Diffusiophoresis in porous media saturated with a mixture of electrolytes

Diffusiophoresis is the deterministic motion of a colloid induced by a surrounding concentration gradient of solutes. Here, we develop a mathematical model, based upon the regular perturbation method and numerical integration, to compute the diffusiophoretic mobility of a colloid in porous media saturated with a general mixture of electrolytes. We model the electrokinetics using the Poisson-Nernst-Planck equations and the fluid transport in porous media using the Brinkman equation with an electric body force. We report three novel key findings. First, we demonstrate that, in the same electrolyte concentration gradient, lowering the permeability of the porous medium can significantly weaken the colloid diffusiophoretic motion. Second, we show that, surprisingly, by using a valence asymmetric electrolyte the colloid diffusiophoretic motion in a denser porous medium can be stronger than that in a less dense porous medium saturated with a symmetric electrolyte. Third, we demonstrate that varying the composition of an electrolyte mixture does not only change the strength of the colloid diffusiophoretic motion drastically, but also qualitatively its direction. The model developed from this work can be used to understand and predict natural phenomena such as intracellular transport, as well as design technological applications such as enhanced oil recovery, nanoparticle drug delivery, and colloidal species separation.