Three-dimensional simulation of capillary rheometry for an estimation of extensional viscosity
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Huan-Chang Tseng
Abstract
It is difficult to directly measure the steady extensional viscosity of thermoplastic composite materials, especially at high extension rates. The famous Cogswell method was derived analytically from the pressure drop of entrance flow in commercial capillary rheometers for estimating the extensional viscosity. However, using Cogswell´s extensional viscosity has always resulted in over-predictions of pressure drop. Recently, the GNF-X (eXtended Generalized Newtonian Fluid) model with a weighted shear/extensional viscosity was proposed to show the typical extension-induced vortex growth in entrance flow simulations. Under given various values of Trouton’s ratio for extensional viscosity, the GNF-X model is introduced to perform three-dimensional flow simulations of capillary rheometry over a range of apparent shear rates. The difference between the predicted pressure drops and the relevant experimental data is minimized such that the estimation of extensional viscosity is optimized herein.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Binding, D.M. (1988). An approximate analysis for contraction and converging flows. J. Non-Newtonian Fluid Mech. 27: 173–189, https://doi.org/10.1016/0377-0257(88)85012-2.Search in Google Scholar
Chang, R.Y. and Yang, W.H. (2001). Numerical simulation of mold filling in injection molding using a three-dimensional finite volume approach. Int. J. Numer. Methods Fluid. 37: 125–148, https://doi.org/10.1002/fld.166.Search in Google Scholar
Cogswell, F.N. (1972). Converging flow of polymer melts in extrusion dies. Polym. Eng. Sci. 12: 64–73, https://doi.org/10.1002/pen.760120111.Search in Google Scholar
Gibson, A.G. (1989). Die entry flow of reinforced polymers. Composites 20: 57–64, https://doi.org/10.1016/0010-4361(89)90683-6.Search in Google Scholar
Kwag, C. and Vlachopoulos, J. (1991). An assessment of Cogswell’s method for measurement of extensional viscosity. Polym. Eng. Sci. 31: 1015–1021, https://doi.org/10.1002/pen.760311404.Search in Google Scholar
Laun, H.M. and Münstedt, H. (1976). Comparison of the elongational behaviour of a polyethylene melt at constant stress and constant strain rate. Rheol. Acta 15: 517–524, https://doi.org/10.1007/bf01515874.Search in Google Scholar
Laun, H.M. and Schuch, H. (1989). Transient elongational viscosities and drawability of polymer melts. J. Rheol. 33: 119–175, https://doi.org/10.1122/1.550058.Search in Google Scholar
Macosko, C.W. (1994). Rheology: principles, measurements, and applications. Wiley VCH, New York.Search in Google Scholar
Meissner, J., Stephenson, S.E., Demarmels, A., and Portman, P. (1982). Multiaxial elongational flows of polymer melts – classification and experimental realization. J. Non-Newtonian Fluid Mech. 11: 221–237, https://doi.org/10.1016/0377-0257(82)80031-1.Search in Google Scholar
Metzner, A.B. and Metzner, A.P. (1970). Stress levels in rapid extensional flows of polymeric fluids. Rheol. Acta 9: 174–181, https://doi.org/10.1007/bf01973476.Search in Google Scholar
Mitsoulis, E., Battisti, M., Neunhäuserer, A., Perko, L., Friesenbichler, W., Ansari, M., and Hatzikiriakos, S.G. (2017). Flow behaviour of rubber in capillary and injection moulding dies. Plast. Rubber Compos. 46: 110–118, https://doi.org/10.1080/14658011.2017.1298207.Search in Google Scholar
Mitsoulis, E., Luger, H.J., Miethlinger, J., and Friesenbichler, W. (2018). Flow behavior of a polypropylene melt in capillary dies. Int. Polym. Process. 33: 642–651, https://doi.org/10.3139/217.3581.Search in Google Scholar
Morrison, F.A. (2001). Understanding rheology. Oxford University, New York.Search in Google Scholar
Obendrauf, W. (1996). New methods for temperature and strain viscosity measurement for the simulation of plastics processing processes, Ph.D. thesis. Institute of Polymer Processing, Montanuniversität Leoben, Austria.Search in Google Scholar
Park, J.M. (2020). Comment on “A revisitation of generalized Newtonian fluids”. J. Rheol. 64: 493–503, https://doi.org/10.1122/1.5139198.Search in Google Scholar
Perko, L., Friesenbichler, W., Obendrauf, W., Buchebner, V., and Chaloupka, G. (2013). Elongational viscosity of rubber compounds and improving corresponding models. Adv. Prod. Eng. Manag. 8: 126–133, https://doi.org/10.14743/apem2013.2.160.Search in Google Scholar
Petrie, C.J.S. (2006). Extensional viscosity: a critical discussion. J. Non-Newtonian Fluid Mech. 137: 15–23, https://doi.org/10.1016/j.jnnfm.2006.01.011.Search in Google Scholar
Sarkar, D. and Gupta, M. (2001). Further investigation of the effect of elongational viscosity on entrance flow. J. Reinf. Plast. Compos. 20: 1473–1484, https://doi.org/10.1177/073168401772679101.Search in Google Scholar
Schunk, P.R. and Scriven, L.E. (1990). Constitutive equation for modeling mixed extension and shear in polymer solution processing. J. Rheol. 34: 1085–1119, https://doi.org/10.1122/1.550075.Search in Google Scholar
Tanner, R.I. (1989). Engineering rheology. Oxford University Press, New York.Search in Google Scholar
Tseng, H.C. (2020). A revisitation of generalized Newtonian fluids. J. Rheol. 64: 493–504, https://doi.org/10.1122/1.5139198.Search in Google Scholar
Tseng, H.C. (2021a). A constitutive analysis of stress overshoot for entangled polymers under start-up shear flow. Phys. Fluids 33: 051706, https://doi.org/10.1063/5.0054379.Search in Google Scholar
Tseng, H.C. (2021b). A constitutive equation for fiber suspensions in viscoelastic media. Phys. Fluids 33: 071702, https://doi.org/10.1063/5.0057072.Search in Google Scholar
Tseng, H.C. (2021c). A revisitation of White-Metzner viscoelastic fluids. Phys. Fluids 33: 057115, https://doi.org/10.1063/5.0049132.Search in Google Scholar
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Articles in the same Issue
- Frontmatter
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- Vibration damping properties of graphene nanoplatelets filled glass/carbon fiber hybrid composites
- Optical and temperature dependent electrical properties of poly (vinyl chloride)/copper alumina nanocomposites for optoelectronic devices
- Numerical visualization of extensional flows in injection molding of polymer melts
- Thermal, mechanical and dielectric properties of glass fiber reinforced epoxy-lanthanum manganite nanocomposites
- Statistical research on the mixing properties of wave based screws by numerical simulations
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- Development of a prototype for the rubber latex industry to detect dry rubber content of fresh natural rubber latex using a novel measurement system with proton-electron transfer
- Effect of molding history on molecular orientation relaxation during physical aging of polystyrene injection moldings
- A comparative analysis of the effect of post production treatments and layer thickness on tensile and impact properties of additively manufactured polymers
- Fabrication of flame-retardant and smoke-suppressant rigid polyurethane foam modified by hydrolyzed keratin
- Study on flame retardancy and thermal stability of rigid polyurethane foams modified by amino trimethylphosphonate cobalt and expandable graphite
- Three-dimensional simulation of capillary rheometry for an estimation of extensional viscosity
Articles in the same Issue
- Frontmatter
- Research Articles
- Influence of process parameters of a continuous final mixer on the properties of carbon black/rubber composites
- Time series data for process monitoring in injection molding: a quantitative study of the benefits of a high sampling rate
- Vibration damping properties of graphene nanoplatelets filled glass/carbon fiber hybrid composites
- Optical and temperature dependent electrical properties of poly (vinyl chloride)/copper alumina nanocomposites for optoelectronic devices
- Numerical visualization of extensional flows in injection molding of polymer melts
- Thermal, mechanical and dielectric properties of glass fiber reinforced epoxy-lanthanum manganite nanocomposites
- Statistical research on the mixing properties of wave based screws by numerical simulations
- Influence of mold cavity thickness on electrical, morphological and thermal properties of polypropylene/carbon micromoldings
- Development of a prototype for the rubber latex industry to detect dry rubber content of fresh natural rubber latex using a novel measurement system with proton-electron transfer
- Effect of molding history on molecular orientation relaxation during physical aging of polystyrene injection moldings
- A comparative analysis of the effect of post production treatments and layer thickness on tensile and impact properties of additively manufactured polymers
- Fabrication of flame-retardant and smoke-suppressant rigid polyurethane foam modified by hydrolyzed keratin
- Study on flame retardancy and thermal stability of rigid polyurethane foams modified by amino trimethylphosphonate cobalt and expandable graphite
- Three-dimensional simulation of capillary rheometry for an estimation of extensional viscosity
