Inequalities constraining the value of the averaged diffusion coefficient in a heterogeneous layer
Yu. I. Babenko · Theoretical Foundations of Chemical Engineering · 2007
A problem describing the steady-state diffusion in a heterogeneous medium bounded by parallel planes with fixed concentrations at the boundaries is studied. An analytical solution in terms of a small-parameter power series taking into account a quadratic expansion term is obtained. It is shown that the effective diffusion coefficient in this approximation is constrained by two nontrivial inequalities. Reasons suggesting that these inequalities will also be valid for the exact solution to the problem are given.