Characterization of structures of particles
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Characterization of structures of particles Konstantinos Manikas1,2 · Georgios G. Vogiatzis1 · Patrick D. Anderson1 · Markus Hütter1 Received: 5 March 2020 / Accepted: 8 May 2020 © The Author(s) 2020
Abstract A methodology for the characterization of particle structures, especially networks, is developed. This scheme combines 3D image analysis techniques with graph theory tools for the simplification of a structure of thick agglomerates to its skeleton. The connectivity graph of the initial structure is compared with the one of the corresponding skeleton, as a measure of simplification. Examples are used to illustrate the effectiveness of our scheme. Particle structures obtained by Brownian Dynamics simulations are characterized qualitatively and quantitatively. Instead of looking at the characteristics of the structure at the level of the individual particles or neighborhoods of particles, our scheme results in quantitative measures of the network, e.g. the number density of branch-points, the degree of branch-points, and the thickness and the orientation of the branches.
1 Introduction Suspensions of particles have been a matter of scientific interest since the beginning of the twentieth century [1, 2]. These systems have a lot of applications, e.g. in the food industry [3], cosmetics [4], medicine [5], water treatment [6], paint [7], and ceramics [8]. Their microstructure is interesting both from a scientific and an industrial point of view. The microstructure determines the macroscopic properties of the suspension, especially the mechanical ones [9, 10]. In the following, we focus on the characterization of the microstructure of this kind of systems, and especially of network structures. Many techniques have been used for the characterization of the arrangement of the suspended particles in a suspension, often using only two-particle correlations. The most * Konstantinos Manikas [email protected] * Markus Hütter [email protected] Georgios G. Vogiatzis [email protected] Patrick D. Anderson [email protected] 1
Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Brightlands Materials Center, 6167 RD Geleen, The Netherlands
2
common is the pair-correlation function, g(r) [11–16], and related to that the fractal dimension [17, 18]. The radial paircorrelation function is a powerful tool that quantifies the distribution of the inter-particle distances, which, however, give an accurate description only if the structure is homogeneous and spherically symmetric. The cylindrical pair-correlation function in two dimensions is another example [19, 20]. To quantify the orientation of the connector vector between any two bonded particles, the second Legendre polynomial, S2 [20], is used, which quantifies the orientation of the bond direction with respect to an external (imposed) direction. The information obtained by studying the relative arrangement of only two particles is many times insufficient, so a variety of technique
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