The Donnan equilibrium is still valid in high-volume HDF

Clinical studies have shown that hemodiafiltration reduces morbidity and mortality of dialysis patients compared to hemodialysis alone. This is attributed to its superior middle molecule clearance compared to standard hemodialysis. However, doubts arose as to whether a high convective flux through the dialyzer membrane has an influence on the equilibrium concentration of small ions, especially that of sodium. Due to the presence of negatively charged impermeable proteins on the blood side, the Gibbs-Donnan effect leads to an asymmetric distribution of membrane permeable ions on both sides of the membrane. In thermodynamic equilibrium, the concentrations of those ions can easily be calculated. However, the convective fluid flow leads to deviations from thermodynamic equilibrium. In this article, the effect of a convective flow on the ion distribution across a semipermeable membrane is analyzed in a theoretical model. Starting from the extended Nernst-Planck equation, including diffusive, convective, and electrostatic effects, a set of differential equations is derived. An approximate solution for flow speeds up to 0.1 ms^-1 as well as a numerical solution are given. The results show that in any practical dialysis setting the convective flow has negligible influence on the electrolyte concentrations.