Effective molecular diffusion coefficient in a two-phase gel medium.
We derive a mean-field expression for the effective diffusion coefficient of a probe molecule in a two-phase medium consisting of a hydrogel with large gel-free solvent inclusions, in terms of the homogeneous diffusion coefficients in the gel and in the solvent. Upon comparing with exact numerical lattice calculations, we find that our expression provides a remarkably accurate prediction for the effective diffusion coefficient, over a wide range of gel concentration and relative volume fraction of the two phases. Moreover, we extend our model to handle spatial variations of viscosity, thereby allowing us to treat cases where the solvent viscosity itself is inhomogeneous. This work provides robust grounds for the modeling and design of multiphase systems for specific applications, e.g., hydrogels as novel food agents or efficient drug-delivery platforms.
Hickey
Owen A
OA
Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario K1N 6N5, Canada.
Mercier
Jean-François
JF
Gauthier
Michel G
MG
Tessier
Frédéric
F
Bekhechi
Smaine
S
Slater
Gary W
GW