Effect of the interphase zone on the conductivity or diffusivity of a particulate composite using Maxwell's homogenization method

An analytical model is developed for the conductivity (diffusivity, permeability, etc.) of a material that contains a dispersion of spherical inclusions, each surrounded by an inhomogeneous interphase zone in which the conductivity varies radially according to a power law. The method of Frobenius series is used to obtain an exact solution for the problem of a single such inclusion in an infinite matrix. Two versions of the solution are developed, one of which is more computationally convenient for interphase zones that are less conductive than the pure matrix, and vice versa. Maxwell's homogenization method is then used to estimate the effective macroscopic conductivity of the medium. The developed model is used to analyze some data from the literature on the ionic diffusivity of concrete. Use of the model in an inverse mode permits the estimation of the local diffusivity variation within the interphase, and in particular at the interface with the inclusion.