Diffusiophoresis of a highly charged rigid colloid in a hydrogel incorporating ion steric interactions

Abstract

Diffusiophoresis, mediated by an imposed ionic concentration gradient, is a useful technique in directed migration of colloids. Theoretical studies on diffusiophoresis in a polymer hydrogel medium are rather limited owing to the presence of nonlinear terms in the fluid transport equations. The hydrogel creates a hydrodynamic interaction and short-range steric interaction to the dispersing particle and macromolecules. The volume exclusion due to a finite ion size consideration is important in the context of a highly charged particle. In this study, we consider the finite ion size effects on diffusiophoresis of a charged particle with ζ≥1 in a hydrogel medium. The modified ion transport equations coupled with the Brinkman equation for fluid flow and the Poisson equation for electric field are solved numerically in a coupled manner through a control volume approach. Our results based on the Brinkman model incorporating only the hydrodynamic interactions deviate from the existing experimental results. A close comparison with this experimental data is established when the computed mobility is modified to incorporate the short-range steric factor. We have considered the impact of the hindered diffusivity of ions in the gel medium. Our results show that the modification in the ionic diffusivity is significant for low porosity and high charge density situations. The impact of the finite ion size effect is found to be significant when the bulk ionic concentration is large enough to create an electric double layer thinner than the particle size. We have analyzed the size dependency of the mobility in the gel medium. A simplified expression for the mobility in a hydrogel medium is proposed.