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Effective conductivity in a lattice model for binary disordered media with complex distributions of grain sizes
Author(s) -
Piasecki R.
Publication year - 2003
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200301641
Subject(s) - conductivity , dispersity , lattice (music) , materials science , equivalence (formal languages) , statistical physics , binary number , grain size , condensed matter physics , microstructure , thermodynamics , physics , mathematics , quantum mechanics , discrete mathematics , composite material , arithmetic , acoustics , polymer chemistry
Using numerical simulations and analytical approximations we study a modified version of the two‐dimensional lattice model [R. Piasecki, phys. stat. sol. (b) 209 , 403 (1998)] for random p H : (1– p ) L systems consisting of grains of high (low) conductivity for the H‐(L‐)phase, respectively. The modification reduces a spectrum of model bond conductivities to the two pure ones and the mixed one. The latter value explicitly depends on the average concentration γ ( p ) of the H‐component per model cell. The effective conductivity as a function of content p of the H‐phase in such systems can be modelled making use of three model parameters that are sensitive to both grain size distributions, GSD(H) and GSD(L). However, to incorporate into the model information directly connected with a given GSD, a computer simulation of the geometrical arrangement of grains is necessary. By controlling the polydispersity in grain sizes and their relative area frequencies, the effective conductivity could be raised or decreased and correlated with γ ( p ). When the phases are interchanged, a hysteresis‐loop‐like behaviour of the effective conductivity, characteristic of dual media, is found. We also show that the topological non‐equivalence of the system's microstructure accompanies some GSDs, and it can be detected by the entropic measure of the spatial inhomogeneity of model cells.