Thermal percolation in mixtures of monodisperse spheres
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ORIGINAL PAPER
Thermal percolation in mixtures of monodisperse spheres Ali Khoubani1,2 · T. Matthew Evans2 · Tae Sup Yun3 Received: 13 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The connectivity of individual species in a locally heterogeneous granular mixture strongly influences assembly-scale behavior. A behavioral transition is observed at the percolation threshold for a given constituent; that is, the mixing fraction at which the constituent has statistical connectivity between two opposing boundaries. This behavior is particularly evident in conductivity phenomena, e.g., the percolation of conductive particles (thermal, electric) or the relative degree of connectivity of the void space (hydraulic). Hard-core (first nearest-neighbor or lattice) percolation has been extensively studied experimentally, theoretically, and numerically. That hard-core percolation occurs in dense randomly packed bi-phasic mixtures of monodisperse spheres occurs at a mixing fraction of 0.15 v/v is well-accepted. Radiant conduction (e.g., heat), however, is influenced by hard-core “soft-shell” percolation, which is an nth-nearest neighbor problem and less well-studied. In the current work, we use discrete element method simulations coupled with a thermal network model that leverages a robust domain decomposition algorithm to simulate large assemblies of spheres to investigate soft-shell percolation numerically. Our results show that the thermal conductivity of a randomly packed assembly obeys a power law with respect to volume fraction of conductive particles while percolation threshold follows a power law with respect to coordination number. The ability of the pore fluid to transmit heat over a longer distance results in an increase of thermal conductivity and a decrease in thermal percolation threshold. Moreover, we observe that, contrary to previous findings, critical percolation density is not a dimensional invariant and depends on the microstructure of the assembly. Keywords Network model · Thermal conductivity · Percolation
1 Introduction In a granular mixture of two types of particles, a given species is said to percolate if it forms a continuous pathway for information transfer from one boundary of the assembly to another. The mixing fraction at which this continuous pathway will statistically form is known as the percolation threshold. Percolation theory seeks to predict this threshold and is of wide applicability in describing the critical
Ali Khoubani: Formerly, Graduate Research Assistant, School of Civil and Construction Engineering, Oregon State University. * T. Matthew Evans [email protected] 1
Jacobs Associates, Corvallis, OR, USA
2
School of Civil and Construction Engineering, Oregon State University, Corvallis, OR, USA
3
Department of Civil and Environmental Engineering, Yonsei University, Seoul, Korea
behavior of disordered media where two sets of atoms (sites) with different properties (e.g., electrical or thermal conductivities) are interacting
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