Determination of the contribution of an imperfectly bonded inhomogeneity to macroscopic diffusivity

The paper contributes to the development of micromechanical approaches for determining the effective diffusivity of micro-heterogeneous materials, taking into account segregation, which is the accumulation of impurities at the phase interface. Two analytical approaches are investigated and compared with numerical simulation. In the first analytical approach, segregation is expressed in terms of a segregation parameter that prescribes the jump in concentration at the phase interface. In the second approach, an inhomogeneity with an ultra-thin mass isolating coating is introduced, and segregation is expressed in terms of equivalent surface resistivity. The developed numerical method considers inhomogeneities with an outer weakly permeable shell of thickness that tends to zero. Comparison among various models made it possible to estimate their limitations and perspectives.