Impact of particle size ratio on the percolation thresholds of 2D bidisperse granular systems composed of overlapping superellipses

Abstract

Critical percolation threshold is a crucial parameter that describes the connectivity of heterogeneous structures. In recent decades, numerical researches in the field of 2D continuum percolation have been carried out based on the simple models of identical disks, rectangles and ellipses. However, not all of physically granular media in nature can be represented by the assembly of identical disks or ellipses, especially when it involves the existence of the diversity of object sizes. For the study of the impact of polydispersity of particle sizes on the percolation of granular networks with more complex particle geometries, a versatile class of superellipses with both deformation coefficient m in [0.5, + ∞) and aspect ratio a/b in [0.1, 1.0] is introduced. The 2D bidisperse models composed of overlapping superellipses of two different sizes are constructed then. By using the generally continuum percolation algorithm, the critical percolation thresholds ϕc for different binary-sized superellipse systems with the ranges of the equivalent radii ratio λ in [0.1, 1.0] and the number fraction of smaller superellipses f in [0.0, 1.0] are studied. Furthermore, the numerically generalized fitting functions of ϕc are further proposed for these polydisperse media with the broad ranges of m, a/b, λ and f. From the research, we can find that for 2D binary-sized superellipse systems, the intrinsic symmetry of ϕc occurs at the area proportion of smaller superellipses υ≈ 0.5. The maximum threshold is generally achieved in the case of (1−f) ≈λ2 and the minimum one is obtained for the corresponding monodispersion.