剪切流场中聚乙烯结晶过程的建模与模拟

Numerical simulation of morphology and kinetics of polyethylene in shear flow

基于Eder模型推导了剪切流场中球晶、串晶形态演化的数学模型,将第一法向应力差作为串晶成核的驱动,并引入两相悬浮模型描述体系,认为其由无定形相和半结晶相组成,分别用FENE-P模型和刚性哑铃模型描述。基于上述数学模型,分别构造了捕捉球晶、串晶生长的Monte Carlo法与体系控制方程求解的有限差分法,成功模拟了二维剪切流场中聚乙烯的结晶过程,给出了球晶、串晶的形态演化,分析了剪切时间、剪切速率对串晶成核密度、结晶速率、流体黏度等的影响。数值结果表明:所构造的Monte Carlo法合理有效,不仅成功捕捉了晶体的生长与碰撞,而且较为准确地预测了结晶速率。此外,提高剪切时间或剪切速率,将增加串晶成核密度、提高结晶速率、使流体黏度突增的时间点提前。

The mathematical model of morphology evolution of spherulites and shish-kebabs in the shear flow is deduced based on the Eder model. The model considers that the nucleation and growth of spherulites are determined by the static temperature, while the nucleation and growth of shish-kebabs are determined by the flow, which is depended on the first normal stress difference of the system and the shear rate respectively. In order to calculate the nucleation density of the shish-kebabs, the two-phase suspension model of Zheng is introduced. The model treats the stress as the combination of the amorphous phase and semi-crystalline phase. The amorphous phase is described by FENE-P model while the semi-crystalline phase is depicted by a rigid dumbbell model. Based on the mathematical model, the Monte Carlo method and the finite difference method are constructed, respectively. The former is to capture the crystal growth while the latter is to calculate the equation of the system. By using these methods, the 2D crystallization in the shear flow is simulated. The evolution of spherulites and shish-kebabs is given. Also, the effects of shear time and shear rate on the nucleation density of shish-kebabs, crystallization rate, the viscosity of the fluid and the system stress are discussed. Numerical results show that the Monte Carlo method is valid which not only captures the morphology evolution of crystals successfully, but also predicts the crystallization rate well. In addition, the increase of the shear time or the shear rate will increase the nucleation density of shish-kebabs and the crystallization rate.