棒状分子聚合物溶液的微宏观数值模拟

Micro-macro numerical simulation of rod-like polymeric solutions

利用微宏观耦合方法模拟了棒状分子聚合物溶液在平板Couette流动中的复杂流变行为,其中微宏观模型通过非均匀Doi理论来描述.数值模拟中,应用有限体积方法耦合求解了介观尺度上的Smoluchowski方程和宏观尺度上的流场守恒方程.数值结果不仅得到了若干种典型的流动类型,而且还预测了另外两种新的复合瑕疵结构.数值试验表明:棒状分子聚合物的流变结构主要依赖于De数、分子相对尺度以及溶液浓度常数的取值;并且De数对分子指向矢的翻滚周期、随流取向角等微观特性也均有明显影响.

In this paper the complex rheological behaviors of rod-like polymer solutions in plane Couette flow are studied using micro-macro simulation. The micro-macro model is described by Doi theory with local inhomogeneous fluid. The finite volume method is used to solve the conservation equation on the macroscopic level and the Smoluchowski equation on the microscopic level in the numerical simulation. The numerical results predict several plane flow modes including some typical plane modes and two new complicated modes. Furthermore,simulation results show that the rheological phase diagrams for solutions of rigid rod molecules are mainly dependent on the Deborah number,the concentration of solutions and molecular scale,and the varying Deborah number have great influence on some micro-properties of tumbling period and orientation angle of flow-aligning.