Estimation of effective conductivity for aligned elliptic cylinder dispersions

摘要

An equivalent inclusion model is proposed to estimate the effective conductivity of dispersions containing aligned long elliptic cylinders. The cylinders are either in perfect contact with the matrix, possessive of certain contact resistance or coated with a confocal elliptic layer of a third material. The parallel and perpendicular components of the effective conductivity tensor for the plain cylinder case are shown to satisfy Keller's reciprocal theorem, while those for the coated cylinder case follow a reciprocal relation similar to Keller's. Unlike the plain cylinder case, the inclusion effect for the contact resistance and coated cylinder cases can be enhancing in one direction, but impairing in the other direction. For the plain cylinder problem, the reduced effective conductivity (sigma(eff)) is found to depend on the cylinder volume fraction (f), cylinder aspect ratio (a(0)/b(0)), and reduced cylinder conductivity (sigma(0)). One more parameter, the semi-major axis based Blot number (Bi), is needed for the contact resistance problem, while two more parameters, the reduced coating layer conductivity (sigma(c)) and the relative coating thickness (delta/a(0)), appear for the coated cylinder problem. Effects of these parameters on sigma(eff) are thoroughly investigated. [References: 16]