Modeling of Imperfect Contacts in Determining the Effective Diffusion Permeability

Abstract

The work develops a universal approach to accounting for imperfect contacts in determining effective properties of various nature, namely, effective diffusivity and thermal and electrical conductivity. Imperfect contacts appear when fields at the microlevel are not continuous. The possibility of creating a unified approach is due to the similarity of the governing equations. At the same time, the appearance of imperfect contacts may be caused by microstructural features and by the specifics of the process itself. For concreteness, the effective diffusion permeability is determined, since various reasons for the appearance of imperfect contacts can be considered. The reasons can be associated both with the formation of structural defects and with the presence of the specific segregation effect. The paper generalizes and compares two approaches to accounting for imperfect contacts. In the first case, a field jump is set. In the second case, an inhomogeneity with a thin coating possessing extreme properties is introduced. A comprehensive analysis is carried out on the example of a material with spherical inhomogeneities. Analytical expressions for the contribution tensor of the equivalent inhomogeneity are obtained, which results in simplification of the generalization of various homogenization methods.