Abstract
An expression for the reduced effective thermal conductivity. k <sub>eff</sub> /k <sub>1</sub> . 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 k <sub>eff</sub> /k <sub>1</sub> is of O(f <sup>2</sup> ) accuracy, where f is the combined volume fraction of the inclusion and interface. The effect of interfacial characteristics manifested as the reduced thermal conductivity. σ <sub>3</sub> . and relative thickness, δa, of the interfacial layer is thoroughly investigated. It is found that k <sub>eff</sub> /k <sub>1</sub> can be approximately viewed as a function of f and the dimensionless dipole polarizability, θ <sub>1</sub> , over a large parameter domain, despite the existence of higher order polarizabilities in the expression of k <sup>eff</sup> /k <sup>1</sup> . The value of θ1 alone determines whether the effective inclusion is enhancing θ1>0), neutral (θ <sub>1</sub> =0), or impairing (θ<0) to the matrix. Furthermore, the evaluation of k <sub>eff</sub> /k <sub>l</sub> 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 +2θ <sub>1</sub> )/(1-θ <sub>1</sub> ). A contour plot of k <sub>eff</sub> /k <sub>1</sub> on the θ1-f domain that is useful in estimating k <sub>eff</sub> /k <sub>1</sub> for interfacial properties characterized by an arbitrary combination Of σ <sub>3</sub> and δ/a, is constructed. © 1996 American Institute of Physics.