Investigation of stationary solutions of viscoelastic melt spinning equations and stability with respect to increasing viscoelasticity
The one‐dimensional equations governing the formation of viscoelastic fibers using Giesekus constitutive equation were studied. Existence and uniqueness of stationary solutions was shown and relation between the stress at the spinneret and the take‐up velocity was found. Further, the value of the Gi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2010-07-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/6023 |
| _version_ | 1819350066438078464 |
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| author | R. Dhadwal S. K. Kudtarkar |
| author_facet | R. Dhadwal S. K. Kudtarkar |
| author_sort | R. Dhadwal |
| collection | DOAJ |
| description | The one‐dimensional equations governing the formation of viscoelastic fibers using Giesekus constitutive equation were studied. Existence and uniqueness of stationary solutions was shown and relation between the stress at the spinneret and the take‐up velocity was found. Further, the value of the Giesekus model parameter for which the fibre exhibits Newtonian behaviour was found analytically. Using numerical simulations it was shown that below this value of the parameter the fluid shows extension thickening behaviour and above, extension thinning. In this context, by simulating the non‐stationary equations the effect of viscoelasticity on the stability of the spinning process was studied.
First published online: 09 Jun 2011 |
| first_indexed | 2024-12-24T19:10:30Z |
| format | Article |
| id | doaj.art-cc380078aea74c0abd8243e0eea4e837 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-24T19:10:30Z |
| publishDate | 2010-07-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-cc380078aea74c0abd8243e0eea4e8372022-12-21T16:43:00ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102010-07-0115310.3846/1392-6292.2010.15.287-298Investigation of stationary solutions of viscoelastic melt spinning equations and stability with respect to increasing viscoelasticityR. Dhadwal0S. K. Kudtarkar1Center for Mathematical Modeling, FLAME 150/7,"Jaideep Bungalow", Prathamesh Park, Baner-Balewadi Road, Baner, Pune, IndiaCenter for Mathematical Modeling, FLAME 150/7,"Jaideep Bungalow", Prathamesh Park, Baner-Balewadi Road, Baner, Pune, IndiaThe one‐dimensional equations governing the formation of viscoelastic fibers using Giesekus constitutive equation were studied. Existence and uniqueness of stationary solutions was shown and relation between the stress at the spinneret and the take‐up velocity was found. Further, the value of the Giesekus model parameter for which the fibre exhibits Newtonian behaviour was found analytically. Using numerical simulations it was shown that below this value of the parameter the fluid shows extension thickening behaviour and above, extension thinning. In this context, by simulating the non‐stationary equations the effect of viscoelasticity on the stability of the spinning process was studied. First published online: 09 Jun 2011https://journals.vgtu.lt/index.php/MMA/article/view/6023melt spinningGiesekus model parameterviscoelasticityanalytic stationary solutions |
| spellingShingle | R. Dhadwal S. K. Kudtarkar Investigation of stationary solutions of viscoelastic melt spinning equations and stability with respect to increasing viscoelasticity Mathematical Modelling and Analysis melt spinning Giesekus model parameter viscoelasticity analytic stationary solutions |
| title | Investigation of stationary solutions of viscoelastic melt spinning equations and stability with respect to increasing viscoelasticity |
| title_full | Investigation of stationary solutions of viscoelastic melt spinning equations and stability with respect to increasing viscoelasticity |
| title_fullStr | Investigation of stationary solutions of viscoelastic melt spinning equations and stability with respect to increasing viscoelasticity |
| title_full_unstemmed | Investigation of stationary solutions of viscoelastic melt spinning equations and stability with respect to increasing viscoelasticity |
| title_short | Investigation of stationary solutions of viscoelastic melt spinning equations and stability with respect to increasing viscoelasticity |
| title_sort | investigation of stationary solutions of viscoelastic melt spinning equations and stability with respect to increasing viscoelasticity |
| topic | melt spinning Giesekus model parameter viscoelasticity analytic stationary solutions |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/6023 |
| work_keys_str_mv | AT rdhadwal investigationofstationarysolutionsofviscoelasticmeltspinningequationsandstabilitywithrespecttoincreasingviscoelasticity AT skkudtarkar investigationofstationarysolutionsofviscoelasticmeltspinningequationsandstabilitywithrespecttoincreasingviscoelasticity |