Multiscale Simulations of Flows of a Well-Entangled Polymer Melt in a Contraction-Expansion Channel

We have successfully applied a multiscale simulation (MSS) method [Murashima, T.; Taniguchi, T. Europhys. Lett. 2011, 96, 18002] to flows of a monodispersed linear entangled polymer melt in a contraction-expansion channel. In our MSS method, a macroscopic model is coupled with a microscopic model through the velocity gradient tensor and the stress tensor. The smoothed particle hydrodynamics (SPH) method is employed as the macroscopic model, and a slip-link model is employed as the microscopic model. Two-dimensional flows in a 4:1:4 contraction-expansion channel are examined using our MSS method. From our MSSs, we have evaluated detailed microscopic information from the polymer chain dynamics, such as the local orientation of polymer chains, the average number of entanglements, and the number density of entanglements along a polymer chain. To further understand entanglements on a chain in a polymer melt under flows, we have developed a model equation that describes the time evolution of the number density of entanglements along a polymer chain. The model equation can successfully reproduce the profile of the number density of entanglements along a polymer chain in steady states. These microscopic insights will provide us with a stepping stone for designing a polymer melt that has a specific property.