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

Thermodynamic framework of poroelasticity Weight, P Solvent Pump, 

Linear poroelasticity Free energy Material law Force balance Darcy’s law

Stress in a body induced by drying B.C. Stress in a thin film due to change of the humidity in the enviroment

A test of soil (Biot) t U

Flory-Rehner free energy Free energy of stretching Flory, Rehner, J. Chem. Phys., 11, 521 (1943) Swelling decreases entropy by straightening polymers. Swelling increases entropy by mixing solvent and polymers. Free energy of mixing Free-energy function

Nonlinear models for gels Physically Mathematically Constitutive law

Kinetic process Diffusion in true quantities Mass conservation Force balance Kinetics law

Swelling process of a gel ball Force balance Geometrical relationship Constitutive law Force balance

Mass conservation Chemical potential driven flux Incompressibility assumption Diffusion equation

My research: Swelling Packer in Oil Industry “Swelling Elastomers” talk given by John Dewar in SPE conferenceA product of TAM Company 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 distributionStress distribution

B A b a Kinetics of Swelling Packer 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