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Open AccessArticle

Tumbling-Snake Model for Polymeric Liquids Subjected to Biaxial Elongational Flows with a Focus on Planar Elongation

1
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus
2
Polymer Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
*
Authors to whom correspondence should be addressed.
Polymers 2018, 10(3), 329; https://doi.org/10.3390/polym10030329
Received: 6 March 2018 / Revised: 14 March 2018 / Accepted: 14 March 2018 / Published: 16 March 2018
(This article belongs to the Special Issue Polymer Dynamics)
We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate. View Full-Text
Keywords: polymer melt; stochastic differential equation; link tension coefficient; entanglements; biaxial flow polymer melt; stochastic differential equation; link tension coefficient; entanglements; biaxial flow
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MDPI and ACS Style

Stephanou, P.S.; Kröger, M. Tumbling-Snake Model for Polymeric Liquids Subjected to Biaxial Elongational Flows with a Focus on Planar Elongation. Polymers 2018, 10, 329.

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