Diffusion of Large Molecules in Porous Media

Abstract

The results of computer simulations of transport of macromolecules in a disordered porous medium, represented by a network of capillary tubes with random radii, are reported. We develop a method for determining the macroscopic diffusivity $D$ which, in principle, is exact. The effects of both convection and diffusion are taken into account. We find $\frac{D}{{D}_{\ensuremath{\infty}}}\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}\frac{a}{{r}_{m}})$, independent of the morphology of the medium or the microscopic transport laws, where $a$ is the effective size of the molecules, ${D}_{\ensuremath{\infty}}$ the diffusivity in an unbounded solvent, and ${r}_{m}$ the mean effective size of the pores, consistent with experimental data.