Numerical study of the rheology of rigid fillers suspended in long-chain branched polymer under planar extensional flow
We report a detailed numerical study of the rheology of two-dimensional rigid fillers suspended in branched polymer melt under planar extensional flow. The polymer melt is modelled using the pom-pom constitutive equation. The numerical method uses a finite element solution of the flow in a unit cell...
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| Veröffentlicht in: | Journal of non-Newtonian fluid mechanics 2010-03, Vol.165 (5), p.281-291 |
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| container_title | Journal of non-Newtonian fluid mechanics |
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| creator | Ahamadi, M. Harlen, O.G |
| description | We report a detailed numerical study of the rheology of two-dimensional rigid fillers suspended in branched polymer melt under planar extensional flow. The polymer melt is modelled using the pom-pom constitutive equation. The numerical method uses a finite element solution of the flow in a unit cell within the self-replicating lattice for planar extensional flow identified by Kraynik and Reinelt [Int. J. Multiphase flow 18 (1992) 1045]. This is implemented using a quotient space representation that maps all points in space onto points within the unit cell. We show that the Kraynik and Reinelt cell allows simulations of suspensions under planar extensional flow to be conducted to large strains in a truly periodic cell. The influence of both the pom-pom parameters and the particle area fraction on the rheology of the suspension are investigated. We find a reduction in the degree of extension-rate thickening with the increase of both particles concentration and Weissenberg numbers in agreement with published experimental and numerical findings on other viscoelastic models. This reduction is found to be due to flow disturbance created by the particles which disrupts the alignment of backbone tube segments with the extensional axis. |
| doi_str_mv | 10.1016/j.jnnfm.2010.01.002 |
| format | Article |
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The polymer melt is modelled using the pom-pom constitutive equation. The numerical method uses a finite element solution of the flow in a unit cell within the self-replicating lattice for planar extensional flow identified by Kraynik and Reinelt [Int. J. Multiphase flow 18 (1992) 1045]. This is implemented using a quotient space representation that maps all points in space onto points within the unit cell. We show that the Kraynik and Reinelt cell allows simulations of suspensions under planar extensional flow to be conducted to large strains in a truly periodic cell. The influence of both the pom-pom parameters and the particle area fraction on the rheology of the suspension are investigated. We find a reduction in the degree of extension-rate thickening with the increase of both particles concentration and Weissenberg numbers in agreement with published experimental and numerical findings on other viscoelastic models. This reduction is found to be due to flow disturbance created by the particles which disrupts the alignment of backbone tube segments with the extensional axis.</description><subject>Applied sciences</subject><subject>Branched</subject><subject>Composites</subject><subject>Constitutive relationships</subject><subject>Exact sciences and technology</subject><subject>Fillers</subject><subject>Finite elements (65M60)</subject><subject>Fluid mechanics</subject><subject>Forms of application and semi-finished materials</subject><subject>Mathematical models</subject><subject>Melts</subject><subject>Periodic boundary conditions</subject><subject>Planar extension</subject><subject>Polymer industry, paints, wood</subject><subject>Reduction</subject><subject>Rheology</subject><subject>Suspensions rheology</subject><subject>Technology of polymers</subject><subject>Unit cell</subject><subject>Viscoelastic fluid</subject><issn>0377-0257</issn><issn>1873-2631</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kE2PFCEQholxE8d1f8FeuBhPPfLRQPfBg9n4lWz04p4JDcUMEwZa6Hadfy-zs_EoF6iqt96iHoRuKdlSQuX7w_aQkj9uGWkZQreEsBdoQwfFOyY5fYk2hCvVESbUK_S61gNpR3C5QY_f1yOUYE3EdVndCWePlz3gsocc8-4pLmEXHPYhRigV17XOkBw4HBKOOe06uzftORWT7L6l5xxPzROvTVTwHE0yBcOfBVINObVBPubHN-jKm1jh5vm-Rg-fP_28-9rd__jy7e7jfWd7TpduEl4p7yWfjPWKsNGCGEnvjZokmRiTTtjReSC0H3sHfGJyEIPzI2FDKzB-jd5dfOeSf61QF30M1UJsv4K8Vq0EV1wOcmhKflHakmst4PVcwtGUk6ZEnynrg36irM-UNaG6UW5db5_9TW0Q_RlCqP9aGRODIKJvug8XHbRlfwcoutoAyYILBeyiXQ7_nfMXzVOWYw</recordid><startdate>20100301</startdate><enddate>20100301</enddate><creator>Ahamadi, M.</creator><creator>Harlen, O.G</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20100301</creationdate><title>Numerical study of the rheology of rigid fillers suspended in long-chain branched polymer under planar extensional flow</title><author>Ahamadi, M. ; Harlen, O.G</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c431t-b5f77ff63bacf7029ce5904fa7b60b226d5c9dfe01494de3b26858df9028c9d23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Applied sciences</topic><topic>Branched</topic><topic>Composites</topic><topic>Constitutive relationships</topic><topic>Exact sciences and technology</topic><topic>Fillers</topic><topic>Finite elements (65M60)</topic><topic>Fluid mechanics</topic><topic>Forms of application and semi-finished materials</topic><topic>Mathematical models</topic><topic>Melts</topic><topic>Periodic boundary conditions</topic><topic>Planar extension</topic><topic>Polymer industry, paints, wood</topic><topic>Reduction</topic><topic>Rheology</topic><topic>Suspensions rheology</topic><topic>Technology of polymers</topic><topic>Unit cell</topic><topic>Viscoelastic fluid</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ahamadi, M.</creatorcontrib><creatorcontrib>Harlen, O.G</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of non-Newtonian fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ahamadi, M.</au><au>Harlen, O.G</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical study of the rheology of rigid fillers suspended in long-chain branched polymer under planar extensional flow</atitle><jtitle>Journal of non-Newtonian fluid mechanics</jtitle><date>2010-03-01</date><risdate>2010</risdate><volume>165</volume><issue>5</issue><spage>281</spage><epage>291</epage><pages>281-291</pages><issn>0377-0257</issn><eissn>1873-2631</eissn><coden>JNFMDI</coden><abstract>We report a detailed numerical study of the rheology of two-dimensional rigid fillers suspended in branched polymer melt under planar extensional flow. The polymer melt is modelled using the pom-pom constitutive equation. The numerical method uses a finite element solution of the flow in a unit cell within the self-replicating lattice for planar extensional flow identified by Kraynik and Reinelt [Int. J. Multiphase flow 18 (1992) 1045]. This is implemented using a quotient space representation that maps all points in space onto points within the unit cell. We show that the Kraynik and Reinelt cell allows simulations of suspensions under planar extensional flow to be conducted to large strains in a truly periodic cell. The influence of both the pom-pom parameters and the particle area fraction on the rheology of the suspension are investigated. We find a reduction in the degree of extension-rate thickening with the increase of both particles concentration and Weissenberg numbers in agreement with published experimental and numerical findings on other viscoelastic models. 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| identifier | ISSN: 0377-0257 |
| ispartof | Journal of non-Newtonian fluid mechanics, 2010-03, Vol.165 (5), p.281-291 |
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| language | eng |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Applied sciences Branched Composites Constitutive relationships Exact sciences and technology Fillers Finite elements (65M60) Fluid mechanics Forms of application and semi-finished materials Mathematical models Melts Periodic boundary conditions Planar extension Polymer industry, paints, wood Reduction Rheology Suspensions rheology Technology of polymers Unit cell Viscoelastic fluid |
| title | Numerical study of the rheology of rigid fillers suspended in long-chain branched polymer under planar extensional flow |
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