The effective diffusion coefficient of a small molecule in a two-phase gel medium

Using simple theoretical arguments and exact numerical lattice calculations, Hickey [J. Chem. Phys. 124, 204903 (2006)] derived and tested an expression for the effective diffusion coefficient of a probe molecule in a two-phase medium consisting of a hydrogel with large gel-free inclusions. Although providing accurate predictions, this expression neglects important characteristics that such two-phase systems can present. In this article, we extend the previously derived expression in order to include local interactions between the gel and the analyte, interfacial effects between the main phase and the inclusions, and finally a possible incomplete separation between the two phases. We test our new, generalized expressions using exact numerical calculations. These generalized equations should be a useful tool for the development of novel multiphase systems for specific applications, such as drug-delivery platforms.