EFFECTIVE CONDUCTIVITY OF PERIODIC ARRAYS OF SPHERES WITH INTERFACIALRESISTANCE

We consider the problem of analytically determining the effective ther mal 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 i nterface case, i.e. no jump in the temperature across the interface. R esults are presented for simple, body-centred and face-centred cubic a rrays, and each for a wide range of volume fractions. Our calculations were based on very accurate lattice sums in all three lattice cases a nd temperature fields were resolved to very high multipole moments, in cluding all azimuthal terms. In the case of zero interfacial strength, our formulation recovers all previously reported benchmark results.