Multi-Scale Simulation of Well-Entangled Polymer Melt Flows in a Channel

Abstract

In order to produce better polymeric goods, it is important to predict and to control a flow behavior of a polymeric fluid. To understand a flow behavior of a polymeric fluid, computational approach is quite effective. It is well-known that polymeric fluids exhibit complex flow behaviors owing to a strong correlation between the state of macroscopic flow and the microscopic state of polymer chains. The complex flow behaviors are originated from the stress tensor in the Cauchy momentum equation. When solving the equation, a constitutive equation is usually used to evaluate the stress tensor from the local deformation rate tensor and a set of parameters. By using a constitutive equation, however, it is difficult to reflect the microscopic state to the macroscopic flow. As one of the methods to overcome the difficulty, it has been proposed to use a multi-scale simulation (MSS) method where local microscopic states and the macroscopic flow are directly connecting each other. So far, the MSS method has succeeded in predicting the flow in simpler geometries such as a flow in between two parallel plates and polymer melt flows passing a circular object in a two-dimensional periodic system. To develop further the MSS method that can deal with more industrially oriented problems, it is necessarily to investigate the applicability of the method to a flow in complicated geometry of boundary. In this context, we have applied the multiscale simulation technique to flows of polymer melts in a channel with 4:1:4 contraction and expansion geometry. In the MSS method, we introduced Lagrangian particles which contain many chains to precisely maintain the microscopic states. As the microscopic polymer model, a slip-link model is used. Using the multiscale simulation method, we investigated the macroscopic spatial distribution of microscopic quantities, such as the spatial distribution of polymer chain orientation and the number of entanglements. We found that the number of entanglements strongly decreases around the middle of the polymer chains. This kind of information can be helpful when designing polymer melts with specific properties.