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Effective Conductivity of Disordered Three-Phase Media
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 Title & Authors
Effective Conductivity of Disordered Three-Phase Media
Kim, In-Chan;
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 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 ((phase 2) and concentric shells of conductivity (phase 3), are randomly distributed in a matrix of conductivity ( (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 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 . Mathematically rigorous first-order cluster bounds on are derived for these models of three-phase composite media, and as computation examples, first-order cluster bounds on for three-phase composites consisting of largely different phase conductivities are computed and compared as function of concnectivity parpmeter . 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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