IMPROVED VARIATIONAL BOUNDS ON SOME BULK PROPERTIES OF A 2-PHASE RANDOM MEDIUM

The Hashin-Shtrikman bounds on the bulk magnetic permeability (or dielectric constant, thermal and electric conductivity, solute diffusion coefficient) for a random two-phase material can be considerably improved by the inclusion of experimentally accessible information, such as the bulk permeability of the material at a different temperature [the main results are expressed in the inequalities (27), (45), and (51)]. These inequalities can also be written as bounds on the rate at which the bulk permeability changes with changing permeabilities of the individual phases [(29) and (30)]. In particular, application of (30) yields the upper and lower bounds (59) on the observed energy of activation for diffusion through a two-phase medium. The inequalities (27), (45), and (51) can be expressed in a mixed form to bound, for example, the bulk permeability through use of data on the thermal conductivities of the mixed material and the individual phases. Bounds on the viscosity and elastic moduli of a two-phase medium are also discussed briefly.