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A review of thermodynamic concepts
Published in Ronald L. Fournier, Basic Transport Phenomena in Biomedical Engineering, 2017
The net charge of the macromolecule will create, at equilibrium, an uneven distribution of these small ions between the region that contains the macromolecule and the region on the other side of the semipermeable membrane that does not have the macromolecule. This difference in the concentrations of these ions will then create an osmotic pressure difference across the semipermeable membrane because the “solvent” on the macromolecule side of the semipermeable membrane is not the same as the “solvent” on the opposite side of the semipermeable membrane. This means that when finding the osmotic pressure of the macromolecule in an electrolyte solution, we will need to correct for what is known as the Gibbs-Donnan effect. Here, we will find an expression that allows for the calculation of this correction to the osmotic pressure of a macromolecule in a solution with a 1:1 electrolyte like NaCl.
Simulating cerebral edema and delayed fatality after traumatic brain injury using triphasic swelling biomechanics
Published in Traffic Injury Prevention, 2019
Andrew V. Basilio, Peng Xu, Yukou Takahashi, Toshiyuki Yanaoka, Hisaki Sugaya, Gerard A. Ateshian, Barclay Morrison
Since electroneutrality must be satisfied at every point in the mixture, the concentrations of ions inside the mixture are affected by the FCD, such that they differ from those in the surrounding fluid bath. The imbalance of ion concentrations between the interstitial and external fluids is called the Gibbs-Donnan effect; it produces an osmotic pressure difference between the interstitial fluid and external bath, called the Gibbs-Donnan pressure (Overbeek 1956). Under steady-state conditions, when the fluxes of interstitial fluid and ions have subsided, the hydraulic pressure reduces to zero so that the only contribution to the interstitial fluid pressure is the Gibbs-Donnan osmotic pressure, given by where is the universal gas constant, is the absolute temperature in the tissue and bath, and and respectively represent the ambient pressure and osmolarity of the external bath fluid. This expression was derived under the assumption of ideal physico-chemical conditions for mixtures containing two monovalent counter-ions. It is common to set so that represents the gage pressure.