Abstract
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.
Highlights
Long-chain polymers may crosslink by strong chemical bonds into a three-dimensional network
We will develop a finite element method using the free-energy function of Flory and Rhener1943͒ and the kinetic model proposed by Hong et al
V where N is the number of polymer chains in the gel divided by the volume of the gel in the reference state, kT is the temperature in the unit of energy, v is the volume per solvent molecule, and is a dimensionless parameter characterizing the enthalpy of mixing
Summary
Long-chain polymers may crosslink by strong chemical bonds into a three-dimensional network. This paper studies the concurrent deformation and migration in the gel by a finite element method. Biot1941͒ combined the thermodynamic theory and Darcy’s law for mass transport in a porous medium Both Gibbs and Biot used phenomenological freeenergy functions, and their works were not specific for the polymeric gel. Suematsu et al. conducted the threedimensional explicit finite element analysis to study the pattern formation of swelling gels by introducing a friction constant between the polymeric chains and solvents.. Dolbow et al. used a hybrid eXtended-Finite-Element/Level-Set method to study the swelling of gels. We will develop a finite element method using the free-energy function of Flory and Rhener1943͒ and the kinetic model proposed by Hong et al..
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