A Finite Element Method for Transient Analysis of Concurrent Large Deformation and Mass Transport in Gels

A gel is an aggregate of polymers and solvent molecules. The polymers crosslink into a three-dimensional network by strong chemical bonds, and enable the gel to retain its shape after a large deformation. The solvent molecules, however, interact among themselves and with the network by weak physical bonds, and enable the gel to be a conduit of mass transport. The time-dependent concurrent process of large deformation and mass transport is studied by developing a finite element method. We combine the kinematics of large deformation, the conservation of the solvent molecules, the conditions of local equilibrium, and the kinetics of migration to evolve simultaneously two fields: the displacement of the network and the chemical potential of the solvent. The finite element method is demonstrated by analyzing several phenomena, such as swelling, draining and buckling. This work builds a platform to study diverse phenomena in gels with spatial and temporal complexity.