Deficiencies of FENE dumbbell models in describing the rapid stretching of dilute polymer solutions

Abstract

A wide variety of bead-spring kinetic theory models have been proposed to explain the stress growth and hysteretic behavior of dilute polymer solutions in uniaxial extension. We analyze the Kramers chain, a fine-scale model for polymer dynamics, in order to assess the validity of the coarser-grained bead-spring models in these deformations. Whereas the spring force is a simple function of the dumbbell length for the FENE spring, we find that the relationship between the ensemble-averaged end-to-end force and the extension for a Kramers chain depends on the kinematic history to which it has been subjected. In a quiescent fluid, the Kramers chain force–extension relationship is identical to the FENE force law. However, during start up of elongational flow, the ensemble-averaged end-to-end force for a given (end-to-end) length of the molecule increases with strain until steady state is reached. If the extensional flow is suddenly stopped, the Kramers chain force–extension relationship relaxes back to the FEN...