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1

Stell, G., and C. G. Joslin. "The Donnan Equilibrium." Biophysical Journal 50, no. 5 (November 1986): 855–59. http://dx.doi.org/10.1016/s0006-3495(86)83526-3.

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2

DAVIES, I. ab I. "Intralysosomal pH: a Donnan equilibrium." Biochemical Society Transactions 14, no. 2 (April 1, 1986): 479–81. http://dx.doi.org/10.1042/bst0140479.

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3

Jiménez-Ángeles, Felipe, and Marcelo Lozada-Cassou. "Simple Model for Semipermeable Membrane: Donnan Equilibrium." Journal of Physical Chemistry B 108, no. 5 (February 2004): 1719–30. http://dx.doi.org/10.1021/jp035829p.

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4

Castelnovo, M., and A. Evilevitch. "Binding effects in multivalent Gibbs-Donnan equilibrium." Europhysics Letters (EPL) 73, no. 4 (February 2006): 635–41. http://dx.doi.org/10.1209/epl/i2005-10425-3.

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5

Räsänen, Erkki, Per Stenius, and Pekka Tervola. "Model describing Donnan equilibrium, pH and complexation equilibria in fibre suspensions." Nordic Pulp & Paper Research Journal 16, no. 2 (May 1, 2001): 130–39. http://dx.doi.org/10.3183/npprj-2001-16-02-p130-139.

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6

Bryant, Winnifred. "Modeling the Effects of Intracellular Anions on Membrane Potential: An Active-Learning Exercise." American Biology Teacher 81, no. 5 (May 1, 2019): 373–76. http://dx.doi.org/10.1525/abt.2019.81.5.373.

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In biological membranes that are permeable to water and ions but impermeable to other solutes, the diffusible ions cannot reach a concentration equilibrium. Instead, a state of electroneutrality is achieved on each side of the membrane, which requires that the diffusible ions be found in different concentrations on either side of the membrane. The Donnan equilibrium is a major contributing factor to the polarized state of cells, and appreciating it is vital to the understanding of neuronal physiology. This article presents a nonmathematical active-learning exercise that will help AP and college biology students understand how the Donnan equilibrium is achieved.
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7

Philipse, A., and A. Vrij. "The Donnan equilibrium: I. On the thermodynamic foundation of the Donnan equation of state." Journal of Physics: Condensed Matter 23, no. 19 (April 27, 2011): 194106. http://dx.doi.org/10.1088/0953-8984/23/19/194106.

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8

Marang, Laura, Pascal Reiller, Monique Pepe, and Marc F. Benedetti. "Donnan Membrane Approach: From Equilibrium to Dynamic Speciation." Environmental Science & Technology 40, no. 17 (September 2006): 5496–501. http://dx.doi.org/10.1021/es060608t.

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9

Odijk, Theo, and Flodder Slok. "Nonuniform Donnan Equilibrium within Bacteriophages Packed with DNA†." Journal of Physical Chemistry B 107, no. 32 (August 2003): 8074–77. http://dx.doi.org/10.1021/jp0224822.

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10

Algotsson, Jenny, Torbjörn Åkesson, and Jan Forsman. "Monte Carlo simulations of Donnan equilibrium in cartilage." Magnetic Resonance in Medicine 68, no. 4 (August 13, 2012): 1298–302. http://dx.doi.org/10.1002/mrm.24409.

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11

Takashima, Wataru, Kengo Hayasi, and Keiichi Kaneto. "Force detection with Donnan equilibrium in polypyrrole film." Electrochemistry Communications 9, no. 8 (August 2007): 2056–61. http://dx.doi.org/10.1016/j.elecom.2007.05.019.

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12

Masuda, T., G. P. Dobson, and R. L. Veech. "The Gibbs-Donnan near-equilibrium system of heart." Journal of Biological Chemistry 265, no. 33 (November 1990): 20321–34. http://dx.doi.org/10.1016/s0021-9258(17)30507-0.

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13

Mapleson, W. W. "Computation of the effect of Donnan equilibrium on pH in equilibrium dialysis." Journal of Pharmacological Methods 17, no. 3 (May 1987): 231–42. http://dx.doi.org/10.1016/0160-5402(87)90053-2.

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14

Sukhorukov, Gleb B., Milan Brumen, Edwin Donath, and Helmuth Möhwald. "Hollow Polyelectrolyte Shells: Exclusion of Polymers and Donnan Equilibrium." Journal of Physical Chemistry B 103, no. 31 (August 1999): 6434–40. http://dx.doi.org/10.1021/jp990095v.

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15

Tian, Huanhuan, Li Zhang, and Moran Wang. "Applicability of Donnan equilibrium theory at nanochannel–reservoir interfaces." Journal of Colloid and Interface Science 452 (August 2015): 78–88. http://dx.doi.org/10.1016/j.jcis.2015.03.064.

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16

Pochard, I., J. P. Boisvert, A. Malgat, and C. Daneault. "Donnan equilibrium and the effective charge of sodium polyacrylate." Colloid & Polymer Science 279, no. 9 (September 1, 2001): 850–57. http://dx.doi.org/10.1007/s003960100497.

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17

Stigter, Dirk. "Donnan membrane equilibrium, sedimentation equilibrium, and coil expansion of DNA in salt solutions." Cell Biophysics 11, no. 1 (December 1987): 139–58. http://dx.doi.org/10.1007/bf02797120.

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18

Nguyen, Minhtri K., and Ira Kurtz. "Quantitative interrelationship between Gibbs-Donnan equilibrium, osmolality of body fluid compartments, and plasma water sodium concentration." Journal of Applied Physiology 100, no. 4 (April 2006): 1293–300. http://dx.doi.org/10.1152/japplphysiol.01274.2005.

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The presence of negatively charged, impermeant proteins in the plasma space alters the distribution of diffusible ions in the plasma and interstitial fluid (ISF) compartments to preserve electroneutrality. We have derived a new mathematical model to define the quantitative interrelationship between the Gibbs-Donnan equilibrium, the osmolality of body fluid compartments, and the plasma water Na+ concentration ([Na+]pw) and validated the model using empirical data from the literature. The new model can account for the alterations in all ionic concentrations (Na+ and non-Na+ ions) between the plasma and ISF due to Gibbs-Donnan equilibrium. In addition to the effect of Gibbs-Donnan equilibrium on Na+ distribution between plasma and ISF, our model predicts that the altered distribution of osmotically active non-Na+ ions will also have a modulating effect on the [Na+]pw by affecting the distribution of H2O between the plasma and ISF. The new physiological insights provided by this model can for the first time provide a basis for understanding quantitatively how changes in the plasma protein concentration modulate the [Na+]pw. Moreover, this model defines all known physiological factors that may modulate the [Na+]pw and is especially helpful in conceptually understanding the pathophysiological basis of the dysnatremias.
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19

Weng, Liping, Flora Alonso Vega, and Willem H. Van Riemsdijk. "Strategies in the application of the Donnan membrane technique." Environmental Chemistry 8, no. 5 (2011): 466. http://dx.doi.org/10.1071/en11021.

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Environmental context Free ion concentrations determine the effects of nutrients and pollutants on organisms in the environment. The Donnan membrane technique provides a measure of free ion concentrations. This paper presents clear guidelines on the application of the Donnan membrane technique for determining free ion concentrations in both synthetic and natural samples. Abstract The Donnan membrane technique (DMT) can be applied to measure free ion concentrations both in laboratory and in situ in the field. In designing DMT experiments, different strategies can be taken, depending on whether accumulation is needed. (1) When the free ion concentration is above the detection limit of the analytical technique (e.g. ICP-MS), no accumulation is needed and no ligand is added to the acceptor. Measurement can be based on the Donnan membrane equilibrium. (2) When an accumulation of less than 500 times is needed, an appropriate amount of ligand can be added to the acceptor and measurement can be based on the Donnan membrane equilibrium. (3) When an accumulation factor of larger than 500 times is needed, a relatively large amount of ligand is added to the acceptor and measurement can be based on the transport kinetics. In this paper, several issues in designing the DMT experiments are discussed: choice of DMT cell, measurement strategies and ligands and possible implication of slow dissociation of metal complexes in the sample solution (lability issue). The objective of this paper is to give better guidance in the application of DMT for measuring free ion concentrations in both synthetic and natural samples.
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20

Vis, Mark, Remco Tuinier, Bonny W. M. Kuipers, Agienus Vrij, and Albert P. Philipse. "Interactions between amphoteric surfaces with strongly overlapping double layers." Soft Matter 14, no. 23 (2018): 4702–10. http://dx.doi.org/10.1039/c8sm00662h.

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21

Nguyen, Minhtri K., Vahram Ornekian, Liyo Kao, Anthony W. Butch, and Ira Kurtz. "Defining the role of albumin infusion in cirrhosis-associated hyponatremia." American Journal of Physiology-Gastrointestinal and Liver Physiology 307, no. 2 (July 15, 2014): G229—G232. http://dx.doi.org/10.1152/ajpgi.00424.2013.

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The presence of negatively charged, impermeant proteins in the plasma space alters the distribution of diffusible ions in the plasma and interstitial fluid (ISF) compartments to preserve electroneutrality and is known as Gibbs-Donnan equilibrium. In patients with hypoalbuminemia due to underlying cirrhosis, the decrease in the plasma water albumin concentration ([Alb−]pw) would be expected to result in a decrease in the plasma water sodium concentration ([Na+]pw) due to an alteration in the distribution of Na+ between the plasma and ISF. In addition, cirrhosis-associated hyponatremia may be due to the renal diluting defect resulting from the intravascular volume depletion due to gastrointestinal losses and overdiuresis and/or decreased effective circulatory volume secondary to splanchnic vasodilatation. Therefore, albumin infusion may result in correction of the hyponatremia in cirrhotic patients either by modulating the Gibbs-Donnan effect due to hypoalbuminemia or by restoring intravascular volume in patients with intravascular volume depletion due to gastrointestinal losses and overdiuresis. However, the differential role of albumin infusion in modulating the [Na+]pw in these patients has not previously been analyzed quantitatively. In the present study, we developed an in vitro assay system to examine for the first time the quantitative effect of changes in albumin concentration on the distribution of Na+ between two compartments separated by a membrane that allows the free diffusion of Na+. Our findings demonstrated that changes in [Alb−]pw are linearly related to changes in [Na+]pw as predicted by Gibbs-Donnan equilibrium. However, based on our findings, we predict that the improvement in cirrhosis-associated hyponatremia due to intravascular volume depletion results predominantly from the restoration of intravascular volume rather than alterations in Gibbs-Donnan equilibrium.
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22

Hu, Taozhan, Xinhua Wang, Chen Wang, Xiufen Li, and Yueping Ren. "Impacts of inorganic draw solutes on the performance of thin-film composite forward osmosis membrane in a microfiltration assisted anaerobic osmotic membrane bioreactor." RSC Advances 7, no. 26 (2017): 16057–63. http://dx.doi.org/10.1039/c7ra01524k.

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23

Ring, Troels. "Master equation for dysnatremia or intractable abracadabra." Journal of Applied Physiology 101, no. 2 (August 2006): 692–94. http://dx.doi.org/10.1152/japplphysiol.00442.2006.

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The following is the abstract of the article discussed in the subsequent letter: The presence of negatively charged, impermeant proteins in the plasma space alters the distribution of diffusible ions in the plasma and interstitial fluid (ISF) compartments to preserve electroneutrality. We have derived a new mathematical model to define the quantitative interrelationship between the Gibbs-Donnan equilibrium, the osmolality of body fluid compartments, and the plasma water Na+ concentration ([Na+]pw) and validated the model using empirical data from the literature. The new model can account for the alterations in all ionic concentrations (Na+ and non-Na+ ions) between the plasma and ISF due to Gibbs-Donnan equilibrium. In addition to the effect of Gibbs-Donnan equilibrium on Na+ distribution between plasma and ISF, our model predicts that the altered distribution of osmotically active non-Na+ ions will also have a modulating effect on the [Na+]pw by affecting the distribution of H2O between the plasma and ISF. The new physiological insights provided by this model can for the first time provide a basis for understanding quantitatively how changes in the plasma protein concentration modulate the [Na+]pw. Moreover, this model defines all known physiological factors that may modulate the [Na+]pw and is especially helpful in conceptually understanding the pathophysiological basis of the dysnatremias.
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24

Vezzani, Daniele, and Serena Bandini. "Donnan equilibrium and dielectric exclusion for characterization of nanofiltration membranes." Desalination 149, no. 1-3 (September 2002): 477–83. http://dx.doi.org/10.1016/s0011-9164(02)00784-1.

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25

Schlenoff, Joseph B., Mo Yang, Zachary A. Digby, and Qifeng Wang. "Ion Content of Polyelectrolyte Complex Coacervates and the Donnan Equilibrium." Macromolecules 52, no. 23 (November 19, 2019): 9149–59. http://dx.doi.org/10.1021/acs.macromol.9b01755.

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26

Tamashiro, M. N., Y. Levin, and M. C. Barbosa. "Donnan equilibrium and the osmotic pressure of charged colloidal lattices." European Physical Journal B 1, no. 3 (February 1998): 337–43. http://dx.doi.org/10.1007/s100510050192.

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27

Hedström, Magnus, and Ola Karnland. "Donnan equilibrium in Na-montmorillonite from a molecular dynamics perspective." Geochimica et Cosmochimica Acta 77 (January 2012): 266–74. http://dx.doi.org/10.1016/j.gca.2011.11.007.

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28

Thode, J., J. C. Boyd, and J. H. Ladenson. "Activity measurements of calcium, sodium, potassium, and chloride after equilibrium dialysis used to show lack of evidence for protein interference with calcium electrodes." Clinical Chemistry 33, no. 10 (October 1, 1987): 1811–13. http://dx.doi.org/10.1093/clinchem/33.10.1811.

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Abstract We measured the activity of Ca2+, Na+, K+, and Cl- with ion-selective electrodes after equilibrium dialysis of solutions with different albumin concentrations. The calculated Donnan ratio was the same for all ions in the same solution and increased with the albumin concentration, as predicted by the Donnan theory. The Donnan distribution ratio for Ca2+ was similar, as determined with instruments from three different manufacturers. For healthy subjects and patients with renal stone disease, we did not find any correlation between serum concentrations of ionized calcium and albumin. The discordance between measured ionized calcium and albumin-corrected total calcium depended on the correction algorithm we utilized. The difficulties of absolutely proving or disproving a protein error in these measurements are discussed, but our data are not consistent with protein being a source of error in measurements of ionized calcium.
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29

Bleha, Miroslav, and Věra Šumberová. "Equilibrium Sorptions in Heterogeneous Ion Exchange Membranes." Collection of Czechoslovak Chemical Communications 57, no. 9 (1992): 1905–14. http://dx.doi.org/10.1135/cccc19921905.

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The equilibrium sorption of uni-univalent electrolytes (NaCl, KCl) in heterogeneous cation exchange membranes with various contents of the ion exchange component and in ion exchange membranes Ralex was investigated. Using experimental data which express the concentration dependence of equilibrium sorption, validity of the Donnan relation for the systems under investigation was tested and values of the Glueckauf inhomogeneity factor for Ralex membranes were determined. Determination of the equilibrium sorption allows the effect of the total content of internal water and of the ion-exchange capacity on the distribution coefficients of the electrolyte to be determined.
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30

Hua, Xu, and Chen Nian-Yi. "The Research of Donnan Equilibrium with Hypeinetted-chain(HNC) Approximation Method." Acta Physico-Chimica Sinica 12, no. 04 (1996): 320–24. http://dx.doi.org/10.3866/pku.whxb19960407.

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31

Agarwal, Chhavi, Sanhita Chaudhury, Amol Mhatre, and A. Goswami. "Donnan membrane equilibrium studies of mercury salts with Nafion-117 membrane." DESALINATION AND WATER TREATMENT 38 (2012): 222–26. http://dx.doi.org/10.5004/dwt.2012.2324.

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32

Sherwood, J. D., F. Risso, F. Collé-Paillot, F. Edwards-Lévy, and M. C. Lévy. "Rates of transport through a capsule membrane to attain Donnan equilibrium." Journal of Colloid and Interface Science 263, no. 1 (July 2003): 202–12. http://dx.doi.org/10.1016/s0021-9797(03)00140-1.

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33

Agarwal, Chhavi, Sanhita Chaudhury, Amol Mhatre, and A. Goswami. "Donnan membrane equilibrium studies of mercury salts with Nafion-117 membrane." Desalination and Water Treatment 38, no. 1-3 (January 2012): 262–66. http://dx.doi.org/10.1080/19443994.2012.664380.

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34

Langridge-Smith, J. E., and W. P. Dubinsky. "Donnan equilibrium and pH gradient in isolated tracheal apical membrane vesicles." American Journal of Physiology-Cell Physiology 249, no. 5 (November 1, 1985): C417—C420. http://dx.doi.org/10.1152/ajpcell.1985.249.5.c417.

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Apical plasma membrane vesicles isolated from bovine tracheal epithelium were found to possess both an electrical potential gradient (delta psi) and a transmembrane pH gradient (delta pH). The delta psi was calculated from the distribution of 86Rb+ in the presence of the ionophore valinomycin, and delta pH was determined from the distribution of [14C]methylamine under conditions of apparent equilibrium. Maximal values for delta psi of -54.3 +/- 2.5 mV and for delta pH of 0.75 +/- 0.07 pH units were obtained under low ionic strength conditions. Increasing the ionic strength by the addition of 50 mM of either permeant or impermeant electrolytes reduced delta psi to near zero values. The delta pH varied in parallel with the delta psi. The results suggest that both 86Rb+ in the presence of valinomycin and H+ are in a Donnan equilibrium with impermeant negative charge in the vesicle interior.
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35

Buschmann, M. D., and A. J. Grodzinsky. "A Molecular Model of Proteoglycan-Associated Electrostatic Forces in Cartilage Mechanics." Journal of Biomechanical Engineering 117, no. 2 (May 1, 1995): 179–92. http://dx.doi.org/10.1115/1.2796000.

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Measured values of the swelling pressure of charged proteoglycans (PG) in solution (Williams RPW, and Comper WD; Biophysical Chemistry 36:223, 1990) and the ionic strength dependence of the equilibrium modulus of PG-rich articular cartilage (Eisenberg SR, and Grodzinsky AJ; J Orthop Res 3: 148, 1985) are compared to the predictions of two models. Each model is a representation of electrostatic forces arising from charge present on spatially fixed macromolecules and spatially mobile micro-ions. The first is a macroscopic continuum model based on Donnan equilibrium that includes no molecular-level structure and assumes that the electrical potential is spatially invariant within the polyelectrolyte medium (i.e. zero electric field). The second model is based on a microstructural, molecular-level solution of the Poisson-Boltzmann (PB) equation within a unit cell containing a charged glycosaminoglycan (GAG) molecule and its surrounding atmosphere of mobile ions. This latter approach accounts for the space-varying electrical potential and electrical field between the GAG constituents of the PG. In computations involving no adjustable parameters, the PB-cell model agrees with the measured pressure of PG solutions to within experimental error (10%), whereas the ideal Donnan model overestimates the pressure by up to 3-fold. In computations involving one adjustable parameter for each model, the PB-cell model predicts the ionic strength dependence of the equilibrium modulus of articular cartilage. Near physiological ionic strength, the Donnan model overpredicts the modulus data by 2-fold, but the two models coincide for low ionic strengths (C0 < 0.025M) where the spatially invariant Donnan potential is a closer approximation to the PB potential distribution. The PB-cell model result indicates that electrostatic forces between adjacent GAGs predominate in determining the swelling pressure of PG in the concentration range found in articular cartilage (20–80 mg/ml). The PB-cell model is also consistent with data (Eisenberg and Grodzinsky, 1985, Lai WM, Hou JS, and Mow VC; J Biomech Eng 113: 245, 1991) showing that these electrostatic forces account for ˜ 1/2 (290kPa) the equilibrium modulus of cartilage at physiological ionic strength while absolute swelling pressures may be as low as ˜ 25 – 100kPa. This important property of electrostatic repulsion between GAGs that are highly charged but spaced a few Debye lengths apart allows cartilage to resist compression (high modulus) without generating excessive intratissue swelling pressures.
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36

Mow, V. C., W. M. Lai, and J. S. Hou. "Triphasic Theory for Swelling Properties of Hydrated Charged Soft Biological Tissues." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S134—S141. http://dx.doi.org/10.1115/1.3120792.

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Swelling phenomenon of biological soft tissues, such as articular cartilage, depends on their fixed charge densities, the stiffness of their collagen-proteoglycan solid matrix and the ion concentration in the interstitium. Based on the thermodynamic continuum mixture theory, a multiphasic mixture model is developed to describe the equilibrium and transient swelling properties. For articular cartilages in a single salt environment (e.g. NaCl), a three phase model (triphasic theory) suffices to describe its swelling behavior. The three phases are: solid matrix, interstitial water and the mobile salt. The equations of motion in this theory shows that the driving forces for interstitial water and salt are the gradients of their chemical potentials. Constitutive equations for the chemical potentials of the phases and for the total stress under infinitesimal strain but large variation of salt concentration are presented based on the physico-chemical theory for polyelectrolytic solutions and continuum theory. Application of this theory to equilibrium problems yields the well known Donnan equilibrium ion distribution and osmotic pressure equations. The theory indicates that at equilibrium the applied load on the tissue is shared by 1) the solid matrix elastic stress due to deformation; 2) the Donnan osmotic pressure; and 3) the chemical expansion stress due to the charge-to-charge repulsive forces between the charged groups in the solid matrix. For the transient isometric swelling problem, the theory is shown to describe the experimentally observed responses very well.
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37

Bygrave, Geoff, and Peter Englezos. "Fibre charge from potentiometric titration of kraft pulp and donnan equilibrium theory." Nordic Pulp & Paper Research Journal 13, no. 3 (August 1, 1998): 220–24. http://dx.doi.org/10.3183/npprj-1998-13-03-p220-224.

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38

Fitch, Alanah, and Philip A. Helmke. "Donnan equilibrium/graphite furnace atomic absorption estimates of soil extract complexation capacities." Analytical Chemistry 61, no. 11 (June 1989): 1295–98. http://dx.doi.org/10.1021/ac00186a023.

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39

Alberghina, Gaetano, Shui-Lin Chen, Salvatore Fisichella, Toshiro Iijima, Ralph McGregor, Rolf M. Rohner, and Heinrich Zollinger. "Donnan Approach to Equilibrium Sorption: Interactions of Cationic Dyes with Acrylic Fibers." Textile Research Journal 58, no. 6 (June 1988): 345–54. http://dx.doi.org/10.1177/004051758805800607.

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The equilibrium sorption of ten cationic dyes by porous and regular acrylic fibers has been investigated. The data have been interpreted by a simple Donnan approach, based on the assumption that there are two different types of acidic groups in these fibers. The ionic distribution coefficients KD for the dyes and the fibers were calculated. These coefficients provide an indirect measure of the “affinity” of the dyes for the fibers. The values of KD have been discussed in relation to the structures of the dyes and fibers, and in relation to the effects of salts, pH, and temperature.
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40

Pivonka, Peter, David Smith, and Bruce Gardiner. "Investigation of Donnan equilibrium in charged porous materials—a scale transition analysis." Transport in Porous Media 69, no. 2 (December 14, 2006): 215–37. http://dx.doi.org/10.1007/s11242-006-9071-6.

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41

Jodra, Y., and F. Mijangos. "Ion exchange selectivities of calcium alginate gels for heavy metals." Water Science and Technology 43, no. 2 (January 1, 2001): 237–44. http://dx.doi.org/10.2166/wst.2001.0095.

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An equilibrium model has been proposed and verified, based on the conditions in the gel phase and Donnan equilibrium theory, for the analysis of the experimental data on the recovery of lead, copper, cadmium, cobalt, nickel and zinc from synthetic, nonmetallic aqueous solutions on calcium alginate gels. This equilibrium model considers that the system behaves as an ion-exchange process between the calcium in the gels and the divalent metals in solution, and that the metallic portion enclosed in gel fluid is supposed an important quantitative contribution to the total amount of metal uptake by gels. According to the equilibrium constants calculated, it is deduced that the selectivity order is: Pb&gt;Cu&gt;Cd&gt;Ni&gt;Zn&gt;Co.
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42

Snyder, Victor A. "Gibbs-Duhem Equation for Ion-Exchanging Mixtures in Donnan Equilibrium with Electrolyte Solutions." Soil Science Society of America Journal 75, no. 6 (November 2011): 2169–77. http://dx.doi.org/10.2136/sssaj2010.0438.

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43

Mafé, S., P. Ramírez, A. Tanioka, and J. Pellicer. "Model for Counterion-Membrane-Fixed Ion Pairing and Donnan Equilibrium in Charged Membranes." Journal of Physical Chemistry B 101, no. 10 (March 1997): 1851–56. http://dx.doi.org/10.1021/jp962601b.

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44

Hsu, Jyh-Ping, and Bo-Tau Liu. "Current Efficiency of Ion-Selective Membranes: Effects of Local Electroneutrality and Donnan Equilibrium." Journal of Physical Chemistry B 101, no. 40 (October 1997): 7928–32. http://dx.doi.org/10.1021/jp970950f.

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45

Ramı&#x;rez, Patricio, Antonio Alcaraz, Salvador Mafé, and Julio Pellicer. "Donnan Equilibrium of Ionic Drugs in pH-Dependent Fixed Charge Membranes: Theoretical Modeling." Journal of Colloid and Interface Science 253, no. 1 (September 2002): 171–79. http://dx.doi.org/10.1006/jcis.2002.8508.

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46

Philipse, Albert P. "Remarks on the Donnan condenser in the sedimentation–diffusion equilibrium of charged colloids." Journal of Physics: Condensed Matter 16, no. 38 (September 11, 2004): S4051—S4062. http://dx.doi.org/10.1088/0953-8984/16/38/020.

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47

Wolf, Matthew B., and Edward C. DeLand. "A mathematical model of blood-interstitial acid-base balance: application to dilution acidosis and acid-base status." Journal of Applied Physiology 110, no. 4 (April 2011): 988–1002. http://dx.doi.org/10.1152/japplphysiol.00514.2010.

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We developed mathematical models that predict equilibrium distribution of water and electrolytes (proteins and simple ions), metabolites, and other species between plasma and erythrocyte fluids (blood) and interstitial fluid. The models use physicochemical principles of electroneutrality in a fluid compartment and osmotic equilibrium between compartments and transmembrane Donnan relationships for mobile species. Across the erythrocyte membrane, the significant mobile species Cl−is assumed to reach electrochemical equilibrium, whereas Na+and K+distributions are away from equilibrium because of the Na+/K+pump, but movement from this steady state is restricted because of their effective short-term impermeability. Across the capillary membrane separating plasma and interstitial fluid, Na+, K+, Ca2+, Mg2+, Cl−, and H+are mobile and establish Donnan equilibrium distribution ratios. In each compartment, attainment of equilibrium by carbonates, phosphates, proteins, and metabolites is determined by their reactions with H+. These relationships produce the recognized exchange of Cl−and bicarbonate across the erythrocyte membrane. The blood submodel was validated by its close predictions of in vitro experimental data, blood pH, pH-dependent ratio of H+, Cl−, and HCO3−concentrations in erythrocytes to that in plasma, and blood hematocrit. The blood-interstitial model was validated against available in vivo laboratory data from humans with respiratory acid-base disorders. Model predictions were used to gain understanding of the important acid-base disorder caused by addition of saline solutions. Blood model results were used as a basis for estimating errors in base excess predictions in blood by the traditional approach of Siggaard-Andersen (acid-base status) and more recent approaches by others using measured blood pH and Pco2values. Blood-interstitial model predictions were also used as a basis for assessing prediction errors of extracellular acid-base status values, such as by the standard base excess approach. Hence, these new models can give considerable insight into the physicochemical mechanisms producing acid-base disorders and aid in their diagnoses.
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48

Fogh-Andersen, N., P. J. Bjerrum, and O. Siggaard-Andersen. "Ionic binding, net charge, and Donnan effect of human serum albumin as a function of pH." Clinical Chemistry 39, no. 1 (January 1, 1993): 48–52. http://dx.doi.org/10.1093/clinchem/39.1.48.

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Abstract The ionic activities and total molalities of sodium, potassium, calcium, lithium, and chloride in a solution of human serum albumin were measured at different values of pH between 4 and 9. The same quantities were measured simultaneously in a protein-free electrolyte solution in membrane equilibrium with the albumin solution. Taking the residual liquid-junction potential and bias from unselectivity of the electrodes into account, we determined the own, bound, and net charges of albumin. Chloride was amply bound at low pH, and calcium at high pH. The varying charge of ions bound to albumin opposed the effect of acid or base on the net charge. All ions were distributed across the membrane according to the same electric potential difference, which equalled the Donnan potential. The high concordance between observation and theory favors the Donnan theory and furthermore implies that the electrodes are as accurate in a solution with albumin as in a protein-free solution.
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49

Dorrington, K. L. "Master dysnatremia equation for Gibbs-Donnan equilibrium and plasma sodium concentration: proof or spoof?" Journal of Applied Physiology 104, no. 2 (February 2008): 569. http://dx.doi.org/10.1152/japplphysiol.01167.2007.

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50

Zhou, Yaoqi, and George Stell. "The theory of semipermeable vesicles and membranes: An integral‐equation approach. II. Donnan equilibrium." Journal of Chemical Physics 89, no. 11 (December 1988): 7020–29. http://dx.doi.org/10.1063/1.455328.

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