A diffuse‐interface modeling for liquid solution–solid gel phase transition of physical hydrogel with nonlinear deformation

Abstract

A diffuse-interface model is presented in this paper for simulation of the evolution of phase transition between the liquid solution and solid gel states for physical hydrogel with nonlinear deformation. The present domain covers the gel and solution states as well as a diffuse interface between them. They are indicated by the crosslink density in such a way that the solution phase is identified as the state when the crosslink density is small, while the gel as the state if the crosslink density becomes large. In this work, a novel order parameter is thus defined as the crosslink density, which is homogeneous in each distinct phase and smoothly varies over the interface from one phase to another. In this model, the constitutive equations, imposed on the two distinct phases and the interface, are formulated by the second law of thermodynamics, which are in the same form as those derived by a different approach. The present constitutive equations include a novel Ginzburg-Landau type of free energy with a double-well profile, which accounts for the effect of crosslink density. The present governing equations include the equilibrium of forces, the conservations of mass and energy, and an additional kinetic equation imposed for phase transition, in which nonlinear deformation is considered. The equilibrium state is investigated numerically, where two stable phases are observed in the free energy profile. As case studies, a spherically symmetrical solution-gel phase transition is simulated numerically for analysis of the phase transition of physical hydrogel.

A review on recent development of theoretical modeling of hydrogel phase behavior subject to mechanics and multiphysics coupled effects

“…where the parameter β is a measurement for the stiffness of the interface relative to the bulk. With respect to physical hydrogels, the authors proposed an electro-chemo-thermo-mechanical coupled phase-field model through taking the crosslink density ρ as a novel order parameter, since the state of physical hydrogel is directly related to ρ [85,86], in which the interface free energy is in the form of…”

“…(21)- (24) and (28) of the sharp interface model [69,70]. Consequently, the interfacial evolution and accompanying phenomena during the gel-sol phase transition are investigated for physical hydrogels by this model [85,86].…”