Viscoelasticity and poroelasticity in elastomeric gels

An elastomeric gel is a mixture of a polymer network and a solvent. In response to changes in mechanical forces and in the chemical potential of the solvent in the environment, the gel evolves by two concurrent molecular processes: the conformational change of the network, and the migration of the solvent. The two processes result in viscoelasticity and poroelasticity, and are characterized by two material-specific properties: the time of viscoelastic relaxation and the effective diffusivity of the solvent through the network. The two properties define a material-specific length. The material-specific time and length enable us to discuss macroscopic observations made over different lengths and times, and identify limiting conditions in which viscoelastic and poroelastic relaxations have either completed or yet started. We formulate a model of homogeneous deformation, and use several examples to illustrate viscoelasticity-limited solvent migration, where the migration of the solvent is pronounced, but the size of the gel is so small that the rate of change is limited by viscoelasticity. We further describe a theory that evolves a gel through inhomogeneous states. Both infinitesimal and finite deformation are considered.