Effective Conductivity of Disordered Three-Phase Media

Title & Authors
Effective Conductivity of Disordered Three-Phase Media
Kim, In-Chan;

Abstract
A problem of determining the effective conductivity of a useful model of sphere-matrix type, disordered three-phase composite media is considered. Specifically, a three-phase media in which two-phase composite spheres, consisting of spheres of conductivity $\small{k_2}$((phase 2) and concentric shells of conductivity $\small{k_3}$(phase 3), are randomly distributed in a matrix of conductivity $\small{k_1}$( (phase 1) is considered. As for the structure models configuring three-phase composite media, three different structure models of PCS, PS-1 and PS-2 models are defined, which are analogous to well-established PCS, PS structure models of two-phase composite media. Futhermore, a generalized PS-PCS structure model is proposed to incorporate thesee three different models in one. Effective condectivity $\small{k^{\ast}}$of multiphaes composite media is greatly influenced by the phase connectivity of each disspersed phase material, as well as phase conductivities and phase volume fractions. Phase connectivity of three-phase PCS, PS-1, PS-2 composite media is quantified by the impentrability parameter $\small{\lambda}$. Mathematically rigorous first-order cluster bounds on $\small{k^{\ast}}$ are derived for these models of three-phase composite media, and as computation examples, first-order cluster bounds on $\small{k^{\ast}}$ for three-phase composites consisting of largely different phase conductivities are computed and compared as function of concnectivity parpmeter $\small{\lambda}$. Results and discussions are given.
Keywords
Effective Conductivity;Disordered Three-Phase Composite Media;Connectivity;Impenetrability Parameter;First-Order Cluster Bound;PS-PCS Model;
Language
Korean
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