Abstract
A simple equivalent inclusion model is proposed to estimate the effective conductivities of dispersions containing aligned spheroids. The spheroids are either in perfect contact with the matrix, possessive of certain contact resistance, or coated with a confocal layer of a third material. For the perfect contact case, our results coincide with Willis' bounds [J. Mech. Phys. Solids 25, 185 (1977)] and, for the coating case, they compare extremely well with those of Hatta and Taya [J. Appl. Phys. 59, 1851 (1986)]. New results are readily obtained for the contact resistance case through use of the proposed model. For the present systems, there exist two independent effective conductivities, one defined in the direction parallel with the symmetric axis of the spheroid and the other defined in the perpendicular direction. Interestingly, the inclusion effect for both the contact resistance and coating cases may be enhancing in one direction, but impairing in the other. But for the perfect contact case, the inclusion effect is always consistent in both directions. It is found that, for the perfect contact case, the reduced effective conductivity (σ eff ) is a function of the spheroid volume fraction, spheroid aspect ratio, and reduced spheroid conductivity. One more parameter, the Biot number, is needed for the contact resistance case, while two more parameters, the reduced coating layer conductivity and the relative coating thickness, appear in the coating problem. Effects of these parameters on σ eff are thoroughly investigated. © 1998 American Institute of Physics.