the full Poisson-Boltzmann (PB) equation (in the direction of the applied ..... based on the Carnahan-Starling equation-of-state, which is very accurate2,33 for ...
Sedimentation-diffusion equilibrium of binary mixtures of charged colloids including volume effects P.M. Biesheuvel and J. Lyklema published in
J. Phys.: Condens. Matter
4
z2=30 3.5 3
φ2
h (cm)
2.5 2 1.5 1
φ1 0.5 0 0
0.025
0.05
0.075
0.1
0.125
0.15
φ
Please cite this publication as follows: M. van Soestbergen, P.M. Biesheuvel, and M.Z. Bazant, “Sedimentation-diffusion equilibrium of binary mixtures of charged colloids including volume effects,” J.Phys.: Condens. Matter 17 6337-6352 (2005). You can download the published version at: http://dx.doi.org/10.1088/0953-8984/17/41/005
The theory in this paper was found to be flawed with respect to the pressure to be used in the term vi⋅dP/dh. Following Maxwell-Stefan theory, use was made of the hydrostatic pressure Ph. However, this must be the total pressure, Ph-Π, where Π is the local osmotic pressure. This has significant consequences. We refer to Spruijt and Biesheuvel, J. Phys.: Condens. Matter (2014) for a correct analysis. Erroneous equations are printed in RED. The prediction of a bimodal density distribution is due to this error and is not found in the correct model.
Sedimentation-diffusion equilibrium of binary mixtures of charged colloids including volume effects P.M. Biesheuvel and J. Lyklema Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, the Netherlands.
Abstract 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 (J. Phys.: Condens. Matter 6, A345, 1994). For a monocomponent system, they included a CarnahanStarling 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 upward) 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 zL/mL
