ON THE OPTIMAL BOUNDS FOR THE EFFECTIVE CONDUCTIVITY OF ISOTROPIC QUASI-SYMMETRICAL MULTIPHASE MEDIA

The bounds on the effective conductivity of isotropic multiphase media with certain symmetry among the phases' geometry are examined. The bo unds of Phan-Thien and Milton and those of Pham partly coincide, partl y differ. Wherever they differ, the bounds of Phan-Thien and Milton ar e more restrictive. Specifically, the bounds for the subclass of spher ical cell materials are identical, while the bounds of Phan-Thien and Milton for the subclass of platelet cell materials, which coincide wit h those of Pham in the case of two-component materials, are tighter in the general multicomponent case. Phan-Thien-Milton upper bound on the conductivity of multicomponent platelet cell materials is attained by a geometric model of Pham, therefore is verified to be the optimal on e. Subsequently, for the whole class of isotropic quasi-symmetric medi a, the respective bound is optimal over a range of parameters. An opti mal lower bound is conjectured. The differential scheme is used to con struct certain spherical and platelet cell models.