Diffusiophoresis of a soft particle incorporating ion partitioning and hydrophobic core

Abstract

The diffusiophoresis of a soft particle governed by an imposed ionic concentration gradient is studied based on a modified ion transport equation. The surface of the rigid core of the soft particle is considered to be hydrophobic, which is coated with a charged polyelectrolyte layer (PEL) whose dielectric constant is different from the dispersion medium. This step-change in the dielectric constant of the PEL and the dispersion medium creates an ion partitioning effect. The governing equations based on the coupled Navier–Stokes–Nernst–Planck–Poisson equations are modified to incorporate the ion partitioning effect. A simplified model based on the linear perturbation technique under a small applied concentration gradient in the scale of the particle radius is developed. The simplified model agrees well with the exact numerical solutions for a Debye length smaller than the particle size. We have analyzed the impact of the core slip length and PEL permittivity on the mobility of the soft particle. The interfacial slip enhances the impact of the core charge density on the diffusiophoresis. In this case, a reversal of mobility occurs at a thinner Debye length compared to a hydrophilic core. Ion partitioning attenuates the concentration of mobile counterions in PEL, leading to a reduction in screening of PEL fixed charge. We find that the diffusiophoresis of the soft particle in a non-z:z asymmetric electrolyte strongly depends on the valence of the counterions. Diffusiophoresis of the soft particle in a KCl-NaCl mixture is considered to achieve positive mobility.