Sedimentation-diffusion equilibrium of binary mixtures of charged colloids including volume effects

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 M-L, charge Z(L)) only levitates from the bottom (with a maximum in concentration displaced upwards) when Z(L)/M-L > Z(H)/M-H (with H indicating the heavier particle). With these volume effects included the fractionation is much sharper and Occurs even for Z(L)/m(L) << Z(H)/M-H. 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.