A coherent description of nonlinear flow behavior of entangled polymers as related to processing and numerical simulations

This Feature Article describes a plausible picture of entangled polymer shear flow behavior, resulting from a decade of efforts in our laboratory to unravel the origins of a host of intricate and interconnected rheological phenomena. The first report of spurt flow by Bagley (1958) raised several key questions: Does the spurt flow reflect a constitutive failure as suggested by Vindogradov et al. (1972), Doi-Edwards (1979) and McLeish-Ball (1986)? How is it related to sharkskin, “melt fracture” and/or wall slip? The subject remained unsettled and “paradoxical” [Denn (1990)] until the 1990\u27s when a first quantitative description of polymer slip was provided by Brochard and de Gennes (1992). The experimental elucidation [Rheol. Acta1998, 37, 415] of the interfacial origin of the spurt flow led to the conclusion that the stress maximum in the Doi-Edwards theory (1979) was a theoretical artefact and to a decade of efforts to derive a constitutive description of polymer flow by incorporating Marrucci\u27s idea of convective constraint release (1996). Ongoing studies (2003–present) of constitutive flow and interfacial slip behavior of entangled polymer solutions have revealed something surprising: the entangled polybutadiene solutions appear to respond differently to rate-controlled vs. stress-controlled shear. The results [Macromolecules2004, 37, 9083] imply that there would not necessarily be a homogeneous shear field in a simple-shear apparatus in the rate-controlled mode. An effective particle tracking velocimetric (PTV) method was developed to allow determination of the velocity profile across the gap in various shear apparatuses including cone-plate and linear sliding-plate setups for startup shear, large amplitude oscillatory shear (LAOS) and step strain experiments. Our PTV observations show an initial linear velocity variation across the gap and a nonlinear velocity profile beyond the shear stress overshoot [Phys. Rev. Lett. 2006, 96, 016001], growth of shear banding in LAOS [Phys. Rev. Lett. 2006, 96, 196001] and elastic breakup of several entangled solutions after step strain [Phys. Rev. Lett. 2006, 97, 187801]. These results present great challenges to both the prevailing theoretical description of entangled polymer flow that is based on tube models and the conventional rheometric protocols used to experimentally determine constitutive flow behavior, and questions the validity to perform numerical simulations of polymer processing based on the available constitutive models