Sedimentation of a charged colloidal sphere in a charged cavity

Abstract

An analytical study is presented for the quasisteady sedimentation of a charged spherical particle located at the center of a charged spherical cavity. The overlap of the electric double layers is allowed, and the polarization (relaxation) effect in the double layers is considered. The electrokinetic equations that govern the ionic concentration distributions, electric potential profile, and fluid flow field in the electrolyte solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetric electrolyte with the surface charge densities of the particle and cavity as the small perturbation parameters. An analytical expression for the settling velocity of the charged sphere is obtained from a balance among the gravitational, electrostatic, and hydrodynamic forces acting on it. Our results indicate that the presence of the particle charge reduces the magnitude of the sedimentation velocity of the particle in an uncharged cavity and the presence of the fixed charge at the cavity surface increases the magnitude of the sedimentation velocity of an uncharged particle in a charged cavity. For the case of a charged sphere settling in a charged cavity with equivalent surface charge densities, the net effect of the fixed charges will increase the sedimentation velocity of the particle. For the case of a charged sphere settling in a charged cavity with their surface charge densities in opposite signs, the net effect of the fixed charges in general reduces/increases the sedimentation velocity of the particle if the surface charge density of the particle has a greater/smaller magnitude than that of the cavity. The effect of the surface charge at the cavity wall on the sedimentation of a colloidal particle is found to increase with a decrease in the particle-to-cavity size ratio and can be significant in appropriate situations.

Sedimentation of a Charged Porous Particle in a Charged Cavity

“…H 1 and H 2 depend on λ a impressively, but H 3 is not a sensitive function of λ a . These coefficients for an impermeable sphere having a surface charge density of σ p = Qa /3 (the same total fixed charge as a porous sphere of equal radius) in a concentric spherical cavity as a function of a / b are also drawn by dashed curves in Figures a, a, and a for comparison. It can be seen that the values of H 1 and H 2 for the impermeable sphere are comparable with those for the porous sphere with λ a = 10, but the value of H 3 is greater for the impermeable sphere than that for the porous sphere with even a very low value of λ a (because the sedimentation-induced electric field around an uncharged particle impermeable to the electrolyte ions in the charged cavity is greater than that around a permeable one).…”

“…This analysis was extended to a numerical calculation for the case of an arbitrary zeta potential . Recently, the sedimentation of a dielectric sphere in a concentric charged spherical cavity was analyzed with the surface charge densities of the particle and cavity wall as small perturbation parameters …”

“…The system of a spherical particle settling at the center of a spherical cavity can be an idealized model for the sedimentation in media constructed from connecting spherical pores. − In this article, the sedimentation of a charged porous sphere, such as a polyelectrolyte molecule (DNA fragment, peptide, etc.) or an aggregate of fine particles bearing surface charges, in a concentric charged spherical cavity is analyzed.…”

Electromagnetophoresis of a Colloidal Sphere in a Spherical Cavity

“…The particle surface and cavity wall are allowed to bear electric charges and the conducting fluid may be an electrolyte solution, but the electric double layersadjacent to the particle and cavity surfaces are assumed to be thin relative to the particle radius and the gap width between the solid surfaces ( ) b a − such that the entire fluid phase is electrically neutral with a uniformity in the ionic composition. Electrokinetic (electrophoretic and/or electro-osmotic) and gravitational effects, which have been considered separately [30]- [32] and can be added directly due to the linearity of the problem, are ignored here. The objective is to determine the boundary effect of the enclosing cavity on the EMP velocity of the particle.…”

Sedimentation Velocity and Potential in Dilute Suspensions of Charged Porous Shells

“…Subsequently, Ohshima et al obtained both analytical formulas and numerical results of the sedimentation velocity and potential for the case of a broad range of zeta potential and double-layer thickness. On the other hand, Booth’s perturbation analysis has also been extended to determine the sedimentation velocity and potential in suspensions of interacting hard spheres, − porous (permeable) spheres, − and soft (composite) spheres − with low fixed charge densities.…”