Effective conductivity of periodic arrays of spheres with interfacial resistance

We consider the problem of analytically determining the effective thermal conductivity of a composite material consisting of periodic arrays of spheres with interfacial resistance. We applied Rayleigh's method which has been used extensively for such calculations in the perfect interface case, i.e. no jump in the temperature across the interface. Results are presented for simple, body-centred and face-centred cubic arrays, and each for a wide range of volume fractions. Our calculations were based on very accurate lattice sums in all three lattice cases and temperature fields were resolved to very high multipole moments, including all azimuthal terms. In the case of zero interfacial strength, our formulation recovers all previously reported benchmark results.