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29-11-2023 | Research Article-Mechanical Engineering

Numerical Investigation of PTT Fluid Under Bidirectional Extensional Forces and Crystallization Effects

Author: Hatice Mercan

Published in: Arabian Journal for Science and Engineering

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Abstract

A numerical simulation of the film blowing process is performed. The Phan–Thien and Tanner (PTT) constitutive equations with quiescent and flow-induced crystallization effects are considered with proper boundary and initial conditions. The PTT model is employed both for molten and crystallized polymer. Modeling of crystallization is done with nested Schneider rate equations and the Kolmogorov–Avrami model. The current model can predict the shape and size of the bubbles, as well as their temperature, stress, space filling and morphological changes for given process conditions. The study focuses on investigating the impact of process conditions on the mechanical response of the blown film, as well as on the morphological structure of the crystallizing molten polymer. It is observed that the axial stress increases at a faster rate compared to the circumferential stress with increase in draw ratio. The trend is reversed for increasing blow-up ratios. Increasing the draw ratio does not result in significant improvement in the quiescent contribution to the crystalline structure, but it leads to a decrease in the flow-induced contribution. Increasing blow-up ratio leads to increase in total space filling and the flow-induced component of the crystalline structure. Finally, three heat transfer coefficients chosen from the literature are compared. It is observed that the model choice is not critical for higher draw ratio values, but for low and moderate values, detailed investigations are required. The presented model enables accurate prediction of both the morphological structure and mechanical properties of semicrystalline polymers in a film blowing process.

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Literature
1.
go back to reference Hodgkinson, R.; Chaffin, S.T.; Zimmerman, W.B.; Holland, C.; Howse, J.R.: Extensional flow affecting shear viscosity: experimental evidence and comparison to models. J. Rheol. 66(4), 793–809 (2022)CrossRef Hodgkinson, R.; Chaffin, S.T.; Zimmerman, W.B.; Holland, C.; Howse, J.R.: Extensional flow affecting shear viscosity: experimental evidence and comparison to models. J. Rheol. 66(4), 793–809 (2022)CrossRef
2.
go back to reference Pearson, J.R.A.; Petrie, C.J.S.: The flow of a tubular film. Part 1. Formal mathematical representation. J. Fluid Mech. 40(1), 1–19 (1970)MATHCrossRef Pearson, J.R.A.; Petrie, C.J.S.: The flow of a tubular film. Part 1. Formal mathematical representation. J. Fluid Mech. 40(1), 1–19 (1970)MATHCrossRef
3.
go back to reference Pearson, J.R.A.; Petrie, C.J.S.: The flow of a tubular film Part 2. Interpretation of the model and discussion of solutions. J. Fluid Mech. 42(3), 609–625 (1970)MATHCrossRef Pearson, J.R.A.; Petrie, C.J.S.: The flow of a tubular film Part 2. Interpretation of the model and discussion of solutions. J. Fluid Mech. 42(3), 609–625 (1970)MATHCrossRef
4.
go back to reference Muslet, I.A.; Kamal, M.R.: Computer simulation of the film blowing process incorporating crystallization and viscoelasticity. J. Rheol. 48(3), 525–550 (2004)CrossRef Muslet, I.A.; Kamal, M.R.: Computer simulation of the film blowing process incorporating crystallization and viscoelasticity. J. Rheol. 48(3), 525–550 (2004)CrossRef
5.
go back to reference Hyun, J.C.; Kim, H.; Lee, J.S.; Song, H.S.; Jung, H.W.: Transient solutions of the dynamics in film blowing processes. J. Nonnewton. Fluid Mech. 121(2–3), 157–162 (2004)MATHCrossRef Hyun, J.C.; Kim, H.; Lee, J.S.; Song, H.S.; Jung, H.W.: Transient solutions of the dynamics in film blowing processes. J. Nonnewton. Fluid Mech. 121(2–3), 157–162 (2004)MATHCrossRef
6.
go back to reference Jung, H.W.; Hyun, J.C.: Instabilities in extensional deformation polymer processing. Rheol. Rev. 2006, 131 (2006) Jung, H.W.; Hyun, J.C.: Instabilities in extensional deformation polymer processing. Rheol. Rev. 2006, 131 (2006)
7.
go back to reference Shin, D.M.; Lee, J.S.; Jung, H.W.; Hyun, J.C.: Multiplicity, bifurcation, stability and hysteresis in dynamic solutions of film blowing process. J. Rheol. 51(4), 605–621 (2007)CrossRef Shin, D.M.; Lee, J.S.; Jung, H.W.; Hyun, J.C.: Multiplicity, bifurcation, stability and hysteresis in dynamic solutions of film blowing process. J. Rheol. 51(4), 605–621 (2007)CrossRef
8.
go back to reference Lee, J.S.; Shin, D.M.; Song, H.S.; Jung, H.W.; Hyun, J.C.: Existence of optimal cooling conditions in the film blowing process. J. Nonnewton. Fluid Mech. 137(1–3), 24–30 (2006)MATHCrossRef Lee, J.S.; Shin, D.M.; Song, H.S.; Jung, H.W.; Hyun, J.C.: Existence of optimal cooling conditions in the film blowing process. J. Nonnewton. Fluid Mech. 137(1–3), 24–30 (2006)MATHCrossRef
9.
go back to reference Lee, J.S.; Jung, H.W.; Hyun, J.C.: Transient solutions of nonlinear dynamics in film blowing process accompanied by on-line crystallization. J. Rheol. 55(2), 257–271 (2011)CrossRef Lee, J.S.; Jung, H.W.; Hyun, J.C.: Transient solutions of nonlinear dynamics in film blowing process accompanied by on-line crystallization. J. Rheol. 55(2), 257–271 (2011)CrossRef
10.
go back to reference Lee, J.S.; Kwon, I.; Jung, H.W.; Hyun, J.C.: Helical instability in film blowing process: analogy to buckling instability. Phys. Fluids 29(12), 121501 (2017)CrossRef Lee, J.S.; Kwon, I.; Jung, H.W.; Hyun, J.C.: Helical instability in film blowing process: analogy to buckling instability. Phys. Fluids 29(12), 121501 (2017)CrossRef
11.
go back to reference Pirkle, J.C., Jr.; Braatz, R.D.: A thin-shell two-phase microstructural model for blown film extrusion. J. Rheol. 54(3), 471–505 (2010)CrossRef Pirkle, J.C., Jr.; Braatz, R.D.: A thin-shell two-phase microstructural model for blown film extrusion. J. Rheol. 54(3), 471–505 (2010)CrossRef
12.
go back to reference Yoon, K.S.; Park, C.W.: Stability of a blown film extrusion process. Int. Polym. Proc. 14(4), 342–349 (1999)CrossRef Yoon, K.S.; Park, C.W.: Stability of a blown film extrusion process. Int. Polym. Proc. 14(4), 342–349 (1999)CrossRef
13.
go back to reference Yoon, K.S.; Park, C.W.: Stability of a two-layer blown film coextrusion. J. Nonnewton. Fluid Mech. 89(1–2), 97–116 (2000)MATHCrossRef Yoon, K.S.; Park, C.W.: Stability of a two-layer blown film coextrusion. J. Nonnewton. Fluid Mech. 89(1–2), 97–116 (2000)MATHCrossRef
14.
go back to reference Pirkle, J., Jr.; Braatz, R.D.: Dynamic modeling of blown-film extrusion. Polym. Eng. Sci. 43(2), 398–418 (2003)CrossRef Pirkle, J., Jr.; Braatz, R.D.: Dynamic modeling of blown-film extrusion. Polym. Eng. Sci. 43(2), 398–418 (2003)CrossRef
15.
go back to reference Liu, C. C.: Studies of Mathematical Modelling and Experimental On-line Measurement for the Tubular Film Blowing Process, MSc Thesis, The University of Tennessee, USA (1991) Liu, C. C.: Studies of Mathematical Modelling and Experimental On-line Measurement for the Tubular Film Blowing Process, MSc Thesis, The University of Tennessee, USA (1991)
16.
go back to reference Liu, C. C.: On-line experimental study and theoretical modelling of tubular film blowing. PhD Thesis, The University of Tennessee, USA (1994). Liu, C. C.: On-line experimental study and theoretical modelling of tubular film blowing. PhD Thesis, The University of Tennessee, USA (1994).
17.
go back to reference Liu, C.C.; Bogue, D.C.; Spruiell, J.E.: Tubular film blowing. Int. Polym. Proc. 10(3), 230–236 (1995)CrossRef Liu, C.C.; Bogue, D.C.; Spruiell, J.E.: Tubular film blowing. Int. Polym. Proc. 10(3), 230–236 (1995)CrossRef
18.
go back to reference Doufas, A.K.; McHugh, A.J.: Simulation of film blowing including flow-induced crystallization. J. Rheol. 45(5), 1085–1104 (2001)CrossRef Doufas, A.K.; McHugh, A.J.: Simulation of film blowing including flow-induced crystallization. J. Rheol. 45(5), 1085–1104 (2001)CrossRef
19.
go back to reference Pirkle, J.C., Jr.; Fujiwara, M.; Braatz, R.D.: Maximum-likelihood parameter estimation for the thin-shell quasi-Newtonian model for a laboratory blown film extruder. Ind. Eng. Chem. Res. 49(17), 8007–8015 (2010)CrossRef Pirkle, J.C., Jr.; Fujiwara, M.; Braatz, R.D.: Maximum-likelihood parameter estimation for the thin-shell quasi-Newtonian model for a laboratory blown film extruder. Ind. Eng. Chem. Res. 49(17), 8007–8015 (2010)CrossRef
20.
go back to reference Denn, M.M.; Petrie, C.J.; Avenas, P.: Mechanics of steady spinning of a viscoelastic liquid. AIChE J. 21(4), 791–799 (1975)CrossRef Denn, M.M.; Petrie, C.J.; Avenas, P.: Mechanics of steady spinning of a viscoelastic liquid. AIChE J. 21(4), 791–799 (1975)CrossRef
21.
go back to reference Anturkar, N.R.; Co, A.: Draw resonance in film casting of viscoelastic fluids: a linear stability analysis. J. Nonnewton. Fluid Mech. 28(3), 287–307 (1988)MATHCrossRef Anturkar, N.R.; Co, A.: Draw resonance in film casting of viscoelastic fluids: a linear stability analysis. J. Nonnewton. Fluid Mech. 28(3), 287–307 (1988)MATHCrossRef
22.
go back to reference Silagy, D.; Demay, Y.; Agassant, J.F.: Stationary and stability analysis of the film casting process. J. Nonnewton. Fluid Mech. 79(2–3), 563–583 (1998)MATHCrossRef Silagy, D.; Demay, Y.; Agassant, J.F.: Stationary and stability analysis of the film casting process. J. Nonnewton. Fluid Mech. 79(2–3), 563–583 (1998)MATHCrossRef
23.
go back to reference Ashok, B.K.; Campbell, G.A.: Two-phase simulation of tubular film blowing of crystalline polymers. Int. Polym. Proc. 7(3), 240–247 (1992)CrossRef Ashok, B.K.; Campbell, G.A.: Two-phase simulation of tubular film blowing of crystalline polymers. Int. Polym. Proc. 7(3), 240–247 (1992)CrossRef
24.
go back to reference Doufas, A.K.: A microstructural flow-induced crystallization model for film blowing: validation with experimental data. Rheol. Acta 53(3), 269–293 (2014)CrossRef Doufas, A.K.: A microstructural flow-induced crystallization model for film blowing: validation with experimental data. Rheol. Acta 53(3), 269–293 (2014)CrossRef
25.
go back to reference Grosso, G.; Troisi, E.M.; Jaensson, N.O.; Peters, G.W.; Anderson, P.D.: Modelling flow induced crystallization of IPP: multiple crystal phases and morphologies. Polymer 182, 121806 (2019)CrossRef Grosso, G.; Troisi, E.M.; Jaensson, N.O.; Peters, G.W.; Anderson, P.D.: Modelling flow induced crystallization of IPP: multiple crystal phases and morphologies. Polymer 182, 121806 (2019)CrossRef
26.
go back to reference van Berlo, F.P.; Cardinaels, R.; Peters, G.W.; Anderson, P.D.: A numerical study of extensional flow-induced crystallization in filament stretching rheometry. Polym. Cryst. 4(1), e10154 (2021) van Berlo, F.P.; Cardinaels, R.; Peters, G.W.; Anderson, P.D.: A numerical study of extensional flow-induced crystallization in filament stretching rheometry. Polym. Cryst. 4(1), e10154 (2021)
27.
go back to reference Ziabicki, A.: Fundamentals of Fibre Formation. Wiley (1976) Ziabicki, A.: Fundamentals of Fibre Formation. Wiley (1976)
28.
go back to reference Shrikhande, P.; Kohler, W.H.; McHugh, A.J.: A modified model and algorithm for flow-enhanced crystallization—application to fiber spinning. J. Appl. Polym. Sci. 100(4), 3240–3254 (2006)CrossRef Shrikhande, P.; Kohler, W.H.; McHugh, A.J.: A modified model and algorithm for flow-enhanced crystallization—application to fiber spinning. J. Appl. Polym. Sci. 100(4), 3240–3254 (2006)CrossRef
29.
go back to reference Mubarak, Y.; Harkin-Jones, E.M.A.; Martin, P.J.; Ahmad, M.: Modeling of non-isothermal crystallization kinetics of isotactic polypropylene. Polymer 42(7), 3171–3182 (2001)CrossRef Mubarak, Y.; Harkin-Jones, E.M.A.; Martin, P.J.; Ahmad, M.: Modeling of non-isothermal crystallization kinetics of isotactic polypropylene. Polymer 42(7), 3171–3182 (2001)CrossRef
30.
go back to reference Nakamura, K.; Katayama, K.; Amano, T.: Some aspects of nonisothermal crystallization of polymers. II. Consideration of the isokinetic condition. J. Appl. Polym. Sci. 17(4), 1031–1041 (1973)CrossRef Nakamura, K.; Katayama, K.; Amano, T.: Some aspects of nonisothermal crystallization of polymers. II. Consideration of the isokinetic condition. J. Appl. Polym. Sci. 17(4), 1031–1041 (1973)CrossRef
31.
go back to reference Ozawa, T.: Kinetics of non-isothermal crystallization. Polymer 12(3), 150–158 (1971)CrossRef Ozawa, T.: Kinetics of non-isothermal crystallization. Polymer 12(3), 150–158 (1971)CrossRef
32.
go back to reference Di Lorenzo, M.L.; Silvestre, C.: Non-isothermal crystallization of polymers. Prog. Polym. Sci. 24(6), 917–950 (1999)CrossRef Di Lorenzo, M.L.; Silvestre, C.: Non-isothermal crystallization of polymers. Prog. Polym. Sci. 24(6), 917–950 (1999)CrossRef
33.
go back to reference Zuidema, H.; Peters, G.W.; Meijer, H.E.: Development and validation of a recoverable strain-based model for flow-induced crystallization of polymers. Macromol. Theory Simul. 10(5), 447–460 (2001)CrossRef Zuidema, H.; Peters, G.W.; Meijer, H.E.: Development and validation of a recoverable strain-based model for flow-induced crystallization of polymers. Macromol. Theory Simul. 10(5), 447–460 (2001)CrossRef
34.
go back to reference Steenbakkers, R.J.; Peters, G.W.: A stretch-based model for flow-enhanced nucleation of polymer melts. J. Rheol. 55(2), 401–433 (2011)CrossRef Steenbakkers, R.J.; Peters, G.W.: A stretch-based model for flow-enhanced nucleation of polymer melts. J. Rheol. 55(2), 401–433 (2011)CrossRef
35.
go back to reference van Erp, T.B.; Roozemond, P.C.; Peters, G.W.: Flow-enhanced crystallization kinetics of i PP during cooling at elevated pressure: characterization, validation, and development. Macromol. Theory Simul. 22(5), 309–318 (2013)CrossRef van Erp, T.B.; Roozemond, P.C.; Peters, G.W.: Flow-enhanced crystallization kinetics of i PP during cooling at elevated pressure: characterization, validation, and development. Macromol. Theory Simul. 22(5), 309–318 (2013)CrossRef
36.
go back to reference van Erp, T. B.: Structure development and mechanical performance of polypropylene. PhD Thesis, Technische Universiteit Eindhoven, The Netherlands (2012). van Erp, T. B.: Structure development and mechanical performance of polypropylene. PhD Thesis, Technische Universiteit Eindhoven, The Netherlands (2012).
37.
go back to reference Roozemond, P.C.; van Drongelen, M.; Ma, Z.; Hulsen, M.A.; Peters, G.W.: Modeling flow-induced crystallization in isotactic polypropylene at high shear rates. J. Rheol. 59(3), 613–642 (2015)CrossRef Roozemond, P.C.; van Drongelen, M.; Ma, Z.; Hulsen, M.A.; Peters, G.W.: Modeling flow-induced crystallization in isotactic polypropylene at high shear rates. J. Rheol. 59(3), 613–642 (2015)CrossRef
38.
go back to reference Custódio, F.J.; Steenbakkers, R.J.; Anderson, P.D.; Peters, G.W.; Meijer, H.E.: Model development and validation of crystallization behavior in injection molding prototype flows. Macromol. Theory Simul. 18(9), 469–494 (2009)CrossRef Custódio, F.J.; Steenbakkers, R.J.; Anderson, P.D.; Peters, G.W.; Meijer, H.E.: Model development and validation of crystallization behavior in injection molding prototype flows. Macromol. Theory Simul. 18(9), 469–494 (2009)CrossRef
39.
go back to reference van Drongelen, M.; Cavallo, D.; Balzano, L.; Portale, G.; Vittorias, I.; Bras, W.; Alfonso, G.C.; Peters, G.W.: Structure development of low-density polyethylenes during film blowing: a real-time wide-angle X-ray diffraction study. Macromol. Mater. Eng. 299(12), 494–1512 (2014) van Drongelen, M.; Cavallo, D.; Balzano, L.; Portale, G.; Vittorias, I.; Bras, W.; Alfonso, G.C.; Peters, G.W.: Structure development of low-density polyethylenes during film blowing: a real-time wide-angle X-ray diffraction study. Macromol. Mater. Eng. 299(12), 494–1512 (2014)
40.
go back to reference Zhang, Q.; Li, L.; Su, F.; Ji, Y.; Ali, S.; Zhao, H.; Meng, L.; Li, L.: From molecular entanglement network to crystal-cross-linked network and crystal scaffold during film blowing of polyethylene: an in situ synchrotron radiation small-and wide-angle x-ray scattering study. Macromolecules 51(11), 4350–4362 (2018)CrossRef Zhang, Q.; Li, L.; Su, F.; Ji, Y.; Ali, S.; Zhao, H.; Meng, L.; Li, L.: From molecular entanglement network to crystal-cross-linked network and crystal scaffold during film blowing of polyethylene: an in situ synchrotron radiation small-and wide-angle x-ray scattering study. Macromolecules 51(11), 4350–4362 (2018)CrossRef
41.
go back to reference Zhang, Q.; Chen, W.; Zhao, H.; Ji, Y.; Meng, L.; Wang, D.; Li, L.: In-situ tracking polymer crystallization during film blowing by synchrotron radiation X-ray scattering: the critical role of network. Polymer 198, 122492 (2020)CrossRef Zhang, Q.; Chen, W.; Zhao, H.; Ji, Y.; Meng, L.; Wang, D.; Li, L.: In-situ tracking polymer crystallization during film blowing by synchrotron radiation X-ray scattering: the critical role of network. Polymer 198, 122492 (2020)CrossRef
42.
go back to reference Zhao, H.; Zhang, Q.; Xia, Z.; Yang, E.; Zhang, M.; Wang, Y.; Ji, Y.; Chen, W.; Wang, D.; Meng, L.; Li, L.: Elucidation of the relationships of structure-process-property for different ethylene/α-olefin copolymers during film blowing: an in-situ synchrotron radiation X-ray scattering study. Polym. Testing 85, 106439 (2020)CrossRef Zhao, H.; Zhang, Q.; Xia, Z.; Yang, E.; Zhang, M.; Wang, Y.; Ji, Y.; Chen, W.; Wang, D.; Meng, L.; Li, L.: Elucidation of the relationships of structure-process-property for different ethylene/α-olefin copolymers during film blowing: an in-situ synchrotron radiation X-ray scattering study. Polym. Testing 85, 106439 (2020)CrossRef
43.
go back to reference Troisi, E.M.; van Drongelen, M.; Caelers, H.J.M.; Portale, G.; Peters, G.W.M.: Structure evolution during film blowing: an experimental study using in-situ small angle X-ray scattering. Eur. Polym. J. 74, 190–208 (2016)CrossRef Troisi, E.M.; van Drongelen, M.; Caelers, H.J.M.; Portale, G.; Peters, G.W.M.: Structure evolution during film blowing: an experimental study using in-situ small angle X-ray scattering. Eur. Polym. J. 74, 190–208 (2016)CrossRef
44.
go back to reference Mercan H.; Anderson, P.D.; Peters, G.W.: Internal Report: Numerical Analysis of Flow-Induced Crystallization in Film Blowing, Tu/e. The Netherlands (2013) Mercan H.; Anderson, P.D.; Peters, G.W.: Internal Report: Numerical Analysis of Flow-Induced Crystallization in Film Blowing, Tu/e. The Netherlands (2013)
45.
go back to reference Kolarik, R.; Zatloukal, M.; Martyn, M.: The effect of polyolefin extensional rheology on non-isothermal film blowing process stability. Int. J. Heat Mass Transf. 56(1–2), 694–708 (2013)CrossRef Kolarik, R.; Zatloukal, M.; Martyn, M.: The effect of polyolefin extensional rheology on non-isothermal film blowing process stability. Int. J. Heat Mass Transf. 56(1–2), 694–708 (2013)CrossRef
46.
go back to reference Tas, P.P.: Film Blowing from Polymer to Product. PhD Thesis, Technische Universiteit Eindhoven, the Netherlands (1994). Tas, P.P.: Film Blowing from Polymer to Product. PhD Thesis, Technische Universiteit Eindhoven, the Netherlands (1994).
47.
go back to reference Kolarik, R.; Zatloukal, M.; Tzoganakis, C.: Stability analysis of non-isothermal film blowing process for non-Newtonian fluids using variational principles. Chem. Eng. Sci. 73, 439–453 (2012)CrossRef Kolarik, R.; Zatloukal, M.; Tzoganakis, C.: Stability analysis of non-isothermal film blowing process for non-Newtonian fluids using variational principles. Chem. Eng. Sci. 73, 439–453 (2012)CrossRef
48.
go back to reference Kolarik, R.; Zatloukal, M.: Modeling of non-isothermal film blowing process for non-Newtonian fluids by using variational principles. J. Appl. Polym. Sci. 122(4), 2807–2820 (2011)CrossRef Kolarik, R.; Zatloukal, M.: Modeling of non-isothermal film blowing process for non-Newtonian fluids by using variational principles. J. Appl. Polym. Sci. 122(4), 2807–2820 (2011)CrossRef
49.
go back to reference Barborik, T.; Zatloukal, M.: Viscoelastic non-isothermal modeling of film extrusion for membrane production including flow induced crystallization. Phys. Fluids. (2022) Barborik, T.; Zatloukal, M.: Viscoelastic non-isothermal modeling of film extrusion for membrane production including flow induced crystallization. Phys. Fluids. (2022)
50.
go back to reference Sidiropoulos, V.: The effects of air cooling on the film blowing process, PhD Thesis, McMaster University, Canada (2000) Sidiropoulos, V.: The effects of air cooling on the film blowing process, PhD Thesis, McMaster University, Canada (2000)
51.
go back to reference Sidiropoulos, V.; Vlachopoulos, J.: The effects of dual-orifice air-ring design on blown film cooling. Polym. Eng. Sci. 40(7), 1611–1618 (2000)CrossRef Sidiropoulos, V.; Vlachopoulos, J.: The effects of dual-orifice air-ring design on blown film cooling. Polym. Eng. Sci. 40(7), 1611–1618 (2000)CrossRef
52.
go back to reference Ismail, M.E.; Awad, M.M.; Hamed, A.M.; Abdelaal, M.Y.; Zeidan, E.B.: Experimental and numerical investigations on a high-density polyethylene (HDPE) blown film cooling with a new design of the counter-flow/radial jet air-ring. J. Plast. Film Sheeting 38(2), 191–224 (2022)CrossRef Ismail, M.E.; Awad, M.M.; Hamed, A.M.; Abdelaal, M.Y.; Zeidan, E.B.: Experimental and numerical investigations on a high-density polyethylene (HDPE) blown film cooling with a new design of the counter-flow/radial jet air-ring. J. Plast. Film Sheeting 38(2), 191–224 (2022)CrossRef
53.
go back to reference Darbandi, M.; Abdollahpour, M.S.; Hasanpour-Matkolaei, M.: A new developed semi-full-scale approach to facilitate the CFD simulation of shell and tube heat exchangers. Chem. Eng. Sci. 245, 116836 (2021)CrossRef Darbandi, M.; Abdollahpour, M.S.; Hasanpour-Matkolaei, M.: A new developed semi-full-scale approach to facilitate the CFD simulation of shell and tube heat exchangers. Chem. Eng. Sci. 245, 116836 (2021)CrossRef
54.
go back to reference Housiadas, K.; Tsamopoulos, J.: Cooling of a viscoelastic film during unsteady extrusion from an annular die. Rheol. Acta 39(1), 44–61 (2000)MATHCrossRef Housiadas, K.; Tsamopoulos, J.: Cooling of a viscoelastic film during unsteady extrusion from an annular die. Rheol. Acta 39(1), 44–61 (2000)MATHCrossRef
55.
go back to reference Demay, Y.; Clamond, D.: A new model for the blown film process. Comptes Rendus Mec. 339(11), 692–699 (2011)CrossRef Demay, Y.; Clamond, D.: A new model for the blown film process. Comptes Rendus Mec. 339(11), 692–699 (2011)CrossRef
56.
go back to reference Butler, T.I.; Lai, S.Y.; Patel, R.; Spuria, J.: Blown film frost line-freeze line interactions. Polymers Laminations and Coatings Conference, 13 (1993). Butler, T.I.; Lai, S.Y.; Patel, R.; Spuria, J.: Blown film frost line-freeze line interactions. Polymers Laminations and Coatings Conference, 13 (1993).
57.
go back to reference Ghaneh-Fard, A.; Carreau, P.J.; Lafleur, P.G.: Study of kinematics and dynamics of film blowing of different polyethylenes. Polym. Eng. Sci. 37(7), 1148–1163 (1997)CrossRef Ghaneh-Fard, A.; Carreau, P.J.; Lafleur, P.G.: Study of kinematics and dynamics of film blowing of different polyethylenes. Polym. Eng. Sci. 37(7), 1148–1163 (1997)CrossRef
58.
go back to reference Muslet, Iyad A.: Computer simulation of the film blowing process incorporating crystallization and viscoelasticity. PhD Thesis, McGill University, Canada (2004). Muslet, Iyad A.: Computer simulation of the film blowing process incorporating crystallization and viscoelasticity. PhD Thesis, McGill University, Canada (2004).
59.
go back to reference Han, C.D.; Park, J.Y.: Studies on blown film extrusion. I. Experimental determination of elongational viscosity. J. Appl. Polym. Sci. 19(12), 3257–3276 (1975)CrossRef Han, C.D.; Park, J.Y.: Studies on blown film extrusion. I. Experimental determination of elongational viscosity. J. Appl. Polym. Sci. 19(12), 3257–3276 (1975)CrossRef
60.
go back to reference Gupta, R.K.; Metzner, A.B.; Wissbrun, K.F.: Modeling of polymeric film-blowing processes. Polym. Eng. Sci. 22(3), 172–181 (1982)CrossRef Gupta, R.K.; Metzner, A.B.; Wissbrun, K.F.: Modeling of polymeric film-blowing processes. Polym. Eng. Sci. 22(3), 172–181 (1982)CrossRef
Metadata
Title
Numerical Investigation of PTT Fluid Under Bidirectional Extensional Forces and Crystallization Effects
Author
Hatice Mercan
Publication date
29-11-2023
Publisher
Springer Berlin Heidelberg
Published in
Arabian Journal for Science and Engineering
Print ISSN: 2193-567X
Electronic ISSN: 2191-4281
DOI
https://doi.org/10.1007/s13369-023-08491-4

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