Theory Manual Version 3.4
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Subsection 5.2.8: Donnan Equilibrium Swelling Up Section 5.2: Compressible Materials Subsection 5.2.10: Large Poisson's Ratio Ligament

5.2.9 Perfect Osmometer Equilibrium Osmotic Pressure

The swelling pressure is described by the equations for a perfect osmometer, assuming that the material is porous, containing an interstitial solution whose solutes cannot be exchanged with the external bathing environment. Similarly, solutes in the external bathing solution cannot be exchanged with the interstitial fluid of the porous material. Therefore, osmotic pressurization occurs when there is an imbalance between the interstitial and bathing solution osmolarities. Since osmotic swelling must be resisted by a solid matrix, this material is not stable on its own. It must be combined with an elastic material that resists the swelling.
The Cauchy stress for this material is the stress from the perfect osmometer equilibrium response [4]: where is the osmotic pressure, given by Here, is the universal gas constant and is the absolute temperature, is the external bath osmolarity and is the interstitial fluid osmolarity in the current configuration, related to the reference configuration osmolarity via,
Though this material is porous, this is not a full-fledged poroelastic material. The behavior described by this material is strictly valid only after the transient response of interstitial fluid and solute fluxes has subsided. The corresponding spatial elasticity tensor is
Subsection 5.2.8: Donnan Equilibrium Swelling Up Section 5.2: Compressible Materials Subsection 5.2.10: Large Poisson's Ratio Ligament