Efficient measurement of the percolation threshold for random systems of congruent overlapping ovoids

• Published in: Powder technology 2020-01, Vol.360, p.598-607
• Main Authors: Li, Mingqi, Chen, Huisu, Lin, Jianjun
• Format: Article
• Language: English
• Subjects: Algorithms; Aspect ratio; Contact detection algorithm; Continuum percolation threshold; Ellipsoids; Geometric properties; Materials science; Mathematical morphology; Monte Carlo simulation; Overlapping ovoids; Particle asymmetry; Particulate composites; Percolation; Tapering
• ISSN: 0032-5910; 1873-328X
• DOI: 10.1016/j.powtec.2019.10.044

The percolation behavior of composites comprising complex-shaped particles is a recurrent problem in materials science. Previous studies focused on the symmetric particles such as spheres, ellipsoids, spherocylinders, etc. The continuum percolation of a family of single axial asymmetric ovoids with tapering parameter T and aspect-ratio c/a is studied here. The geometrical properties and numerical contact detection algorithm of these ovoids are proposed firstly. Using the Monte Carlo finite-size-scaling method, the percolation threshold ϕc of the systems comprising congruent overlapping ovoids is further determined. For a given T, ϕc shows an initially increasing and then decreasing trend with the increasing c/a. Moreover, the value of ϕc at the fixed c/a decreases with the increasing |T| and this trend will be more obvious with the decreasing c/a. Finally, an analytical formula is proposed to quantify the effect of ovoid's morphology, characterized by the dimensionless excluded volume of ovoid, on the percolation thresholds. (a) The system comprising random distributed overlapping asymmetric ovoids in cubic container. (b) The ovoids connected with the upper bound. (c) Percolation path in the system. [Display omitted] •The granular composite is assumed to be the system comprising congruent overlapping asymmetric ovoids.•A formula is proposed to calculate the volume of ovoid.•A new contact detection algorithm of inter-ovoid is developed.•The percolation thresholds of systems comprising randomly distributed overlapping ovoids are calculated.•An analytical formula is derived to predict the percolation threshold of ovoids.