2D vs 3D clustering of the elliptic particulates: The correlation with the percolation thresholds
Applied Mathematical Modelling, cilt.143, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 143
- Basım Tarihi: 2025
- Doi Numarası: 10.1016/j.apm.2025.116007
- Dergi Adı: Applied Mathematical Modelling
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
- Anahtar Kelimeler: Continuum percolation, Elliptic fillers, 2D vs 3D analysis, Original density, Connected density, Elemental density
- Boğaziçi Üniversitesi Adresli: Evet
Özet
We develop a continuum percolation procedure for the aggregation of the elliptic fillers in the 2 and 3-dimensional media. Given random distributions for the locus and rotations of the elements with a specified original density p, each medium achieves chains of elements through overlapping to achieve a connection density of ρ. In this regard, typically 3D aggregation is more efficient than 2D due to the possibility of additional connectivity from the in/out (i.e. depth) directions. Hence, when increasing the number of fillers the 3D percolation system experiences an early increase in the connection density ρ, which typically occurs in the neighborhood of the percolation threshold pc. We initially develop a new iterative method to compute the percolation threshold pc in finite systems. Subsequently, we show that such early divergence between 2D-3D percolation systems is followed by a later convergence stage, as the number of fillers progressively increases. Consequently, we show, conceptually and computationally, that the maximum 2D-3D difference in the connections density Δρmax correlates directly with the respective 2D-3D difference in the percolation thresholds Δpc, where a large pool of computational samples were generated by varying the aspect ratio as well as the relative scale of the particles. The results and respective analyses could be useful for the design of binary composite membranes of a specified thickness (i.e. thin→2D, thick→3D) for achieving the desired homogenized physical property.