Effective conductivity of composites with spherical inclusions: Effect of coating and detachment

Abstract

An expression for the reduced effective thermal conductivity, keff/k1, of a random array of coated or debonded spherical inclusions with pair interactions rigorously taken into account is derived. Pair interactions are evaluated through solution of a boundary value problem involving two coated or debonded spheres with twin spherical expansions. The resulting keff/k1 is of O(f2) accuracy, where f is the combined volume fraction of the inclusion and interface. The effect of interfacial characteristics manifested as the reduced thermal conductivity, σ3, and relative thickness, δ/a, of the interfacial layer is thoroughly investigated. It is found that keff/k1 can be approximately viewed as a function of f and the dimensionless dipole polarizability, θ1, over a large parameter domain, despite the existence of higher order polarizabilities in the expression of keff/k1. The value of θ1 alone determines whether the effective inclusion is enhancing (θ1≳0), neutral (θ1=0), or impairing (θ1<0) to the matrix. Furthermore, the evaluation of keff/k1 for the present model system can be approximately replaced with that for composites containing inclusions of no interface but possessive of a reduced thermal conductivity of (1+2θ1)/(1−θ1). A contour plot of keff/k1 on the θ1−f domain that is useful in estimating keff/k1 for interfacial properties characterized by an arbitrary combination of σ3 and δ/a, is constructed.