The sedimentation of a charged composite particle composed biomedical, and environmental engineering and science. of a solid core and a surrounding porous shell in an electrolyte This problem is more complex than that of uncharged colloisolution is analytically studied. In the solvent-permeable and iondal particles because the electric double layer surrounding penetrable porous surface layer of the particle, idealized hydrodyeach particle is distorted by the fluid flow around the particle.
namic frictional segments with fixed charges are assumed to dis-
The deformation of the double layer resulting from the fluid tribute at a uniform density. The equations which govern the ionic motion is usually referred to as the relaxation effect and concentration distributions, the electric potential profile, and the gives rise to an induced electric field. The sedimentation fluid flow field inside and outside the surface layer of a charged potential, which arises in a suspension of settling charged composite particle migrating in an unbounded solution are linearized assuming that the system is only slightly distorted from equi-particles, was first reported by Dorn in 1878, and this phelibrium. Using a perturbation method, these linearized equations nomenon is often known by his name (1, 2). The sedimentaare solved for a composite sphere with the charge densities of the tion potential gradient (which is of the order 1-10 V/m) rigid core surface and of the surface layer as the small perturbation not only alters the velocity and pressure distributions in the parameters. An analytical expression for the settling velocity of fluid due to its action on the electrolyte ions but also retards the composite sphere in closed form is obtained from a balance the settling of the particles by an electrophoretic effect.
among its gravitational, electrostatic, and hydrodynamic forces.
An important contribution to the sedimentation theory of a
The result demonstrates that the presence of the fixed charges in nonconducting spherical particle with arbitrary double layer the composite sphere slows down its settling velocity relative to thickness was made by Booth (1). He solved a set of electrothat of an uncharged one. A closed-form formula for the sedimenkinetic differential equations using a perturbation method to tation potential in a dilute suspension of identical charged composobtain formulas for the sedimentation velocity and sedimenite spheres is also derived by using the requirement of zero net electric current. The Onsager reciprocal relation is found to be tation potential expressed as power series in the zeta potensatisfied between sedimentation and electrophoresis. It is shown tial (z) of the particle up to O(z 2 ) and O(z), respectively. that spherically-symmetric ''neutral'' composite particles (bearing Using a unit cell model with the condition of zero net electric no net charge) can undergo electrophoresis, induce sedimentation current, Levine et al. (3) derived analytical expressions of potential, and experience a smaller settling velocity relative to the sedimentation velocity and potential in a suspension of corresponding uncharged particles. The direction of the electroidentical charged spheres with small surface potential as phoretic velocity or the induced potential gradient is determined functions of the fractional volume concentration of the partiby the fixed charges in the porous surface layers of the particles.
cles. In the limiting case of a single particle their result
In the limiting cases, the analytical solutions describing the sedisomewhat differs from that obtained by Booth, which is not mentation velocity and sedimentation potential (or electrophoretic subject to the constraint of zero net current. Numerical remobility) for charged composite spheres reduce to those for sults relieving the restriction of low surface potential in charged solid spheres and for charged porous spheres. แญง 1997 Academic Press
Booth's analysis were reported by Stigter (4) using a modi-Key Words: composite particles; porous surface layer; sedimenfication of the theory of electrophoresis by Wiersema et al.