Poroelasticity and Diffusion in Elastic Solids Shengqiang Cai

Poroelasticity and Diffusion in Elastic Solids Shengqiang Cai 2021/2/20

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 Pump, m Solvent Weight, P

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

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

A test of soil (Biot) U t

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

Nonlinear models for gels Physically Mathematically Constitutive law

Force balance Kinetics law Kinetic process Diffusion in true quantities 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 B A Stretch distribution a 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