Modifying the pom-pom model for extensional viscosity overshoots
(2013) British Applied Mathematics Colloquium — Location: Leeds, UK
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- Abstract
- (en) Extensional experiments, on commercial polymer melts which are highly and randomly branched, using rheometers that lack of a feedback mechanism to control extension rates, indicate an extensional hardening behaviour [1]. However, after a particular time (Henky strain) in the hardening regime the samples break or become inhomogeneous and a steady state is not achieved with these devices [1,2,3]. Experiments performed with a Filament Stretch Rheometer (FSR) [1,4,5], that has a feedback mechanism and is able to reach a steady state, indicate that after the initial increase in the hardening regime the extensional viscosity goes through an overshoot before it reaches its steady state. Furthermore, relaxation measurements using the same device indicate that stress relaxation when flow is ceased after the overshoot occurs faster compared to stress relaxation when the flow is ceased before the overshoot. Previous models [2,5] based on the pom-pom theory [3] are unable to capture all experimental trends. Here, we modify the original pom-pom theory [3] to enable overshoots. In addition, we use a multimode version of our modified pom-pom model in order to fit the experimental data from the FSR device. Central to the modification is the assumption that at strong flows some of the entanglements are stripped off due to branch point withdrawal. [1] G.H. McKinle and T. T. Sridhar. Filament-stretching rheometry of complex fluids. Annual Review of Fluid Mechanics, 34:375–415, 2002. [2] N.J. Inkson, T.C.B. McLeish, O.G. Harlen, and D.J. Groves. Predicting low density polyethylene melt rheology in elongational and shear flows with “pom-pom” constitutive equations. The Journal of Rheology, 43:873–896, 1999. [3] T.C.B McLeish and R.G. Larson. Molecular constitutive equations for a class of branched polymers: The pom-pom polymer. The Journal of Rheology, 42:81–110, 1998. [4] H.K. Rasmussen, J.K. Nielsen, A. Bach, and O. Hassager, J. Rheology 49, 369 (2005). [5] D.M. Hoyle, Q. Huang, D. Auhl, D. Hassell, H.K. Rasmussen, A.L. Skov, O.G. Harlen, O. Hassager, and T.C.B. McLeish. Transient overshoot extensional rheology of long-chain branched polyethylenes: Experimental and numerical comparisons between filament stretching and cross-slot flow. Journal of Rheology, 57(1):293–313, 2013.
- Affiliations
Department of Applied Mathematics University of Leeds
Citations
Hawke, L. G. D., & Read, D. J. (2013). Modifying the pom-pom model for extensional viscosity overshoots. British Applied Mathematics Colloquium, Leeds, UK. https://hdl.handle.net/2078.5/180844