Diffusiophoresis in Suspensions of Charged Porous Particles

An analysis of the diffusiophoretic motion in a suspension of charged porous spheres in an electrolytic solution with a macroscopic concentration gradient is presented. Each porous particle can be a solvent-permeable and ion-penetrable charged floc or polyelectrolyte molecule, in which the densities of the fixed charges and frictional segments are constant, surrounded by an arbitrary electric double layer. The multiparticle interaction effects are considered through the use of a unit cell model, which allows the overlap of adjacent double layers. The differential equations governing the electric potential, ionic concentration, and fluid velocity distributions inside and outside the porous particle in a unit cell are linearized by assuming that the system is only slightly deviated from equilibrium and then solved as power expansions in its dimensionless fixed-charge density. A closed-form expression for the diffusiophoretic velocity of the porous particle correct to the second order of the fixed charge density is obtained from a balance between the electrostatic and hydrodynamic forces acting on it. Detailed comparisons of the results for the multiparticle diffusiophoresis obtained from the cell model with various boundary conditions are made. The effect of particle interactions on the diffusiophoresis, which is a linear combination of electrophoresis and chemiphoresis, can be significant and complicated in typical situations. Although the electrophoretic mobility of the particles decreases with an increase in the particle volume fraction, their chemiphoretic mobility is not necessarily a monotonic function of it.