Interface behavior of physical hydrogel subject to solution-gel phase transition and nonlinear deformation

Abstract

In this paper, a multiphysics model is developed for simulation of the interface behavior of physical hydrogel subject to solution-gel phase transition and nonlinear deformation, in which the solution and gel states are considered as two distinct phases and separated by a sharp interface approach. The presently developed model accounts for the multiphysics effects of the mechanical, chemical and thermal coupled fields. Apart from the classical governing equations for mass and energy conservations, and for the force equilibrium in the two bulk phases and on their interface, an additional equilibrium equation for a so-called configurational force is imposed in the two bulk phases and on their interface for the effect of the solution-gel phase transition. The corresponding configurational heating and mass supply are also proposed to account for energy change due to the migration of the control volume. By the second law of thermodynamics, the constitutive equations are formulated, including an evolution equation for the interface. The present model will reduce to Suo's non-equilibrium thermodynamic theory, if the interface is ignored when only a single bulk phase exists, i.e. no phase transition occurs. In order to model the phase behavior of physical hydrogel, which directly results from breaking and forming of crosslinks, a novel formulation of the free energy is proposed, which accounts for the effect of crosslink density to characterize the phases, and may reduce to that for a chemical hydrogel when the crosslink density is constant. Moreover, the present model may also reduce to Ji's work that coupled the mechanical field with the thermal field if the chemical field is ignored, or to Dolbow's chemo-mechanical model when the thermal field is ignored. Therefore, the present model is more generalized since the mechanical field is coupled with both the thermal and chemical fields simultaneously, and thus is able to model both the bulk phase and the interface behaviors. As case studies, the system at equilibrium state and a spherically symmetrical solution-gel phase transition at non-equilibrium states are investigated numerically for analysis of the effects of mobility, surface tension and other parameters on the interface behavior.