Transport coefficients in random two-phase media with interfacial resistance

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Abstract
Rigorous variational upper and lower bounds on the effective conductivity of a two-phase dispersion with resistance at the spherical particle-matrix interface are considered. We believe that our lower bound is a uniform and significant improvement over recently published bounds by Torquato and Rintoul, and Lipton and Vernescu. For conducting spheres and higher particle concentrations, upper bounds previously derived by Zoia and Strieder, and Lipton and Vernescu, always lie below the upper bound of Torquato and Rintoul. Inverse in situ upper and lower bounds on the dimensionless Kapitza interfacial resistance of a copper particle/epoxy matrix composite are calculated from low-temperature composite conductivity data.