A critical and constructive analysis of nonstretching approximations in a family of Rolie-Poly models

Entangled polymers are an important class of materials for their toughness, processability, and functionalizability. During processing, deformation introduces elastic stresses due to a combination of polymer orientation and polymer stretching. For many flows, however, the elastic contribution from chain stretching is not significant, and so-called “nonstretching” approximations have been developed to help explain and interpret experimental observations. Unfortunately, these nonstretching models tend to be limited to simple polymer formulations (linear and monodisperse) and are not useful for understanding any effects from marginal chain stretching that may be present. In this paper, we show that nonstretching approximations can be formally constructed as a perturbation expansion starting from a fully stretching constitutive equation. We apply this framework to the Rolie-Poly model, deriving the existing nonstretching variation and expanding to the second order. The second-order continuation provides quantitatively improved accuracy for both steady and unsteady flows and prevents a pathological/nonphysical blowup that can occur when effects from marginal chain stretching are ignored. We also derive and discuss leading order nonstretching approximations for more complex models of entangled polymers, accounting for disentanglement dynamics, polydispersity, and reversible scission reactions. Alternatives to the formal perturbation framework are also discussed, with potential trade-offs between accuracy, versatility, and computational cost.