Osmotic coefficient phenomena

Within PB theory [2] and on the level of a cell model the cylindrical geometry can be treated exactly in the salt-free case [3, 4]. The Poisson-Boltzmann (PB) solution for the cell model is reviewed in the chapter in this volume on the osmotic coefficient. The PB approach can provide for instance new insights into the phenomenon of Manning condensation [5-7]. For example, the distance up to which counterions can be called condensed can be conveniently found via the inflection point in the log plot of the integrated radial distribution function P(r) of counterions [8, 9], defined as... 

Apart from the phenomenon of a negative osmotic coefficient the remarks which have been made on monovalent measurements also apply here. The actual p is smaller than the PB prediction, only this effect is much more pronounced in the multivalent systems. This overestimation of p is again accompanied by an underestimation of counterion condensation see for instance Figure 9. The osmotic coefficient converges to the PB result upon dilution, but already at intermediate densities it is surprisingly well described by the Manning limit l/2 w. Notice finally that contrary to Figure 12 the curves for different valences intersect. The reason for this is the way in which Eq. 40 depends on valence. 

A phenomenon that is particularly important in the design of reverse osmosis units is that of concentration polarization. This occurs on the feed-side (concentrated side) of the reverse osmosis membrane. Because the solute cannot permeate through the membrane, the concentration of the solute in the liquid adjacent to the surface of the membrane is greater than that in the bulk of the fluid. This difference causes mass transfer of solute by diffusion from the membrane surface back to the bulk liquid. The rate of diffusion back into the bulk fluid depends on the mass transfer coefficient for the boundary layer on feed-side. Concentration polarization is the ratio of the solute concentration at the membrane surface to the solute concentration in the bulk stream. Concentration polarization causes the flux of solvent to decrease since the osmotic pressure increases as the boundary layer concentration increases and the overall driving force (AP - An) decreases. 

In a binary mixture, diffusion coefficients are equal to each other for dissimilar molecules, and Fick s law can determine the molecular mass flows in an isotropic medium at isothermal and isobaric conditions. In a multicomponent diffusion, however, various interactions among the molecules may arise. Some of these interactions are (i) diffusion flows may vanish despite the nonvanishing driving force, which is known as the mass transfer barrier, (ii) diffusion of a component in a direction opposite to that indicated by its driving force leads to a phenomenon called the reverse mass flow, and (iii) diffusion of a component in the absence of its driving force, which is called the osmotic mass flow. 

---