamel’s Theorem at the particle scale provides the local relationship between the temperature profile in a particle and the matrix that surrounds it. A simple spatial discretization at the macro-scale leads to an easily solvable system of coupled Ordinary Differential Equations for the matrix temperature, particle surface temperature and a series of ψ-terms related to the heat exchange between phases. The interfacial thermal resistance between the two phases can lead to the particle temperature lagging behind that of the surrounding matrix. The resulting transient response of the matrix temperature cannot be reproduced by a material with a single effective thermal conductivity. In the case where transient methods are used to determine effective thermal conductivity, this transient response may introduce errors into the measurement

A novel FastRSA algorithm: Statistical properties and evolution of microstructure

While the Random Sequential Adsorption (RSA) process for the generation of 2D geometries containing discrete entities has been extensively studied, both in terms of numerical simulations and in terms of its statistical properties, all the mechanisms involved are not fully understood, especially in dense configurations of elongated particles. This is mainly due to the very slow asymptotic approach to high packing configurations, especially when highly elongated particles are involved, which makes the creation of such configurations a time consuming task. For the estimation of the statistical properties of such configurations we therefore have to resort to extrapolations that do not always give accurate results. In this work we reveal the interaction of the mechanisms that come into play in the RSA process. We specifically show that the overall result of an RSA process is the summary outcome of these interwoven mechanisms, namely those involving the formation and destruction of Particle Area, Overlap Area and Influence Area – terms which we introduce and define in this work – resulting in a behavior that often appears counter-intuitive. We also show the shift of their importance as the particle aspect ratio α varies and explain how nematic structures are created when high aspect ratio particles are involved as well as the mechanisms behind their appearance. Following this, we propose a new algorithm for the process of random sequential adsorption (named FastRSA) which is capable of creating very high count configurations through all the range of particle aspect ratios and which follows Feder's law with a θ∼τ−1∕2 behavior instead of the θ∼τ−1∕3 of the classic approach, where τ is the number of attempts to place a particle and θ is the degree of packing. We show how the new algorithm can be coupled with the classic RSA approach and point out the benefits of such a coupling. Use of the FastRSA algorithm has enabled us to study the evolution of the extent of packing using actual geometries, without the need to resolve to extrapolations and assumptions. For the case of highly elongated particles, this is the first time in our knowledge that estimations of maximum packing from actual configurations near the jamming limit have been obtained. © 2019 Elsevier B.V

Multi-scale modeling of the dynamics of a fibrous reactor: Use of an analytical solution at the micro-scale to avoid the spatial discretization of the intra-fiber space

Direct modeling of time-dependent transport and reactions in realistic heterogeneous systems, in a manner that considers the evolution of the quantities of interest in both, the macro-scale (suspending fluid) and the micro-scale (suspended particles), is currently well beyond the capabilities of modern supercomputing. This is understandable, since even a simple system such as this can easily contain over 107 particles, whose length and time scales differ from those of the macro-scale by several orders of magnitude. While much can be gained by applying direct numerical solution to representative model systems, the direct approach is impractical when the performance of large, realistic systems is to be modeled. In this study we derive and analyze a “hybrid” model that is suitable for fibrous reactors. The model considers convection/diffusion in the bulk liquid, as well as intra-fiber diffusion and reaction. The essence of our approach is that diffusion and (first-order) reaction in the intra-fiber space are handled semi-analytically, based on well-established theory. As a result, the problem of intra-fiber transport and reaction is reduced to an easily solvable set of n0 ODEs, where n0 is the number of terms in the Bessel expansion evaluated without recourse to approximation; this set is coupled, point-wise, with a numerical model of the macro-scale. When the latter is discretized using N nodes, the total “hybrid” model for the system consists of a system of N(2 + n0) ODEs, which is easily solvable on a modest workstation. Parametric analyses are presented and discussed. © 2019 by the author

A general scaling for the barrier factor of composites containing thin layered flakes of rectangular, circular and hexagonal shape

We propose a general scaling which allows for the results of 3D mass transfer computations in layered flake composites containing square, circular or hexagonal flakes to collapse on a single master curve. We show that the Barrier Improvement Factor (BIF ~ 1/Deff) of such composites is well represented by a power function of that scale (M) namely BIF=(1+M)2. Our simulations are carried out in three-dimensional multi-particle RVEs each containing up to 4000 randomly placed individual flakes. The flakes are represented as two-dimensional squares, disks or hexagons; this representation is suitable for very thin flakes, such as exfoliated nano-platelets. Around 3000 simulations are carried out, and the effective BIF is computed for different values of flake orientation, shape, dimensions and number density. We show that our scaling is consistent with the traditional representation of the BIF as a power function of (αϕ), (α) and (ϕ) being the aspect ratio and the volume fraction of the flakes, while at the same time offering a generalized approach that is valid for all flake shapes. When the flakes are layered at an angle (θ) to the direction of macroscopic diffusion, we propose a model for the BIF in terms of the principal diffusivity and (θ); this is found to be in very good agreement with computational results, which show that while the BIF increases with increasing (M), this increase is no longer monotonic but, instead, BIF approaches an asymptotic plateau value which is determined by (θ). © 2020 Elsevier Lt

The effect of shape and orientation on the barrier properties of flake-filled composites: A 3D approach

We carry out fully three-dimensional (3D) simulations in flake-filled composites with the objective of determining the effect of flake shape and orientation on their barrier properties. Our simulations are carried out in multi-particle unit cells, each containing up to 4,000 individual flakes. We represent the flakes as 2D rectangles of dimensions (l) and (w); this representation is suitable for very thin flakes, such as exfoliated nano-platelets of montmorillonite or graphene-oxide. We analyze the effect of flake shape on the effective diffusivity Deff and find that square flakes offer the best barrier improvement. For constant flake area, the barrier properties are predicted to decrease as the diagonal and/or the aspect ratio of the flake increase. We also analyze the effect of flake misalignment with respect to the direction of macroscopic diffusion and find that, in a manner similar to what has been seen in 2D systems, the decrease in Deff with flake loading and/or flake diameter is less severe as the degree of misalignment increases. Finally, fully 3D systems are compared to systems in which one flake dimension is progressively approaching the dimensions of the unit cell, thus rendering mass transport essentially two-dimensional. We find that in this case the predicted Deff is lower than that of a system in which mass transfer is three-dimensional in nature. Copyright 2019. Used by the Society of the Advancement of Material and Process Engineering with permission

Orientational randomness and its influence on the barrier properties of flake-filled composite films

This direct numerical study investigated the effect of orientational randomness on the barrier properties of flake-filled composites. Over 2500 simulations have been conducted in two-dimensional, doubly periodic unit cells, each containing 500 individual flake cross-sections which, besides being spatially random, assume random orientations within an interval [a'É, +E] (0 ≤ É ≤ I€ / 2). We consider long flake systems (aspect ratio α = 50, 100, and 1000) from the dilute (αI• = 0.01) to the concentrated (αI• = 15) regime, where (I•) is the flake volume fraction. At each (É) and (αI•), several realizations are generated. At each of those, the steady-state diffusion equation is solved, the mass flux across a boundary normal to the diffusion direction is computed and an effective diffusivity Deff calculated from Fick's Law. The computational results for Deff are analyzed and the effects of (É) and (αI•) are quantified. These differ in the dilute (αI• < 1) and in the concentrated regimes (1 < αI• < 15). In the dilute regime, the barrier improvement factor is a linear function of (É) and a power function of (αI•), with the exponent (â1/41.07) independent of orientation. In concentrated systems, we find that for aligned flakes or flakes showing small deviations from perfect alignment, the barrier improvement factor approaches the quadratic dependence on (αI•) predicted by theory. However, the power exponent is found to decrease as (É) increases, from 1.71 in the aligned system (É = 0) to â1/40.9 in the fully random system (É = I€/2). We propose a scaling which incorporates the effects of both (αI•) and (É) on the barrier improvement factor, resulting in a master curve for all (αI•) and (É). Our results suggest that the anticipated barrier property improvement may not be realized if the flake orientations exhibit a significant scatter around the desired direction. © SAGE Publications