Packing fraction of particles with a Weibull size distribution

Brouwers, Hjh Jos

doi:10.1103/physreve.94.012905

Cited by 14 publications

(3 citation statements)

References 34 publications

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“…The Weibull distribution has a lot of applications in many different fields of science and technology, − in particular, among others, it has been profitably employed to describe the size of particles obtained in fragmentation processes (e.g., grinding, milling, and crushing operations). − It goes without saying that our size distribution has to do with a kind of “particles” of completely different nature: they are holes, namely lack of molecules. This simple fact is already interesting in itself, and we wondered if we were dealing with something more general.…”

Section: Resultsmentioning

confidence: 99%

Morphological Study of a Self-Organized Corrole Film on a Gold Crystal, both in Solution and after Solvent Evaporation

et al. 2023

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The morphology of the film created by the aggregation of corrole molecules from ethanol solution onto the surface of gold substrate was studied by scanning tunneling microscopy both: (i) in situ, namely in quasi-equilibrium (wet sample), and (ii) ex situ, i.e., removing the substrate from the fluid cell and leaving the residual amount of solution on the substrate to desiccate (dry sample). Despite the different conditions, the morphology of the corrole overlayer formed on the film of molecules is reminiscent, in both cases, of the leopard skin; the "speckles" are actually areas where the molecular overlayer of flat molecules is not completed. We quantitatively compared these two similar morphologies by studying the power spectral density of the images, the fractal dimension D P of the hole perimeters, and the cumulative distribution function of the hole areas. We found that the last layer of both films, in spite of very different formation conditions, differed from each other only by a scale factor.

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Section: Resultsmentioning

confidence: 99%

Morphological Study of a Self-Organized Corrole Film on a Gold Crystal, both in Solution and after Solvent Evaporation

et al. 2023

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“…For the RCP particle conformation, the quantities f L rcp = 0.64 and ß rcp = 0.20 were defined as fixed values. In later works, Brouwers extended the mathematical relationship to determine the packing fractions of particles with a lognormal or a Weibull particle size distribution. The particles within the DEM particle packing models are depicted as spheres within a three‐dimensional volume.…”

Section: Conversion Of Highly Filled Papers Into Paper‐derived Sintermentioning

confidence: 99%

Highly Filled Papers, on their Manufacturing, Processing, and Applications

et al. 2019

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Since more than a decade ago, the research on highly filled papers, as well as paper-derived inorganic materials, has greatly intensified. As presented in this review, highly filled papers as preforms allow for the design of porous or dense, multilayered, and geometrically complex structures. These paperderived ceramic-or metal-based materials are generated by the heattreatment of highly filled papers. Paper-derived materials are potential materials of choice for applications in transportation, energy-generation, environmental conservation, support structures, medical uses, and electronic components. Due to the adjustability of the filler content and the good machinability of highly filled papers, paper-derived sheets or multilayers may include intricate structures and tailored gradients in phase structure or porosity. Paper-derived multilayers also may contain cast ceramic tapes or other functionalized layers, as presented in some examples. Computer-aided manufacturing processes for paper-derived materials can be supplemented by prediction models for the sintering shrinkage in order to identify optimal post-processing steps, stacking orders and orientations for highly filled paper layers within multilayer green bodies. The accuracy of established component-level sintering models can be significantly increased by microstructure models of the highly filled paper. ParameterName Unit α Mismatch parameter for fiber cross-sections, Equation (5) Dimensionless α p Layer position in viscoelastic paper structure model, Equation (2) Dimensionless A 0 Initial amplitude of perturbation, Equations (15) 10 À6 m A(f) Parameter for evolution of instantaneous carbon conversion rate, Equation (7) Dimensionless A diff Source controlled diffusion parameter, Equations (9) 10 À7 N A match Modeling parameter, Equations (8) Dimensionless a Inter-particle contact-area radius, Equations (19) 10 À8 m a Local average pore area, Equation (4) 10 À6 m 2 b Pore geometry constant, Equation (20) Dimensionless ß evo , m evo Empirical constants for grain evolution in SOVS model, Equation (8) Dimensionless ß r(c)p Proportionality constant for bimodal packing fraction determination, Equation (18) Dimensionless C Modeling constant for debindering pressure calculation, Equation (7) 10 À6 (m 2 Á s)/K C 1 , C 2 , C 3 , C 4 , C 5 Parameters in the Riedel model that are determined by the dihedral angle, Equations (9) Dimensionless c glue Heat capacity of the adhesive layers, Equation (3) 10 À6 s c L , c s Volume fraction of larger-sized/smaller-sized particles in a multimodal mixture of particles, Equation (17)and (18) 10 0 vol% c vol Volume concentration of pulp fibers, Equation (4) 10 0 vol% γ, γ 0 Strain relaxation rate of calendered paper with initial value, Equation (2) Dimensionless γ B Grain boundary energy density, Equation (13) 10 0 J m À2 γ b Specific energy for grain boundary diffusion, Equation (9) 10 3 J mol À1 γ S Material surface energy, Equation (8, 11, and 13) 10 0 J m À2 Δ Half of the inter-particle boundary thickness, Equation (19) 10 À8...

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“…These particles block the connection between pores and induce the effect on water penetration and ion transportation (Wongkeo et al, 2014). Furthermore, since the pozzolanic materials show different particle size and morphology, a specific mix design can introduce a dense packing for concrete, which presents a denser microstructure and a better mechanical performance (Brouwers, 2016).…”

Section: Microstructure Characterizationmentioning

confidence: 99%