Draw resonance in film casting of viscoelastic fluids: A linear stability analysis |
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| Institution: | 1. Department of Chemistry, University of California, Berkeley, CA 94720, USA;2. Department of Bioengineering, University of California, Berkeley, CA 94720, USA;3. Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720, USA;4. QB3 Institute, University of California, Berkeley, CA 94720, USA;5. Chemical Sciences Division, Lawrence Berkeley National Labs, Berkeley, CA 94720, USA;6. Pharmaceutical Chemistry, University of California, San Francisco, CA, USA;7. Committee on Molecular Metabolism and Nutrition, University of Chicago, 1027 E. 57th Street, Chicago, IL 60637, USA;1. Cornell University, United States;2. American University of Beirut, Lebanon;1. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong;2. Center for applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA;3. Department Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3;4. Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA;1. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada;2. Zu Chongzhi Center for Mathematics and Computational Sciences, Division of Natural and Applied Sciences, Duke Kunshan University, Kunshan, China;3. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois;4. Department of Physiology & Biophysics, Rush University, Chicago, Illinois;5. Research Centre for Mathematics, Advanced Institute of Natural Sciences, Beijing Normal University (Zhuhai), Zhuhai, China;6. Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China;1. College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China;2. Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary T2N1N4, Canada |
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| Abstract: | In order to understand the role of viscoelasticity on draw resonance in the isothermal film casting process, a steady state analysis and a linear stability analysis for three-dimensional flow disturbances have been conducted. The constitutive equation used is a modified convected Maxwell model, with shear-rate dependent viscosity and fluid characteristic time. The numerical results indicate that the flow is stable below a lower critical draw ratio and above an upper critical draw ratio. Shear thinning in viscosity reduces the lower critical draw ratio and somewhat increases the upper critical draw ratio—thereby enlarging the region of instability. Slower shear reduction in fluid characteristic time dramatically decreases the upper critical draw ratio but has no significant effect on the lower critical draw ratio; therefore, fluids with higher characteristic time are more stable. |
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