The diffusiophoresis of a concentrated spherical dispersion of colloidal particles subject to a small electrolyte gradient is analyzed theoretically for an arbitrary zeta potential and double layer thickness. In particular, the influence of the difference in the diffusivities of cations and anions is discussed. A unit cell model is used to simulate a spherical dispersion, and a pseudospectral method is adopted to solve the equations governing the phenomenon under consideration. We show that, as in the case of an infinitely dilute dispersion, when the diffusivities of cations and anions are different, the diffusiophoretic mobility is no longer an even function of the zeta potential or double layer thickness. In contrast to the case of identical diffusivity of cations and anions, a local electric field is induced in the present case due to an unbalanced charge distribution between higher and lower concentration regions. Depending upon the direction of this induced electric field, the diffusiophoretic mobility can be larger or smaller than that for the case of identical diffusivity. The diffusiophoretic mobility is influenced mainly by the induced electric field arising from the difference in the ionic diffusivities, the concentration gradient, and the effect of double layer polarization.

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Electrophoresis of a soft particle along the centerline of a cylindrical pore is investigated theoretically in this study. The soft particle consists of an inner hard sphere covered by a concentric porous layer with fixed charge uniformly distributed in it. The polarization effect, the deformation of ion clouds surrounding the particle due to convection flow, is taken into account properly by adopting the full nonlinear Poisson-Boltzmann equation. The study reveals that recent investigation in the literature without consideration of the polarization effect could severely overestimate the particle mobility up to nearly two times if the fixed charge in the porous layer is high. The boundary effect in terms of the reduction of particle mobility is very significant when the double layer is thick and diminishes as it gets very thin. The effect of the highly charged cylindrical wall is analyzed, in particular, among other factors of electrokinetic interest. The presence of the cylindrical wall retards the particle motion in general, as compared with an isolated particle. With the generation of an electroosmotic flow, however, the charged wall can either enhance the particle motion or deter it, depending on the surface potential on the wall and the double-layer thickness. The thinner the double layer, the more significant the influence of the osmotic flow on the particle motion in general. The direction of particle motion may even change twice as the reciprocal of the double-layer thickness increases when both the wall and the particle are highly charged. This is due to the competition between the electric driving force of the charged particle and the hydrodynamic retarding force from the background electroosmotic flow. This has direct impact in practical applications of nanofluidics when a weak electric field is applied. Conducting operations near these critical double-layer thicknesses should be avoided in practice.

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