Multiscale simulation of polymer melt spinning by using the dumbbell model

We investigated the spinning process of a polymeric material by using a multiscale simulation method which connects the macroscopic and microscopic states through the stress and strain-rate tensor fields, by using Lagrangian particles (filled with polymer chains) along the spinning line. We introduce a large number of Lagrangian fluid particles into the fluid, each containing Np-Hookean-dumbbells to mimic the polymer chains (Np=$10^4$), which is equivalent to the upper convected Maxwell fluid in the limit that Np$\rightarrow \infty$. Depending on the Reynolds number Re, we studied the dynamical behaviors of fibers for the (a) Re =0 and (b) finite Re cases, for different draw ratios Dr, ranging from 10 to 30, and two typical Deborah numbers De=$10^{-3}$ and De=$10^{-2}$. In the limit Re$\rightarrow$ 0 (a), as the Deborah number De increases, the elastic effect makes the system stable. At finite Re (b), we found that inertial effects play an important role in determining the dynamical behavior of the spinning process, and for Dr=$10^{-2}$ the system is quite stable, at least up to a draw ratio of Dr=30. We also found that the fiber velocity and cross section area are determined solely by the draw ratio. By comparing the velocity and cross section area profiles with the end-point distribution for the dumbbell connective vectors, for dumbbells located in Lagrangian particles along typical places along the spinning line, we show that our multiscale simulation method successfully bridges the microscopic state of the system with its simultaneous macroscopic flow behavior. It is also confirmed that the present schemes gives good agreements with the results obtained by the Maxwell constitutive equation.