We describe the sedimentation–diffusion equilibrium of binary mixtures of charged colloids
in the presence of small ions and for non-dilute conditions, by extending the work of Biben
and Hansen (1994 J. Phys.: Condens. Matter 6 A345). For a monocomponent system, they
included a Carnahan–Starling hard-sphere correction and a pressure term due to
the small ions. We extend this approach to mixtures of spheres of unequal size,
and implement the fact that the effective buoyant mass of a particle is based on
the difference in mass density between the particle itself and the local average
mass density, and not on the difference with the mass density of the pure liquid.
Without the three volume effects (hard-sphere repulsion, ion pressure, buoyant particle
mass based on local, average, mass density), the lighter particle (buoyant mass
mL,
charge zL) only levitates from the bottom (with a maximum in concentration displaced upwards) when
zL/mL>
zH/mH
(with H indicating the heavier particle). With these volume effects included the
fractionation is much sharper and occurs even for
.
For certain parameter settings we find a bimodal distribution of the heavier particles with
most of them in the bottom region, but with a small fraction forming a thin layer higher up
in the column. This second layer is not found when the buoyant particle mass is based on
the mass density difference with the pure liquid and/or when the ion pressure is neglected,
suggesting that it is due to a subtle interplay between these two contributions.