Liquid–solid phase transition of physical hydrogels subject to an externally applied electro-chemo-mechanical coupled field with mobile ionic species

Abstract

In this study, a model was multiphysically developed for the simulation of the phase transition of physical hydrogels between liquid solution and solid gel states, subject to an electro-chemo-mechanically coupled field, with the effect of the mobile ionic species in the solution. The present model consists of the governing equations for the equilibrium of forces and the conservation of mass, Maxwell's equations, and an evolution equation for the interface. Based on the second law of thermodynamics, the constitutive equations are formulated from the energy viewpoint, including a novel formulation of free energy with the effect of crosslink density. The present model may be reduced to Suo's non-equilibrium thermodynamic theory if the interface is ignored when only a single phase exists. It may also be reduced to Dolbow's model for gel–gel phase transition when the electric field is ignored. Therefore, the present model becomes more generalized since it is able to represent both the bulk phase and the interface behaviors, and the mechanical field is simultaneously coupled with both the electric and chemical fields. In the first case study, the system at equilibrium state was numerically investigated for analysis of the influences of the electrical and chemical potentials as well as the mechanical pressure externally imposed on the boundary of the system domain. The second case study presents a spherically symmetrical solution–gel phase transition at non-equilibrium states, with the emphasis on the evolution of both the interface and electrochemical potentials.