Phase-field model for liquid–solid phase transition of physical hydrogel in an ionized environment subject to electro–chemo–thermo–mechanical coupled field

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In this paper, a phase-field model is developed for simulation of the phase transition of physical hydrogels between the liquid solution and solid gel states in an ionized environment, subject to an externally applied electro-chemo-thermo-mechanical multiphysics coupled field. The presently developed model consists of the governing equations for the equilibrium of forces, the conservations of energy and mass, and the Maxwell's equations. Based on the second law of thermodynamics, the constitutive equations are formulated from the entropy viewpoint, including a novel Ginzburg–Landau type of free energy with the effect of crosslink density, which may be reduced to that for a chemical hydrogel if a constant crosslink density is considered. In order to identify the phases for the present domain covering the gel and solution states, the crosslink density is defined as a novel phase field in such a way that the solution phase is identified when the crosslink density is small, while the gel identified if the crosslink density becomes large, and an addition kinetic equation is imposed on the crosslink density as the phase field for phase transition. It is examined that the present model can be reduced to a published non-equilibrium thermodynamic theory, if the interface is ignored when only a single bulk phase exists, i.e. no phase transition occurs. Furthermore, the mechanical field formulated in the present paper is coupled with the thermal, electrical, and chemical multiphysics fields simultaneously, while the mechanical fields in the published works were coupled with either the thermal or electro–chemical field only. As a case study, the system at equilibrium state is investigated numerically to analyze the influences of the electrical and chemical potentials as well as mechanical pressure externally imposed on the boundary of the system domain. Another case study presents a spherically symmetrical liquid-solid phase transition at non-equilibrium states in an ionized environment, with the emphasis on the evolutions of the interface, crosslink density and chemical potentials.