Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics
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 <i>β<sub>ccr</sub></i> had to be used i...
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MDPI AG
2020-06-01
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| Online Access: | https://www.mdpi.com/1996-1944/13/12/2867 |
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| author | Pavlos S. Stephanou Ioanna Ch. Tsimouri Vlasis G. Mavrantzas |
| author_facet | Pavlos S. Stephanou Ioanna Ch. Tsimouri Vlasis G. Mavrantzas |
| author_sort | Pavlos S. Stephanou |
| collection | DOAJ |
| description | 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 <i>β<sub>ccr</sub></i> 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 <i>β<sub>ccr</sub></i> ≥ 0, thus allowing for more realistic values of <i>β<sub>ccr</sub></i> 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 <i>ξ</i>. 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. |
| first_indexed | 2024-03-10T18:52:39Z |
| format | Article |
| id | doaj.art-be8c90065d534ef797ae1ed7069952de |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-10T18:52:39Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-be8c90065d534ef797ae1ed7069952de2023-11-20T05:03:34ZengMDPI AGMaterials1996-19442020-06-011312286710.3390/ma13122867Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium ThermodynamicsPavlos S. Stephanou0Ioanna Ch. Tsimouri1Vlasis G. Mavrantzas2Department of Chemical Engineering, Cyprus University of Technology, 30 Archbishop Kyprianou Str., Limassol 3036, CyprusDepartment of Materials, ETH Zürich, CH-8093 Zürich, SwitzerlandDepartment of Chemical Engineering, University of Patras & FORTH-ICE/HT, GR-26504 Patras, GreeceIn 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 <i>β<sub>ccr</sub></i> 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 <i>β<sub>ccr</sub></i> ≥ 0, thus allowing for more realistic values of <i>β<sub>ccr</sub></i> 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 <i>ξ</i>. 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.https://www.mdpi.com/1996-1944/13/12/2867entangled polymer meltsconcentrated polymer solutionsnonequilibrium thermodynamicspolymer tumblingtransient shear viscosity undershoot |
| spellingShingle | Pavlos S. Stephanou Ioanna Ch. Tsimouri Vlasis G. Mavrantzas Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics Materials entangled polymer melts concentrated polymer solutions nonequilibrium thermodynamics polymer tumbling transient shear viscosity undershoot |
| title | Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics |
| title_full | Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics |
| title_fullStr | Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics |
| title_full_unstemmed | Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics |
| title_short | Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics |
| title_sort | simple accurate and user friendly differential constitutive model for the rheology of entangled polymer melts and solutions from nonequilibrium thermodynamics |
| topic | entangled polymer melts concentrated polymer solutions nonequilibrium thermodynamics polymer tumbling transient shear viscosity undershoot |
| url | https://www.mdpi.com/1996-1944/13/12/2867 |
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