Prediction of the effects of constitutive viscoelasticity on stress-diffusion coupling in gels

Modeling of stress/diffusion coupling in gels, originally developed by Doi for the case where the solid component of the gel is a linear elastic network, is here extended to the case of a linear viscoelastic solid component, thereby allowing for a mechanism of intrinsic relaxation. The extended model is solved for a cylindrical gel subjected to unconfined uniaxial compression. Depending on the respective values of the two characteristic times, i.e., diffusive and viscoelastic, measurable quantities like axial force and external radius of the cylindrical gel are calculated to display different qualitative behaviors. Calculated results for the case of uniaxial traction are also reported, which compare favorably with some available experimental results.