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

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