Modeling phase inversion using Cahn-Hilliard equations – Influence of the mobility on the pattern formation dynamics

Abstract This paper presents a phase-field simulation of phase separation for a polymer/solvent system and aims at investigating in a systematic way the influence of the mobility model on the simulation results. In 2D geometry, the Flory-Huggins theory was used to describe the thermodynamics of the PMMA/cyclohexanol system and four mobility models were tested: a constant model, a slow model, a fast model and a mobility model based on the free-volume theory of Vrentas. The simulated patterns were analyzed by Fourier transform and using Minkowski descriptors. Growth laws deduced from a Fourier Transform of the patterns exhibited that the power laws were ranged between 1/5 and 1/3 depending on the quenching conditions ( T and initial composition) and the mobility model. Using the Vrentas mobility model, growth laws of L c ∼ t 1 / 5 , L c ∼ t 1 / 4 and L c ∼ t 1 / 3 were found for initial compositions in the range ϕ init = 0.075 , 0.140 and 0.200, respectively, whereas due to faster phase inversion dynamics, a growth law close to L c ∼ t 1 / 3 was simulated for the constant mobility model whatever the quenching conditions ( T and initial composition), thus demonstrating the importance to choose an appropriate mobility model for simulating the phase separation of polymer/solvent system.