Diffusiophoresis of a spherical particle in porous media*

Diffusiophoresis refers to the deterministic motion of particles induced by a surrounding concentration gradient of solutes. Recent experiments demonstrated and measured colloid diffusiophoresis in porous media, but existing theories cannot predict the observed colloid motion. In this work, we develop a mathematical model that can predict the diffusiophoretic mobility of a charged colloidal particle driven by a binary monovalent electrolyte concentration gradient in porous media. The porous medium is modeled as a Brinkman medium with a constant Darcy permeability. The linearized Poisson-Boltzmann equation is invoked to model a weakly or moderately charged particle. We report three new significant findings. First, compared to diffusiophoresis in a free electrolyte solution, we show that the particle mobility could be significantly hampered by a porous medium due to the additional hydrodynamic drag. Second, we demonstrate that particle diffusiophoresis in response to a change in the electrolyte concentration in a porous medium could be qualitatively different from that in a free electrolyte solution. Third, a comparison between our model predictions and experiments demonstrates excellent agreements within the scope of the model, highlighting the predictive power of the model. The mathematical developed here could be employed to design diffusiophoretic colloid transport in porous media, which are central to applications such as nanoparticle drug delivery and enhanced oil recovery.