Voronoi polygon

Figure 2.12. Construction of the Voronoi polygon of particle 1 in a two-dimensional system of particles.

Further, a point-pattern analysis was applied. This is especially suitable for the quantification of particle distribution patterns [Tanaka et al., 1989], The nearest-neighbor center-to-center distance and effective coordination number (number of cell sides of corresponding Voronoi polygons) of dispersed particles were measured. For a ternary system, PPE/PA/rubber, TEM micrographs were analyzed to estimate the randomness and the degree of clustering [Hayashi et al., 1992]. 

Fig. 1.10 Average areas of the Voronoi polygons ranging from pentagons to heptagons (from Deng et al. (1989a) courtesy of the Royal Society of London).

Fig. 5.3. A two-dimensional system with its network of Voronoi polygons. Heavy lines boundaries of the Voronoi polygons. Light lines the dual network of polygons, constructed by lines kj connecting pairs of particles which contribute a boundary for the Voronoi polygons of i and j.

However, the computation of the coordination number is much easier than is that of the volume of the Voronoi polygon of each particle. Both of these properties provide a measure of the local density around particles in the liquid. [For more details see Ben-Naim (1973b).]... 

In general, different lattices with the same dimensionality and coordination number, e.g. the hexagonal and Voronoi polygon, exhibit similar behavior [40]. More importantly, the effective diffusion coefficient on these lattice structures can be closely approximated by selecting a Bethe lattice with an appropriate effective coordination number For example, three-dimensional cubic and Voronoi polyhedron lattices, with coordination numbers of 6 and 16, have the same effective diffusion coefficient behavior as Bethe lattices with coordination number of 5 and 7 [44]. Therefore, the effective diffusion coefficient and tortuosity trends shown in Figure 6 are applicable to percolation lattices with widely different geometries. Prediction of the effective diffusivity of a given real lattice follows directly from selection of an effective Bethe coordination number. 

Fig. 2 Illustration of our developing procedure of automatic mesh subdivision on the basis of Voronoi Polygon and Delaunay Tessellation a) Initial geometric model, b) Automatic node generation, c) Intermediate search for new DT s in sequence by edge control, d) Automatic triangulation and e) Transformation to quadrilateral elements.

---