Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics

S. Stephanou, Pavlos; Ch. Tsimouri, Ioanna; G. Mavrantzas, Vlasis

doi:10.3390/ma13122867

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Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics

Pavlos S. Stephanou

^1,*

Ioanna Ch. Tsimouri

² and

Vlasis G. Mavrantzas

^3,4

Department of Chemical Engineering, Cyprus University of Technology, 30 Archbishop Kyprianou Str., Limassol 3036, Cyprus

Department of Materials, ETH Zürich, CH-8093 Zürich, Switzerland

Department of Chemical Engineering, University of Patras & FORTH-ICE/HT, GR-26504 Patras, Greece

⁴

Particle Technology Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, Sonneggstrasse 3, CH-8092 Zürich, Switzerland

Author to whom correspondence should be addressed.

Materials 2020, 13(12), 2867; https://doi.org/10.3390/ma13122867

Received: 8 June 2020 / Revised: 18 June 2020 / Accepted: 22 June 2020 / Published: 26 June 2020

(This article belongs to the Special Issue Rheology of Advanced Complex Fluids)

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Abstract

In a recent reformulation of the Marrucci-Ianniruberto constitutive equation for the rheology of entangled polymer melts in the context of nonequilibrium thermodynamics, rather large values of the convective constraint release parameter β_ccr had to be used in order for the model not to violate the second law of thermodynamics. In this work, we present an appropriate modification of the model, which avoids the splitting of the evolution equation for the conformation tensor into an orientation and a stretching part. Then, thermodynamic admissibility simply dictates that β_ccr ≥ 0, thus allowing for more realistic values of β_ccr to be chosen. Moreover, and in view of recent experimental evidence for a transient stress undershoot (following the overshoot) at high shear rates, whose origin may be traced back to molecular tumbling, we have incorporated additional terms into the model accounting, at least in an approximate way, for non-affine deformation through a slip parameter ξ. Use of the new model to describe available experimental data for the transient and steady-state shear and elongational rheology of entangled polystyrene melts and concentrated solutions shows close agreement. Overall, the modified model proposed here combines simplicity with accuracy, which renders it an excellent choice for managing complex viscoelastic fluid flows in large-scale numerical calculations. View Full-Text

Keywords: entangled polymer melts; concentrated polymer solutions; nonequilibrium thermodynamics; polymer tumbling; transient shear viscosity undershoot

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MDPI and ACS Style

S. Stephanou, P.; Ch. Tsimouri, I.; G. Mavrantzas, V. Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics. Materials 2020, 13, 2867. https://doi.org/10.3390/ma13122867

AMA Style

S. Stephanou P, Ch. Tsimouri I, G. Mavrantzas V. Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics. Materials. 2020; 13(12):2867. https://doi.org/10.3390/ma13122867

Chicago/Turabian Style

S. Stephanou, Pavlos, Ioanna Ch. Tsimouri, and Vlasis G. Mavrantzas. 2020. "Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics" Materials 13, no. 12: 2867. https://doi.org/10.3390/ma13122867

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Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics

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