Analysis of a viscosity model for concentrated polymers
The paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier-Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic-hyperbolic integro-differential equation describing the evolution of the polymer distribu...
| Main Authors: | , , , |
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| Format: | Journal article |
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World Scientific Publishing
2016
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| _version_ | 1797104115898122240 |
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| author | Bulíček, M Gwiazda, P Süli, E Świerczewska-Gwiazda, A |
| author_facet | Bulíček, M Gwiazda, P Süli, E Świerczewska-Gwiazda, A |
| author_sort | Bulíček, M |
| collection | OXFORD |
| description | The paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier-Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic-hyperbolic integro-differential equation describing the evolution of the polymer distribution function in the solvent, and a parabolic integro-differential equation for the evolution of the monomer density function in the solvent. The viscosity coefficient appearing in the balance of linear momentum equation in the Navier-Stokes system includes dependence on the shear-rate as well as on the weight-averaged polymer chain length. The system of partial differential equations under consideration captures the impact of polymerization and depolymerization effects on the viscosity of the fluid. We prove the existence of global-in-time, large-data weak solutions under fairly general hypotheses. |
| first_indexed | 2024-03-07T06:29:17Z |
| format | Journal article |
| id | oxford-uuid:f568e927-c063-4445-813c-510fe83de22a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:29:17Z |
| publishDate | 2016 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:f568e927-c063-4445-813c-510fe83de22a2022-03-27T12:27:07ZAnalysis of a viscosity model for concentrated polymersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f568e927-c063-4445-813c-510fe83de22aSymplectic Elements at OxfordWorld Scientific Publishing2016Bulíček, MGwiazda, PSüli, EŚwierczewska-Gwiazda, AThe paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier-Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic-hyperbolic integro-differential equation describing the evolution of the polymer distribution function in the solvent, and a parabolic integro-differential equation for the evolution of the monomer density function in the solvent. The viscosity coefficient appearing in the balance of linear momentum equation in the Navier-Stokes system includes dependence on the shear-rate as well as on the weight-averaged polymer chain length. The system of partial differential equations under consideration captures the impact of polymerization and depolymerization effects on the viscosity of the fluid. We prove the existence of global-in-time, large-data weak solutions under fairly general hypotheses. |
| spellingShingle | Bulíček, M Gwiazda, P Süli, E Świerczewska-Gwiazda, A Analysis of a viscosity model for concentrated polymers |
| title | Analysis of a viscosity model for concentrated polymers |
| title_full | Analysis of a viscosity model for concentrated polymers |
| title_fullStr | Analysis of a viscosity model for concentrated polymers |
| title_full_unstemmed | Analysis of a viscosity model for concentrated polymers |
| title_short | Analysis of a viscosity model for concentrated polymers |
| title_sort | analysis of a viscosity model for concentrated polymers |
| work_keys_str_mv | AT bulicekm analysisofaviscositymodelforconcentratedpolymers AT gwiazdap analysisofaviscositymodelforconcentratedpolymers AT sulie analysisofaviscositymodelforconcentratedpolymers AT swierczewskagwiazdaa analysisofaviscositymodelforconcentratedpolymers |