Hysteretic behavior of a moment-closure approximation for FENE model

We discuss hysteretic behaviors of dilute viscoelastic polymeric fluids with moment-closure approximation approach in extensional/enlongational flows. Polymeric fluids are modeled by the finite extensible nonlinear elastic (FENE) spring dumbbell model. Hysteresis is one of key features to describe FENE model. We here investigate the hysteretic behavior of FENE-D model introduced in [Y. Hyon et al., Multiscale Model. Simul., 7(2008), pp.978--1002]. The FENE-D model is established from a special equilibrium solution of the Fokker-Planck equation to catch extreme behavior of FENE model in large extensional flow rates. Since the hysteresis of FENE model can be seen during a relaxation in simple extensional flow employing the normal stress/the elongational viscosity versus the mean-square extension, we simulate FENE-D in simple extensional flows to investigate its hysteretic behavior comparing to FENE-P, FENE-L [G. Lielens et al., J. Non-Newtonian Fluid Mech., 76(1999), pp.249--279]. The FENE-P is a well-known pre-averaged approximated model, and it shows a good agreement to macroscopic induced stresses. However, FENE-P does not catch any hysteretic phenomenon. In contrast, the FENE-L shows a better hysteretic behavior than the other models to FENE, but it has a limitation for macroscopic induced stresses in large shear rates. On the other hand, FENE-D presents a good agreement to macroscopic induced stresses even in large shear rates, and moreover, it shows a hysteretic phenomenon in certain large flow rates.