Mass transport in porous media at the micro- and nanoscale: A novel method to model hindered diffusion

Abstract Mass transport in liquid-filled pores at the micro- and nanoscale can play an important role in applications such as membrane separations, chromatography, and catalytic processes. In this work, we use Brownian dynamics in order to describe the motion of spherical solute molecules at a pore-scale. The method can be used to calculate effective parameters intrinsically related to the porous medium such as the effective diffusivity and the hindrance factor for diffusion. The latter is calculated using a novel probabilistic model derived in the present study, which uses the Lennard-Jones potential to reproduce the hindering effect of the interaction between solute molecules and the wall atoms on the diffusivity. In addition, we introduce a fitting function that can be used to estimate the diffusive hindrance factor of a complex geometry when the pore size distribution of the porous network is known. Finally, a multiscale approach is presented and illustrated with an application example, whereby the hindrance factors of the micro- and nanoscale are used in the simulations of the mass transport at the larger scale.