Numerical study on diffusiophoresis of a hydrophobic nanoparticle in a monovalent or multivalent electrolyte

A numerical study on the diffusiophoresis of a hydrophobic charged colloid driven by an imposed concentration gradient of an electrolyte is made. Our numerical model is based on the computation of Navier-Stokes-NernstPlanck-Poisson equations. Diffusiophoresis of hydrophobic particles and size-based sorting has not been attempted before. The present numerical model elucidates the nonlinear effects on diffusiophoresis in a valence asymmetric electrolyte, which have been ignored in previous studies. The particle hydrophobicity, characterized by the slip length, modifies the zeta-potential and the Debye layer, which in turn creates a significant impact on the particle diffusiophoresis. An analytical solution, valid for a lower range of slip length and imposed concentration gradient is obtained under the thin Debye layer consideration, which compares well with the numerical solution for a thin Debye length when the slip length is a few tens of nanometer. We investigate the impact of slip length on the diffusiophoresis by considering different types of monovalent and valence asymmetric electrolytes. The surface hydrophobicity enhances the particle zeta-potential by reducing the shielding effect and the impact becomes stronger at a thinner Debye layer. For this, the mobility reversal manifests for a hydrophobic particle when the electrophoresis and chemiphoresis parts are competitive. Hydrophobicity enhances the mobility of the particle when electrophoresis and chemiphoreis are cooperative. The higher valence of the counterions of the electrolyte enhances the mobility for the moderate range of the Debye length by increasing the chemiphoresis part. The sizebased sorting of the particle by diffusiophoresis is analyzed. At a thinner Debye length the diffusiophoretic mobility of a hydrophobic particle exhibits a size dependency.