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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.

Diffusiophoresis of a spherical colloidal particle normal to a plane subject to a uniform electrolyte concentration gradient is investigated theoretically for arbitrary double layer thickness and surface potential. The governing general electrokinetic equations are put in terms of bipolar spherical coordinates and solved numerically with a pseudospectral method based on Chebyshev polynomial. The effects of key parameters are examined such as the double layer thickness, surface potential, and the distance between the particle and the plane. It is found, among other things, that the presence of the boundary has a retardation effect on the motion of the particle, provided that the double layer does not touch the planar boundary. If it does, however, the velocity of the particle will exhibit a maximum as the double layer just loses touch of the plane, thanks to the competitive force of the polarization effect. The planar boundary poses not only as a conventional hydrodynamic retarding force, but also may distort the shape of the double layer greatly, hence altering its polarization situation, which has a profound electrostatic impact on the motion of the particle when it is close to the plane.

The electrophoretic behavior of a spherical dispersion of polyelectrolytes of arbitrary concentration is analyzed theoretically under a salt-free condition, that is, the liquid phase contains only counterions which come from the dissociation of the functional groups of polyelectrolytes. We show that, in general, the surface potential of a polyelectrolyte increases nonlinearly with its surface charge. A linear relation exists between them, however, when the latter is sufficiently small; and the more dilute the concentration of polyelectrolytes, the broader the range in which they are linearly correlated. If the amount of surface charge is sufficiently large, counterion condensation occurs, and the rate of increase of surface potential as the amount of surface charge increases declined. Also, it leads to an inverse in the perturbed potential near the surface of a polyelectrolyte, and its mobility decreases accordingly. For a fixed amount of surface charge, the lower the concentration of polyelectrolytes and/or the lower the valence of counterions, the higher the surface potential. The qualitative behavior of the mobility of a polyelectrolyte as the amount of its surface charge varies is similar to that of its surface charge.