Abstract
Separation of two ionic solutions with a permselective membrane that is impermeable to some of the ions leads to an uneven distribution of permeating ions on the two sides of the membrane described by the Gibbs–Donnan (G–D) equilibrium with the G–D factors relating ion concentrations in the two solutions. Here, we present a method of calculating the G–D factors for ideal electroneutral multi-ion solutions with different total charge of non-permeating species on each side of a permselective membrane separating two compartments. We discuss some special cases of G–D equilibrium for which an analytical solution may be found, and we prove the transitivity of G–D factors for multi-ion solutions in several compartments interconnected by permselective membranes. We show a few examples of calculation of the G–D factors for both simple and complex solutions, including the case of human blood plasma and interstitial fluid separated by capillary walls. The article is accompanied by an online tool that enables the calculation of the G–D factors and the equilibrium concentrations for multi-ion solutions with various composition in terms of permeating ions and non-permeating charge, according to the presented method.
Highlights
Separation of two ionic solutions with a permselective membrane that is impermeable to some of the ions leads to an uneven distribution of permeating ions on the two sides of the membrane described by the Gibbs–Donnan (G–D) equilibrium with the G–D factors relating ion concentrations in the two solutions
In medicine and biomedical engineering the Gibbs–Donnan theory is most often used to describe the composition of blood plasma separated by a capillary wall from the interstitial fluid14–17 or by a dialyzer or filter membrane from a protein-free dialysis fluid18–20
In mixtures of ions separated by a permselective membrane that is permeable to some of them and not permeable to other, the G–D equilibrium depends on the ionic equivalents of all ions present in the mixture on one or both sides of the membrane
Summary
Separation of two ionic solutions with a permselective membrane that is impermeable to some of the ions leads to an uneven distribution of permeating ions on the two sides of the membrane described by the Gibbs–Donnan (G–D) equilibrium with the G–D factors relating ion concentrations in the two solutions. We present a method of calculating the G–D factors for ideal electroneutral multiion solutions with different total charge of non-permeating species on each side of a permselective membrane separating two compartments. We show a few examples of calculation of the G–D factors for both simple and complex solutions, including the case of human blood plasma and interstitial fluid separated by capillary walls. The article is accompanied by an online tool that enables the calculation of the G–D factors and the equilibrium concentrations for multi-ion solutions with various composition in terms of permeating ions and non-permeating charge, according to the presented method. The Gibbs–Donnan theory describes the equilibrium conditions for ion solutions separated by a permselective (semipermeable) membrane when one of the solutions contains species that cannot pass through the membrane (non-permeating charge), which distorts the distribution of permeating ions on the two sides of the membrane. Note that this is an aggregated description of non-permeating species, as in general there might be multiple non-permeating species with different charge numbers and concentrations; Z np Cnp denotes the sum of the respective ZC products over all non-permeating species
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