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Poroelasticity and Diffusion in Elastic Solids. Shengqiang Cai. Examples of diffusion in elastic solids. Migration of water into sponges Consolidation of soil Swelling of gels Tissues of animals and plants Insertion of Li-ions in electrodes. Pump, m. Solvent. Weight, P.

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## Poroelasticity and Diffusion in Elastic Solids

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**Poroelasticity and Diffusion in Elastic Solids**Shengqiang Cai**Examples of diffusion in elastic solids**• Migration of water into sponges • Consolidation of soil • Swelling of gels • Tissues of animals and plants • Insertion of Li-ions in electrodes**Pump, m**Solvent Weight, P Thermodynamic framework of poroelasticity**Linear poroelasticity**Free energy Material law Force balance Darcy’s law**B.C.**Stress in a thin film due to change of the humidity in the enviroment Stress in a body induced by drying**U**t A test of soil (Biot)**Flory-Rehner free energy**• Swelling decreases entropy by straightening polymers. • Swelling increases entropy by mixing solvent and polymers. Free-energy function Free energy of mixing Flory, Rehner, J. Chem. Phys., 11, 521 (1943) Free energy of stretching**Nonlinear models for gels**Physically Mathematically Constitutive law**Force balance**Kinetics law Diffusion in true quantities Kinetic process Mass conservation**Swelling process of a gel ball**Geometrical relationship Force balance Constitutive law Force balance**Mass conservation**Chemical potential driven flux Incompressibility assumption Diffusion equation**My research: Swelling Packer in Oil Industry**A product of TAM Company “Swelling Elastomers” talk given by John Dewar in SPE conference The most important problems engineers concerned are: How long does the swelling packer take to attain equilibrium? How does the sealing force depend on the controllable parameters?**Stretches and Stress Distribution**B A b a Stretch distribution Stress distribution**Kinetics of Swelling Packer**B A b a b/B=1.2 Nv=0.01**Summary**• Thermodynamic framework for diffusion in porous media has been established • Linear model for porouselasticity has been analyzed • Non linear model for hydrogel has been setup

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