聚乙烯熔体拉伸流动中流变行为及机理的研究
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摘要
拉伸流动广泛的存在于聚合物材料加工过程中,熔体的拉伸流动行为将对聚合物材料的加工工艺过程和制品的最终力学性能产生重要的影响。深入了解各种聚合物材料体系的拉伸流变性能,能够有效的优化生产过程和提高产品质量。本文从理论建模、数值模拟及实验测量三个方面全面系统的研究了聚乙烯熔体在拉伸流动过程中的行为及其机理。
构建了四个聚合物熔体的拉伸黏度模型,其中,基于White-Metzner模型的拉伸黏度模型可以合理的描述熔体的剪切黏度和拉伸黏度的关系;基于Moore动力学方程的黏度模型改进了原有的动力学方程,能够准确的描述聚合物熔体的剪切流变和拉伸流变行为;引入了温度参数的PTT模型比较清晰的体现了拉伸黏度与温度之间的关系;基于Cross方程的经验模型形式简洁,适合应用于有限元模拟。在本文中,不仅利用实验数据对这四个模型进行了验证,还对模型中各个参数的作用进行了分析。
利用MATLAB对入口收敛流动分析中的Cogswell模型,Binding模型和Liang模型进行了数值模拟,对三个模型中影响入口收敛流动自然收敛角、边界流线以及涡流区长度的各个参数进行了深入的分析和比较。在FLUENT上利用基于Cross方程的拉伸黏度模型对典型的流道收缩比为4:1的入口收敛流动进行了有限元模拟,分析了由于参数变化而造成的特劳顿比(Trouton ratio)的变化对于形成的收敛流道涡流区大小的影响。
用熔融纺丝法测量了低密度聚乙烯(LDPE)、线性低密度聚乙烯(LLDPE)、高密度聚乙烯(HDPE)三种聚乙烯和聚丙烯(PP)熔体的拉伸流变性能。分析了温度对于材料的熔体强度和可拉伸性的影响,进一步利用Arrhenius方程计算了四种材料的熔体强度活化能,比较了四种材料的温度敏感性。利用“局部方法”的计算结果,绘制了拉伸应力与拉伸应变速率,拉伸黏度与拉伸应变速率的关系曲线,研究了拉伸应变速率、温度和挤出速度对于拉伸应力和拉伸黏度的影响。根据熔融纺丝测量结果,绘制了材料的拉伸流变主曲线。利用主曲线对LDPE和LLDPE的拉伸流变性能进行了比较,深入的分析了比例因子b与温度和挤出速度的关系,根据b与不同温度和挤出速度下熔体拉伸曲线的对应关系,对设定条件下的熔体的拉伸黏度进行了估算,将结果与测量数据进行了比较。基于Cogswell模型,用入口收敛法测量了LDPE和LLDPE的拉伸黏度,并与熔融纺丝测量结果进行了比较。
In many processing operations, polymer melts experience extensional flows. The elongation behaviors of polymer melts have important effects on the processing procedures and the mechanical properties of final products. The thorough knowledge of the extensional properties of polymer can effectively optimize the production procedure and improve the products quality. In this article, we comprehensively studied the extensional flow behaviors and mechanisms of polyethylene melts from the modeling, simulation and measurements.
Four extensional viscosity models were derived in this work The model based on White-Metzner equation is reasonable to describe the relation between shear viscosity and extensional viscosity; the model based on Moore dynamic equation that with some modifications of the original Moore equation can correctly describe both the shear and extensional rheology of polymer melts; the PTT model with temperature parameter can clearly demonstrate the relation between temperature and extensional viscosity; the model based on Cross model is simple and suitable to apply in finite element simulation. These four models were verified with experiment results and the effects of their parameters were analyzed
Numerical simulation of Cogswell model, Binding model and Liang model were performed on MATLAB. The effects of model parameters on the natural convergent angle, boundary streamline and vortex length were discussed. Finite element simulations of 4:1 entrance flow were performed on the FLUENT with the extensional viscosity model based on Cross model. The effects of the change of Trouton ratio on the formation of vortex size were discussed.
The extensional rheological properties of low density polyethylene (LDPE), linear low density polyethylene (LLDPE), high density polyethylene (HDPE) and polypropylene (PP) were measured by melt spinning technique. The influences of temperature on the melt strength and draw ability were analyzed. Applied the Arrhenius equation to calculate the activation energy of melt strength for these four materials and compared the temperature sensitivity of them. A“Local match”was used to obtain the extensional stress and viscosity. The curves of extensional stress versus strain rate and extensional viscosity versus strain rate were plotted by the results. The effects of extensional strain rate, temperature and extrusion velocity on the extensional stress and viscosity were discussed. According to the measurement curves, the mastercurves of melt spinning were drawn. The properties of LDPE and LLDPE were compared by their mastercurves. The relations between the ratio b with temperature and with extrusion velocity were comprehensively investigated. According to result that each b had a unique relation with temperature and with extrusion velocity, the extensional viscosities of some setting conditions were calculated. The results of estimation were compared with experimental data. The entrance flow measurements that based on Cogswell model were performed to obtain the extensional viscosity of LDPE and LLDPE and the results were compared with those obtained by melt spinning technique.
构建了四个聚合物熔体的拉伸黏度模型,其中,基于White-Metzner模型的拉伸黏度模型可以合理的描述熔体的剪切黏度和拉伸黏度的关系;基于Moore动力学方程的黏度模型改进了原有的动力学方程,能够准确的描述聚合物熔体的剪切流变和拉伸流变行为;引入了温度参数的PTT模型比较清晰的体现了拉伸黏度与温度之间的关系;基于Cross方程的经验模型形式简洁,适合应用于有限元模拟。在本文中,不仅利用实验数据对这四个模型进行了验证,还对模型中各个参数的作用进行了分析。
利用MATLAB对入口收敛流动分析中的Cogswell模型,Binding模型和Liang模型进行了数值模拟,对三个模型中影响入口收敛流动自然收敛角、边界流线以及涡流区长度的各个参数进行了深入的分析和比较。在FLUENT上利用基于Cross方程的拉伸黏度模型对典型的流道收缩比为4:1的入口收敛流动进行了有限元模拟,分析了由于参数变化而造成的特劳顿比(Trouton ratio)的变化对于形成的收敛流道涡流区大小的影响。
用熔融纺丝法测量了低密度聚乙烯(LDPE)、线性低密度聚乙烯(LLDPE)、高密度聚乙烯(HDPE)三种聚乙烯和聚丙烯(PP)熔体的拉伸流变性能。分析了温度对于材料的熔体强度和可拉伸性的影响,进一步利用Arrhenius方程计算了四种材料的熔体强度活化能,比较了四种材料的温度敏感性。利用“局部方法”的计算结果,绘制了拉伸应力与拉伸应变速率,拉伸黏度与拉伸应变速率的关系曲线,研究了拉伸应变速率、温度和挤出速度对于拉伸应力和拉伸黏度的影响。根据熔融纺丝测量结果,绘制了材料的拉伸流变主曲线。利用主曲线对LDPE和LLDPE的拉伸流变性能进行了比较,深入的分析了比例因子b与温度和挤出速度的关系,根据b与不同温度和挤出速度下熔体拉伸曲线的对应关系,对设定条件下的熔体的拉伸黏度进行了估算,将结果与测量数据进行了比较。基于Cogswell模型,用入口收敛法测量了LDPE和LLDPE的拉伸黏度,并与熔融纺丝测量结果进行了比较。
In many processing operations, polymer melts experience extensional flows. The elongation behaviors of polymer melts have important effects on the processing procedures and the mechanical properties of final products. The thorough knowledge of the extensional properties of polymer can effectively optimize the production procedure and improve the products quality. In this article, we comprehensively studied the extensional flow behaviors and mechanisms of polyethylene melts from the modeling, simulation and measurements.
Four extensional viscosity models were derived in this work The model based on White-Metzner equation is reasonable to describe the relation between shear viscosity and extensional viscosity; the model based on Moore dynamic equation that with some modifications of the original Moore equation can correctly describe both the shear and extensional rheology of polymer melts; the PTT model with temperature parameter can clearly demonstrate the relation between temperature and extensional viscosity; the model based on Cross model is simple and suitable to apply in finite element simulation. These four models were verified with experiment results and the effects of their parameters were analyzed
Numerical simulation of Cogswell model, Binding model and Liang model were performed on MATLAB. The effects of model parameters on the natural convergent angle, boundary streamline and vortex length were discussed. Finite element simulations of 4:1 entrance flow were performed on the FLUENT with the extensional viscosity model based on Cross model. The effects of the change of Trouton ratio on the formation of vortex size were discussed.
The extensional rheological properties of low density polyethylene (LDPE), linear low density polyethylene (LLDPE), high density polyethylene (HDPE) and polypropylene (PP) were measured by melt spinning technique. The influences of temperature on the melt strength and draw ability were analyzed. Applied the Arrhenius equation to calculate the activation energy of melt strength for these four materials and compared the temperature sensitivity of them. A“Local match”was used to obtain the extensional stress and viscosity. The curves of extensional stress versus strain rate and extensional viscosity versus strain rate were plotted by the results. The effects of extensional strain rate, temperature and extrusion velocity on the extensional stress and viscosity were discussed. According to the measurement curves, the mastercurves of melt spinning were drawn. The properties of LDPE and LLDPE were compared by their mastercurves. The relations between the ratio b with temperature and with extrusion velocity were comprehensively investigated. According to result that each b had a unique relation with temperature and with extrusion velocity, the extensional viscosities of some setting conditions were calculated. The results of estimation were compared with experimental data. The entrance flow measurements that based on Cogswell model were performed to obtain the extensional viscosity of LDPE and LLDPE and the results were compared with those obtained by melt spinning technique.
引文
[1] Liang J Z. Estimation of vortical region length of rubber compound during entry flow[J]. Plast. Rubber Compos. Process. Appl. 1996, 25: 495-498.
[2] Liang J Z. Determination of the entry region length of viscoelastic fluid flow in a channel[J]. Chem. Eng. Sci. 1998, 53(17): 3185-3187.
[3]梁基照.聚合物材料加工流变学[M].北京:国防工业出版社, 2008.
[4]吴其晔,巫静安.高分子材料流变学[M].北京:高等教育出版社, 2002.
[5] Ferry J D. Viscoelastic properties of polymers 3rd[M]. New York: Wiley, 1980.
[6] Tanner R I, Walters K. Rheology: An Historical Perspective[M]. Amsterdam: Elsevier, 1998.
[7] Liang J Z. Planar entry converging flow during extrusion of polymer melts[J]. Polymer-Plastics Technol. Eng. 2007, 46(5): 475-480.
[8]陈克权,张飚,张伟.聚对苯二甲酸丙二酯熔体拉伸流变性能研究[J].合成纤维. 2004, 33(3): 4-6.
[9]蔡兵,韩式方.共转Oldroyd B流体剪切-拉伸流动研究[J].应用力学学报. 2003, 20(3): 47-51.
[10]韩式方.高强度液晶高分子纺丝纤维取向机制研究[J].力学与实践. 2004, 26(3): 39-41.
[11]韩式方.液晶高分子-各向异性流体挤出拉伸分岔研究[J].力学与实践. 2006, 28(3): 15-18.
[12]李笑喃,刘鹏波.聚丙烯熔体拉伸流变行为的研究[J].塑料工业. 2007, 35(3): 45-47.
[13]汪永斌,张丽叶.辐照改性聚丙烯拉伸流变行为及其挤出发泡的研究[J].中国塑料. 2005, 19(8): 32-35.
[14]汪永斌,张丽叶.辐照改性制备长支链型高熔体强度聚丙烯流变性能(Ⅱ)拉伸流变[J].化工学报. 2007, 58(2): 481-487.
[15] Dealy J M. Extensional rheometers for molten polymers: a review [J]. Journal of Non-Newtonian Fluid Mechanics. 1978, 4: 9-21.
[16] Petrie C S. Extensional Flow-a mathematical perspective [J]. Rheologica Acta. 1995,34(1): 12-26.
[17] Meissner J, Hostettler J. A new elongational rheometer for polymer melts and other highly viscoelastic liquids [J]. Rheologica Acta. 1994, 33(1): 1-21.
[18] Munstedt H. Viscoelasticity of polystyrene melts in tensile creep experiments[J]. Rheology Acta. 1975, 14: 1077-1088.
[19] Munstedt H. New universal extensional rheometer for polymer melts. Measurements on a polystyrene sample[J]. Journal of Rheology. 1979, 23(4): 421-436.
[20] Schweizer T. The uniaxial elongational rheometer RME - six years of experience [J]. Rheologica. Acta. 2000, 39(5): 428-443.
[21] Levitt L, Macosko W, Schweizer T. Extensional rheometry of polymer multilayers: A sensitive probe of interfaces[J]. Journal of Rheology. 1997, 41(3): 671-685.
[22] Meissner J, Raible T, Stephenson S E. Rotary Clamp in Uniaxial and Biaxial Extensional Rheometry of Polymer Melts [J]. Journal of Rheology. 1981, 25(1): 1-28.
[23] Demarmels A, Meissner J. Multiaxial elongation of polyisobutylene with various and changing strain rate ratios [J]. Rheologica Acta. 1985, 24(3): 253-259.
[24] Berger L, Meissner J. Linear viscoelasticity, simple and planar melt extension of linear polybutadienes with bimodal molar mass distributions [J]. Rheologica Acta. 1992, 31(1): 63-74.
[25] Hachmann P, Meissner J. Rheometer for equibiaxial and planar. elongations of polymer melts [J]. Journal of Rheology. 2003, 47(4): 989-1010.
[26] Handge U A. Experimental investigation of equibiaxial extension and breakup of drops in a molten two phase polymer blend[J]. Phys Rev E. 2005, 72: 11801.
[27] Handge U A, Schmidheiny W. A tool for rapid quenching of elonged polymer melts[J]. Rheologica Acta. 2007, 46(6): 913-919.
[28] Maia J M, Covas J A, Nóbrega J M, et al. Measuring uniaxial extensional viscosity using a modified rotational rheometer [J]. Journal of Non-Newtonian Fluid Mechanics. 1999, 80(2-3): 183-197.
[29] Matta J E, Tytus R P. Liquid stretching using a falling cylinder[J]. Journal of Non-Newtonian Fluid Mechanics. 1990, 35(2-3): 215-229.
[30] Tirtaadmadja V, Sridhar T. A filament stretching device for measurement of extensionalviscosity [J]. Journal of Rheology. 1993, 37(6): 1081-1102.
[31] Ooi Y W, Sridhar T. Resistance to uniaxial extensional flow of fibre suspensions.[J]. Rheology Acta. 2004, 43: 223-231.
[32] Mckinley G H, Sridhar T. Filament-stretching rheometry of complex fluids[J]. Annual Review of Fluid Mechanics. 2002, 34: 375-415.
[33] Anna S L, Mckinley G H, Nguyen D A, et al. An interlaboratory comparison of measurements from filament-stretching rheometers using common test fluids[J]. Journal of Rheology. 2001, 45(1): 83-114.
[34] Bach A, Rasmussen H K, Hassager O. Extensional viscosity for polymer melts measured in the filament stretching rheometer [J]. Journal of Rheology. 2003, 47(2): 429-441.
[35] Sentmanat M. Dual Wind-up drum extensional rheometer [P]. 2004, US Patent No. 6691569.
[36] Sentmanat M. Miniature universal testing platform: from extensional melt rheology to solid-state deformation behavior[J]. Rheologica Acta. 2004, 43(6): 657-669.
[37] Macosko C W. Rheology Principles, Measurements and Applications[M]. VCH, New York, 1994.
[38] Ghijsels A, Ente J. Melt strength behaviour of polyethylene melts[J]. Int Polym Process. 1992, 7: 44-50.
[39] Ghijsels A, Ente J. Melt strength behavior of PE and its relation to bubble stability[J]. Int Polym Process. 1990, 5: 284-286.
[40] Ghijsels A, Clippeleir D. Melt strength behavior of polypropylenes[J]. Int Polym Process. 1994, 9: 252-257.
[41] La Mantia F P, Acierno D. Influence of molecular structure on the melt strength and extensibility of polyethylenes[J]. Polym Eng Sci. 1985, 25: 279-283.
[42] Kao N, Chandra A, Bhattacharya S N. Melt strength of calcium carbonate filled polypropylene melts[J]. Polym Int. 2002, 51: 1385-1389.
[43] Mcinerney L F, Kao N, Bhattacharya S N. Melt strength and extensibility of talc-filled polypropylene[J]. Polym Eng Sci. 2003, 43: 1821-1829.
[44] Laun H M, Schuch H. Transient elongational viscosities and drawability of polymermelts in rheology[J]. Journal of Rheology. 1989, 33(1): 119-175.
[45] Laun H M, Munstedt H. Elongational behavior of a low-density polyethylene melt. 1. Strain rate and stress dependence of viscosity and recoverable strain in steady-state-comparison with shear data influence of interfacial tension[J]. Rheology Acta. 1978, 17: 415-425.
[46] Revenu P, Guillet J, Carrot C. Elongational flow of polyethylenes in isothermal melt spinning[J]. Journal of Rheology. 1993, 37: 1041-1056.
[47] Wagner M H, Collignon B, Verbeke J. Rheotens-mastercurves and elongational viscosity of polymer melts[J]. Rheologica Acta. 1996, 35: 117-126.
[48] Wagner M H, Schulze V, G?ttfert A. Rheotens-mastercurves and drawability of polymer melts.[J]. Polym Eng Sci. 1996, 36: 925-935.
[49] Wagner M H, Bernnat A, Schulze V. The rheology of the Rheotens test[J]. Journal of Rheology. 1998, 42(917-928).
[50] Bernnat A, Wagner M H, Chai C K. Assessment of LDPE melt strength by use of Rheotens mastercurves[J]. Int Polym Process. 2000, 15: 268-272.
[51] Muke S, Ivanov I, Kao N, et al. Extensional rheology of polypropylene melts from the Rheotens test[J]. Journal of Non-Newtonian Fluid Mechanics. 2001, 101: 77-93.
[52] P?tschke P, Brünig H, Janke A, et al. Orientation of multiwalled carbon nanotubes in composites with polycarbonate by melt spinning[J]. Polymer. 2005, 46:10355-10363.
[53] Gotsis D A, Ke Q. Comparison of three methods to measure the elongational viscosity of polymer melts: entry flow, fiber spinning and uniaxial elongation. [R]. New York: SPE ANTEK: 1999.
[54] Cogswell F N. Converging flow of polymer melts in extrusion dies[J]. Polym Eng Sci. 1972, 12: 64-73.
[55] Cogswell F N. Measuring the Extensional Rheology of Polymer Melts[J]. Journal of Rheology. 1972, 16(3): 383-403.
[56] Cogswell F N. Converging flow and stretching flow: A compilationstar[J]. Journal of Non-Newtonian Fluid Mechanics. 1978, 4(1-2): 23-38.
[57] Binding D M. An approximate analysis for contraction and converging flows[J]. Journal of Non-Newtonian Fluid Mechanics. 1988, 27: 173-189.
[58] Binding D M. Further considerations of axisymmetric contraction flows[J]. Journal of Non-Newtonian Fluid Mechanics. 1991, 41: 27-42.
[59] Binding D M, Couch M A, Walters K. The pressure dependence of the shear and elongational properties of polymer melts[J]. Journal of Non-Newton Fluid Mechanics. 1998, 79: 137-155.
[60] Gotsis D A, Odriozola A. The relevance of entry flow measurements for the estimation of extensional viscosity of polymer melts[J]. Rheology Acta. 1998, 37(430-437).
[61] Gotsis A D, Odriozola A. Extensional viscosity of a thermotropic liquid crystalline polymer[J]. Journal of Rheology. 2000, 44: 1205-1223.
[62] Gibson A G. Die entry flow of reinforced polymers[J]. Composites. 1989, 20: 57-64.
[63] Mcleish T C B, Larson R G. Molecular constitutive equations for a class of branched polymers: the Pom–Pom model[J]. Journal of Rheology. 1998, 42(1): 81-110.
[64] Ball R C, Mcleish T C B. Dynamic dilution and the viscosity of star polymer melts[J]. Macromolecules. 1989, 22(4): 1911-1913.
[65] Larson R G. Constitutive Equations for Polymer Melts and Solutions[M]. Boston: Butterworths, 1988.
[66] Rubio P, Wagner M H. LDPE melt rheology and the pom-pom model[J]. Journal of Non-Newtonian Fluid Mechanics. 2000, 92: 245-259.
[67] Clemeur N, Rutgers R P G, Debbaut B. On the evaluation of some differential formulations for the pom-pom constitutive model[J]. Rheology Acta. 2003, 42: 217-231.
[68] Bishko G B, Harlen O G, Mcleish T C B, et al. Numerical simulation of the transient flow of branched polymer melts through a planar contraction using the‘pom-pom’model[J]. Journal of Non-Newtonian Fluid Mechanics. 1999, 82(2-3): 255-273.
[69] Inkson N J, Mcleish T C B, Harlen O G, et al. Predicting low density polyethylene rheology in flows and shear with Pom-Pom constitutive equation[J]. Journal of Rheology. 1999, 43(4): 873-896.
[70] Blackwell R J, Mcleish T C B, Harlen O G. Molecular drag-strain coupling in branched polymer melts[J]. Journal of Rheology. 2000, 44(1): 121-136.
[71] Ottinger H C. A thermodynamically admissible reptation model for fast flows ofentangled polymers[J]. Journal of Rheology. 1999, 43(6): 1461-1493.
[72] Verbeeten W M H, Peters G W M, Baaijens F P T. Differential constitutive equations for polymer melts: extended Pom-Pom model[J]. Journal of Rheology. 2001, 45(4): 823-843.
[73] Verbeeten W M H, Peters G W M, Baaijens F P T. Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model[J]. Journal of Non-Newtonian Fluid Mechanics. 2004, 117(2-3): 73-84.
[74] Meerveld J V. Note on thermodynamic consistency of the integral pom-pom model[J]. Journal of Non-Newtonian Fluid Mechanics. 2002, 108(1-3): 291-299.
[75] Tanner R I. Engineering Rheology 2nd[M]. Oxford Univ Press, 2000.
[76] Huilgol R R, Phan-Thien N. Fluid Mechanics of Viscoelasticity[M]. Amsterdam: Elsevier, 1997.
[77] Tanner R I, Zdilar A M, Nasseri S. Recoil from elongation using general network models[J]. Rheologica Acta. 2005, 44(5): 513-520.
[78] Tanner R I, Nasseri S. Simple constitutive models for linear and branched polymers[J]. Journal of Non-Newtonian Fluid Mechanics. 2003, 116(1): 1-17.
[79] Tanner R I. Revisitation of PTT model [J]. J. Cent. South Univ. Technol. 2007, 14(s1): 26-29.
[80] Kwon Y, Leonov A I. Stability constraints in the formulation of viscoelastic constitutive equations[J]. Journal of Non-Newtonian Fluid Mechanics. 1995, 58(1): 25.
[81] Simhambhatla M, Leonov A I. On the rheological modeling of viscoelastic polymer liquids with stable constitutive-equations[J]. Rheologica Acta. 1995, 34(3): 259-273.
[82] Larson R G. Elongational-flow predictions of the Leonov constitutive equation[J]. Rheologica Acta. 1983, 22: 435-448.
[83] Zatloukal M. Differential viscoelastic constitutive equations for polymer melts in steady shear and elongational flows[J]. Journal of Non-Newtonian Fluid Mechanics. 2003, 113(2-3): 209-227.
[84] Pivokonsky R, Zatloukal M. On the predictive/fitting capabilities of the advanced differential constitutive equations for branched LDPE melts[J]. Journal of Non-Newtonian Fluid Mechanics. 2006, 135(1): 58-67.
[85] Muller R, Froelich D. New extensional rheometer for elongational viscosity and flow birefringence measurements: some results on polystyrene melts[J]. Polymer. 1985, 26: 1477-1482.
[86] Matsumoto T, Bogue D C. Stress birefringence in amorphous polymers under nonisothermal conditions[J]. J Polym Sci Polym Phys. 1977, 15: 1663-1674.
[87] Luap C, Müller C, Schweizer T, et al. Simultaneous stress and birefringence measurements during uniaxial elongation of polystyrene melts with narrow molecular weight distribution[J]. Rheology Acta. 2005, 45: 83-91.
[88] M K. Simple models for complex nonequilibrium fluids[J]. Phys Rep. 2004, 390(6): 453-551.
[89] Gotsis A D, Zeevenhoven B L F, Tsenoglou C. Effect of long branches on the rheology of polypropylene[J]. Journal of Rheology. 2004, 48(4): 895-914.
[90] Munstedt H, Auhl D. Rheological measuring techniques and their relevance for the molecular characterization of polymers[J]. Journal of Non-Newtonian Fluid Mechanics. 2005, 128: 62-69.
[91] Delaby I, Ernst B, Germain Y, et al. Droplet deformation in polymer blends during uniaxial elongational flow: influence of viscosity ratio for large capillary numbers[J]. Journal of Rheology. 1994, 38(6): 1705-1720.
[92] Fornes T D, Baur J W, Sabba Y, et al. Morphology and properties of melt-spun polycarbonate fibers containing single- and multi-wall carbon nanotubes.[J]. Polymer. 2006, 47: 1704-1714.
[93] Handge U A, P?tschke P. Interplay of rheology and morphology in melt elongation and subsequent recovery of polystyrene/poly(methyl methacrylate) blends[J]. Journal of Rheology. 2004, 48: 1103-1122.
[94] Handge U A, Buschnakowski M, Michler G H. Deformation and alignment of lamellae in melt extension of blends of a styrene-butadiene block copolymer with polystyrene[J]. Journal of Applied Polymer Science. 2009, 112(3): 1319-1329.
[95] Heindl M, Sommer M K, Münstedt H. Morphology development in polystyrene/polyethylene blends during uniaxial elongational flow[J]. Rheology Acta. 2004, 44: 55-70.
[96] Lee W K, Kim H D, Kim E Y. Morphological reorientation by extensional flow deformation of a triblock copolymer styrene–isoprene–styrene[J]. Current Applied Physics. 2006, 6(4): 718-722.
[97] Oosterlink F, Mours M, Laun H M. Morphology development of a polystyrene/polymethylmethacrylate blend during start-up of uniaxial elongational flow[J]. Journal of Rheology. 2005, 49(4): 897-918.
[98] Gramespacher H, Meissner J. Melt elongation and recovery of polymer blends, morphology, and influence of interfacial tension[J]. Journal of Rheology. 1997, 41(1): 27-44.
[99] P?tschke P, Abdel-Goad M, Alig I, et al. Rheological and dielectrical characterization of melt mixed polycarbonate-multiwalled carbon nanotube composites[J]. Polymer. 2004, 45: 8863-8870.
[100] Takahashi T, Takimoto J, Koyam K. Uniaxial elongational viscosity of various molten polymer composites[J][J]. Polymer Composites. 1999, 20(3): 357-366.
[101] Gupta R K, Pasanovic-Zujo V, Bhattacharya S N. Shear and extensional rheology of EVA/layered silicate-nanocomposites[J]. Journal of Non-Newtonian Fluid Mechanics. 2005, 128(2-3): 116-125.
[102] Garofalo E, Russo G M, Maio L D, et al. Study on the Effect of Uniaxial Elongational Flow on Polyamide Based Nanocomposites[J]. Macromol. Symp. 2007, 247: 110-119.
[103] Handge U A, P?tschke P. Deformation and orientation during shear and elongation of a polycarbonate/carbon nanotubes composite in the melt[J]. Rheologica Acta. 2007, 46: 889-898.
[104] Wagner M H, Kheirandish S, Yamaguchi M. Quantitative analysis of melt elongational behavior of LLDPE/LDPE blends[J]. Rheologica Acta. 2004, 44: 198-218.
[105] Stange J, Münstedt H. Rheological behavior of blends of alinear and a long-chain branched polypropylene[J]. Journal of Rheology. 2005, 49: 1059-1079.
[106] Wagner M H, Kheirandish S, Stange J. Modeling elongational viscosity of blends of linear and long-chain branched polypropylenes[J]. Rheologica Acta. 2006, 46: 211-221.
[107] Mccallum T J, Kontopoulou M, Park C B, et al. The Rheological and Physical Properties of Linear and Branched Polypropylene Blends[J]. Polymer Engineering andScience. 2007, 47: 1133-1140.
[108] Xue S C, Phan Thein N, Tanner R I. Three dimensional numerical simulations of viscoelastic flows through planar contractions[J]. Journal of Non-Newtonian Fluid Mechanics. 1998, 74(1-3): 195-245.
[109] Purnode B, Crochet M J. Flows of polymer solutions through contractions Part 1: flows of polyacrylamide solutions through planar contractions[J]. Journal of Non-Newtonian Fluid Mechanics. 1996, 65(2-3): 269-289.
[110] Barnes H A, Roberts G P. A simple empirical model describing the steady-state shear and extensional viscosities of polymer melts[J]. Journal of Non-Newtonian Fluid Mechanics. 1992, 44: 113-126.
[111] Moore F. The rheology of ceramic slips and bodies[J]. Trans. Br. Ceram. Soc. 1959, 58: 470-484.
[112] Boek E S, Padding J T, Anderson V J, et al. Constitutive equations for extensional flow of wormlike micelles: stability analysis of the Bautista–Manero model[J]. Journal of Non-Newtonian Fluid Mechanics. 2005, 126: 39-46.
[113] Liang J Z. Estimation of entry natural converging angles during capillary extrusion flow of carbon black filled NR/SBR compound[J]. Polymer Testing. 2005, 24(4): 435-438.
[114] Ma C Y, White J L, Weissert F C, et al. Flow patterns in carbon black filled polyethylene at the entrance to a die[J]. Journal of Non-Newtonian Fluid Mechanics. 1985, 17: 275-287.
[115] Martyn M T, Nakason C, Coates P D. Flow visualisation of polymer melts in abrupt contraction extrusion dies: quantification of melt recirculation and flow patterns[J]. Journal of Non-Newtonian Fluid Mechanics. 2000, 91: 109-122
[116] White S A, Gotsis D A, Baird D G, Review of the entry flow problem: experimental and numerical[J]. Journal of Non-Newtonian Fluid Mechanics. 1987, 24: 121-160
[117]梁基照. LDPE熔体在挤出口模流动时入口区流型的观测[J].合成树脂及塑料. 2003, 20(1): 53-56.
[118] Baldi F, Franceschini A, Ricco T. Determination of the elongational viscosity of polymer melts by melt spinning experiments: A comparison with different experimental
[119] Baldi F, Franceschini A, Bignotti F. Rheological behaviour of nano-composites based on polyamide 6 under shear and elongational flow at high strain rates[J]. Rheologica Acta. 2009, 48(1): 73-88.
[120] Munstedt H, Laun H M. Elongational behaviour of a low density polyethylene melt[J]. Rheologica Acta, 1979, 18:492-504.
[2] Liang J Z. Determination of the entry region length of viscoelastic fluid flow in a channel[J]. Chem. Eng. Sci. 1998, 53(17): 3185-3187.
[3]梁基照.聚合物材料加工流变学[M].北京:国防工业出版社, 2008.
[4]吴其晔,巫静安.高分子材料流变学[M].北京:高等教育出版社, 2002.
[5] Ferry J D. Viscoelastic properties of polymers 3rd[M]. New York: Wiley, 1980.
[6] Tanner R I, Walters K. Rheology: An Historical Perspective[M]. Amsterdam: Elsevier, 1998.
[7] Liang J Z. Planar entry converging flow during extrusion of polymer melts[J]. Polymer-Plastics Technol. Eng. 2007, 46(5): 475-480.
[8]陈克权,张飚,张伟.聚对苯二甲酸丙二酯熔体拉伸流变性能研究[J].合成纤维. 2004, 33(3): 4-6.
[9]蔡兵,韩式方.共转Oldroyd B流体剪切-拉伸流动研究[J].应用力学学报. 2003, 20(3): 47-51.
[10]韩式方.高强度液晶高分子纺丝纤维取向机制研究[J].力学与实践. 2004, 26(3): 39-41.
[11]韩式方.液晶高分子-各向异性流体挤出拉伸分岔研究[J].力学与实践. 2006, 28(3): 15-18.
[12]李笑喃,刘鹏波.聚丙烯熔体拉伸流变行为的研究[J].塑料工业. 2007, 35(3): 45-47.
[13]汪永斌,张丽叶.辐照改性聚丙烯拉伸流变行为及其挤出发泡的研究[J].中国塑料. 2005, 19(8): 32-35.
[14]汪永斌,张丽叶.辐照改性制备长支链型高熔体强度聚丙烯流变性能(Ⅱ)拉伸流变[J].化工学报. 2007, 58(2): 481-487.
[15] Dealy J M. Extensional rheometers for molten polymers: a review [J]. Journal of Non-Newtonian Fluid Mechanics. 1978, 4: 9-21.
[16] Petrie C S. Extensional Flow-a mathematical perspective [J]. Rheologica Acta. 1995,34(1): 12-26.
[17] Meissner J, Hostettler J. A new elongational rheometer for polymer melts and other highly viscoelastic liquids [J]. Rheologica Acta. 1994, 33(1): 1-21.
[18] Munstedt H. Viscoelasticity of polystyrene melts in tensile creep experiments[J]. Rheology Acta. 1975, 14: 1077-1088.
[19] Munstedt H. New universal extensional rheometer for polymer melts. Measurements on a polystyrene sample[J]. Journal of Rheology. 1979, 23(4): 421-436.
[20] Schweizer T. The uniaxial elongational rheometer RME - six years of experience [J]. Rheologica. Acta. 2000, 39(5): 428-443.
[21] Levitt L, Macosko W, Schweizer T. Extensional rheometry of polymer multilayers: A sensitive probe of interfaces[J]. Journal of Rheology. 1997, 41(3): 671-685.
[22] Meissner J, Raible T, Stephenson S E. Rotary Clamp in Uniaxial and Biaxial Extensional Rheometry of Polymer Melts [J]. Journal of Rheology. 1981, 25(1): 1-28.
[23] Demarmels A, Meissner J. Multiaxial elongation of polyisobutylene with various and changing strain rate ratios [J]. Rheologica Acta. 1985, 24(3): 253-259.
[24] Berger L, Meissner J. Linear viscoelasticity, simple and planar melt extension of linear polybutadienes with bimodal molar mass distributions [J]. Rheologica Acta. 1992, 31(1): 63-74.
[25] Hachmann P, Meissner J. Rheometer for equibiaxial and planar. elongations of polymer melts [J]. Journal of Rheology. 2003, 47(4): 989-1010.
[26] Handge U A. Experimental investigation of equibiaxial extension and breakup of drops in a molten two phase polymer blend[J]. Phys Rev E. 2005, 72: 11801.
[27] Handge U A, Schmidheiny W. A tool for rapid quenching of elonged polymer melts[J]. Rheologica Acta. 2007, 46(6): 913-919.
[28] Maia J M, Covas J A, Nóbrega J M, et al. Measuring uniaxial extensional viscosity using a modified rotational rheometer [J]. Journal of Non-Newtonian Fluid Mechanics. 1999, 80(2-3): 183-197.
[29] Matta J E, Tytus R P. Liquid stretching using a falling cylinder[J]. Journal of Non-Newtonian Fluid Mechanics. 1990, 35(2-3): 215-229.
[30] Tirtaadmadja V, Sridhar T. A filament stretching device for measurement of extensionalviscosity [J]. Journal of Rheology. 1993, 37(6): 1081-1102.
[31] Ooi Y W, Sridhar T. Resistance to uniaxial extensional flow of fibre suspensions.[J]. Rheology Acta. 2004, 43: 223-231.
[32] Mckinley G H, Sridhar T. Filament-stretching rheometry of complex fluids[J]. Annual Review of Fluid Mechanics. 2002, 34: 375-415.
[33] Anna S L, Mckinley G H, Nguyen D A, et al. An interlaboratory comparison of measurements from filament-stretching rheometers using common test fluids[J]. Journal of Rheology. 2001, 45(1): 83-114.
[34] Bach A, Rasmussen H K, Hassager O. Extensional viscosity for polymer melts measured in the filament stretching rheometer [J]. Journal of Rheology. 2003, 47(2): 429-441.
[35] Sentmanat M. Dual Wind-up drum extensional rheometer [P]. 2004, US Patent No. 6691569.
[36] Sentmanat M. Miniature universal testing platform: from extensional melt rheology to solid-state deformation behavior[J]. Rheologica Acta. 2004, 43(6): 657-669.
[37] Macosko C W. Rheology Principles, Measurements and Applications[M]. VCH, New York, 1994.
[38] Ghijsels A, Ente J. Melt strength behaviour of polyethylene melts[J]. Int Polym Process. 1992, 7: 44-50.
[39] Ghijsels A, Ente J. Melt strength behavior of PE and its relation to bubble stability[J]. Int Polym Process. 1990, 5: 284-286.
[40] Ghijsels A, Clippeleir D. Melt strength behavior of polypropylenes[J]. Int Polym Process. 1994, 9: 252-257.
[41] La Mantia F P, Acierno D. Influence of molecular structure on the melt strength and extensibility of polyethylenes[J]. Polym Eng Sci. 1985, 25: 279-283.
[42] Kao N, Chandra A, Bhattacharya S N. Melt strength of calcium carbonate filled polypropylene melts[J]. Polym Int. 2002, 51: 1385-1389.
[43] Mcinerney L F, Kao N, Bhattacharya S N. Melt strength and extensibility of talc-filled polypropylene[J]. Polym Eng Sci. 2003, 43: 1821-1829.
[44] Laun H M, Schuch H. Transient elongational viscosities and drawability of polymermelts in rheology[J]. Journal of Rheology. 1989, 33(1): 119-175.
[45] Laun H M, Munstedt H. Elongational behavior of a low-density polyethylene melt. 1. Strain rate and stress dependence of viscosity and recoverable strain in steady-state-comparison with shear data influence of interfacial tension[J]. Rheology Acta. 1978, 17: 415-425.
[46] Revenu P, Guillet J, Carrot C. Elongational flow of polyethylenes in isothermal melt spinning[J]. Journal of Rheology. 1993, 37: 1041-1056.
[47] Wagner M H, Collignon B, Verbeke J. Rheotens-mastercurves and elongational viscosity of polymer melts[J]. Rheologica Acta. 1996, 35: 117-126.
[48] Wagner M H, Schulze V, G?ttfert A. Rheotens-mastercurves and drawability of polymer melts.[J]. Polym Eng Sci. 1996, 36: 925-935.
[49] Wagner M H, Bernnat A, Schulze V. The rheology of the Rheotens test[J]. Journal of Rheology. 1998, 42(917-928).
[50] Bernnat A, Wagner M H, Chai C K. Assessment of LDPE melt strength by use of Rheotens mastercurves[J]. Int Polym Process. 2000, 15: 268-272.
[51] Muke S, Ivanov I, Kao N, et al. Extensional rheology of polypropylene melts from the Rheotens test[J]. Journal of Non-Newtonian Fluid Mechanics. 2001, 101: 77-93.
[52] P?tschke P, Brünig H, Janke A, et al. Orientation of multiwalled carbon nanotubes in composites with polycarbonate by melt spinning[J]. Polymer. 2005, 46:10355-10363.
[53] Gotsis D A, Ke Q. Comparison of three methods to measure the elongational viscosity of polymer melts: entry flow, fiber spinning and uniaxial elongation. [R]. New York: SPE ANTEK: 1999.
[54] Cogswell F N. Converging flow of polymer melts in extrusion dies[J]. Polym Eng Sci. 1972, 12: 64-73.
[55] Cogswell F N. Measuring the Extensional Rheology of Polymer Melts[J]. Journal of Rheology. 1972, 16(3): 383-403.
[56] Cogswell F N. Converging flow and stretching flow: A compilationstar[J]. Journal of Non-Newtonian Fluid Mechanics. 1978, 4(1-2): 23-38.
[57] Binding D M. An approximate analysis for contraction and converging flows[J]. Journal of Non-Newtonian Fluid Mechanics. 1988, 27: 173-189.
[58] Binding D M. Further considerations of axisymmetric contraction flows[J]. Journal of Non-Newtonian Fluid Mechanics. 1991, 41: 27-42.
[59] Binding D M, Couch M A, Walters K. The pressure dependence of the shear and elongational properties of polymer melts[J]. Journal of Non-Newton Fluid Mechanics. 1998, 79: 137-155.
[60] Gotsis D A, Odriozola A. The relevance of entry flow measurements for the estimation of extensional viscosity of polymer melts[J]. Rheology Acta. 1998, 37(430-437).
[61] Gotsis A D, Odriozola A. Extensional viscosity of a thermotropic liquid crystalline polymer[J]. Journal of Rheology. 2000, 44: 1205-1223.
[62] Gibson A G. Die entry flow of reinforced polymers[J]. Composites. 1989, 20: 57-64.
[63] Mcleish T C B, Larson R G. Molecular constitutive equations for a class of branched polymers: the Pom–Pom model[J]. Journal of Rheology. 1998, 42(1): 81-110.
[64] Ball R C, Mcleish T C B. Dynamic dilution and the viscosity of star polymer melts[J]. Macromolecules. 1989, 22(4): 1911-1913.
[65] Larson R G. Constitutive Equations for Polymer Melts and Solutions[M]. Boston: Butterworths, 1988.
[66] Rubio P, Wagner M H. LDPE melt rheology and the pom-pom model[J]. Journal of Non-Newtonian Fluid Mechanics. 2000, 92: 245-259.
[67] Clemeur N, Rutgers R P G, Debbaut B. On the evaluation of some differential formulations for the pom-pom constitutive model[J]. Rheology Acta. 2003, 42: 217-231.
[68] Bishko G B, Harlen O G, Mcleish T C B, et al. Numerical simulation of the transient flow of branched polymer melts through a planar contraction using the‘pom-pom’model[J]. Journal of Non-Newtonian Fluid Mechanics. 1999, 82(2-3): 255-273.
[69] Inkson N J, Mcleish T C B, Harlen O G, et al. Predicting low density polyethylene rheology in flows and shear with Pom-Pom constitutive equation[J]. Journal of Rheology. 1999, 43(4): 873-896.
[70] Blackwell R J, Mcleish T C B, Harlen O G. Molecular drag-strain coupling in branched polymer melts[J]. Journal of Rheology. 2000, 44(1): 121-136.
[71] Ottinger H C. A thermodynamically admissible reptation model for fast flows ofentangled polymers[J]. Journal of Rheology. 1999, 43(6): 1461-1493.
[72] Verbeeten W M H, Peters G W M, Baaijens F P T. Differential constitutive equations for polymer melts: extended Pom-Pom model[J]. Journal of Rheology. 2001, 45(4): 823-843.
[73] Verbeeten W M H, Peters G W M, Baaijens F P T. Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model[J]. Journal of Non-Newtonian Fluid Mechanics. 2004, 117(2-3): 73-84.
[74] Meerveld J V. Note on thermodynamic consistency of the integral pom-pom model[J]. Journal of Non-Newtonian Fluid Mechanics. 2002, 108(1-3): 291-299.
[75] Tanner R I. Engineering Rheology 2nd[M]. Oxford Univ Press, 2000.
[76] Huilgol R R, Phan-Thien N. Fluid Mechanics of Viscoelasticity[M]. Amsterdam: Elsevier, 1997.
[77] Tanner R I, Zdilar A M, Nasseri S. Recoil from elongation using general network models[J]. Rheologica Acta. 2005, 44(5): 513-520.
[78] Tanner R I, Nasseri S. Simple constitutive models for linear and branched polymers[J]. Journal of Non-Newtonian Fluid Mechanics. 2003, 116(1): 1-17.
[79] Tanner R I. Revisitation of PTT model [J]. J. Cent. South Univ. Technol. 2007, 14(s1): 26-29.
[80] Kwon Y, Leonov A I. Stability constraints in the formulation of viscoelastic constitutive equations[J]. Journal of Non-Newtonian Fluid Mechanics. 1995, 58(1): 25.
[81] Simhambhatla M, Leonov A I. On the rheological modeling of viscoelastic polymer liquids with stable constitutive-equations[J]. Rheologica Acta. 1995, 34(3): 259-273.
[82] Larson R G. Elongational-flow predictions of the Leonov constitutive equation[J]. Rheologica Acta. 1983, 22: 435-448.
[83] Zatloukal M. Differential viscoelastic constitutive equations for polymer melts in steady shear and elongational flows[J]. Journal of Non-Newtonian Fluid Mechanics. 2003, 113(2-3): 209-227.
[84] Pivokonsky R, Zatloukal M. On the predictive/fitting capabilities of the advanced differential constitutive equations for branched LDPE melts[J]. Journal of Non-Newtonian Fluid Mechanics. 2006, 135(1): 58-67.
[85] Muller R, Froelich D. New extensional rheometer for elongational viscosity and flow birefringence measurements: some results on polystyrene melts[J]. Polymer. 1985, 26: 1477-1482.
[86] Matsumoto T, Bogue D C. Stress birefringence in amorphous polymers under nonisothermal conditions[J]. J Polym Sci Polym Phys. 1977, 15: 1663-1674.
[87] Luap C, Müller C, Schweizer T, et al. Simultaneous stress and birefringence measurements during uniaxial elongation of polystyrene melts with narrow molecular weight distribution[J]. Rheology Acta. 2005, 45: 83-91.
[88] M K. Simple models for complex nonequilibrium fluids[J]. Phys Rep. 2004, 390(6): 453-551.
[89] Gotsis A D, Zeevenhoven B L F, Tsenoglou C. Effect of long branches on the rheology of polypropylene[J]. Journal of Rheology. 2004, 48(4): 895-914.
[90] Munstedt H, Auhl D. Rheological measuring techniques and their relevance for the molecular characterization of polymers[J]. Journal of Non-Newtonian Fluid Mechanics. 2005, 128: 62-69.
[91] Delaby I, Ernst B, Germain Y, et al. Droplet deformation in polymer blends during uniaxial elongational flow: influence of viscosity ratio for large capillary numbers[J]. Journal of Rheology. 1994, 38(6): 1705-1720.
[92] Fornes T D, Baur J W, Sabba Y, et al. Morphology and properties of melt-spun polycarbonate fibers containing single- and multi-wall carbon nanotubes.[J]. Polymer. 2006, 47: 1704-1714.
[93] Handge U A, P?tschke P. Interplay of rheology and morphology in melt elongation and subsequent recovery of polystyrene/poly(methyl methacrylate) blends[J]. Journal of Rheology. 2004, 48: 1103-1122.
[94] Handge U A, Buschnakowski M, Michler G H. Deformation and alignment of lamellae in melt extension of blends of a styrene-butadiene block copolymer with polystyrene[J]. Journal of Applied Polymer Science. 2009, 112(3): 1319-1329.
[95] Heindl M, Sommer M K, Münstedt H. Morphology development in polystyrene/polyethylene blends during uniaxial elongational flow[J]. Rheology Acta. 2004, 44: 55-70.
[96] Lee W K, Kim H D, Kim E Y. Morphological reorientation by extensional flow deformation of a triblock copolymer styrene–isoprene–styrene[J]. Current Applied Physics. 2006, 6(4): 718-722.
[97] Oosterlink F, Mours M, Laun H M. Morphology development of a polystyrene/polymethylmethacrylate blend during start-up of uniaxial elongational flow[J]. Journal of Rheology. 2005, 49(4): 897-918.
[98] Gramespacher H, Meissner J. Melt elongation and recovery of polymer blends, morphology, and influence of interfacial tension[J]. Journal of Rheology. 1997, 41(1): 27-44.
[99] P?tschke P, Abdel-Goad M, Alig I, et al. Rheological and dielectrical characterization of melt mixed polycarbonate-multiwalled carbon nanotube composites[J]. Polymer. 2004, 45: 8863-8870.
[100] Takahashi T, Takimoto J, Koyam K. Uniaxial elongational viscosity of various molten polymer composites[J][J]. Polymer Composites. 1999, 20(3): 357-366.
[101] Gupta R K, Pasanovic-Zujo V, Bhattacharya S N. Shear and extensional rheology of EVA/layered silicate-nanocomposites[J]. Journal of Non-Newtonian Fluid Mechanics. 2005, 128(2-3): 116-125.
[102] Garofalo E, Russo G M, Maio L D, et al. Study on the Effect of Uniaxial Elongational Flow on Polyamide Based Nanocomposites[J]. Macromol. Symp. 2007, 247: 110-119.
[103] Handge U A, P?tschke P. Deformation and orientation during shear and elongation of a polycarbonate/carbon nanotubes composite in the melt[J]. Rheologica Acta. 2007, 46: 889-898.
[104] Wagner M H, Kheirandish S, Yamaguchi M. Quantitative analysis of melt elongational behavior of LLDPE/LDPE blends[J]. Rheologica Acta. 2004, 44: 198-218.
[105] Stange J, Münstedt H. Rheological behavior of blends of alinear and a long-chain branched polypropylene[J]. Journal of Rheology. 2005, 49: 1059-1079.
[106] Wagner M H, Kheirandish S, Stange J. Modeling elongational viscosity of blends of linear and long-chain branched polypropylenes[J]. Rheologica Acta. 2006, 46: 211-221.
[107] Mccallum T J, Kontopoulou M, Park C B, et al. The Rheological and Physical Properties of Linear and Branched Polypropylene Blends[J]. Polymer Engineering andScience. 2007, 47: 1133-1140.
[108] Xue S C, Phan Thein N, Tanner R I. Three dimensional numerical simulations of viscoelastic flows through planar contractions[J]. Journal of Non-Newtonian Fluid Mechanics. 1998, 74(1-3): 195-245.
[109] Purnode B, Crochet M J. Flows of polymer solutions through contractions Part 1: flows of polyacrylamide solutions through planar contractions[J]. Journal of Non-Newtonian Fluid Mechanics. 1996, 65(2-3): 269-289.
[110] Barnes H A, Roberts G P. A simple empirical model describing the steady-state shear and extensional viscosities of polymer melts[J]. Journal of Non-Newtonian Fluid Mechanics. 1992, 44: 113-126.
[111] Moore F. The rheology of ceramic slips and bodies[J]. Trans. Br. Ceram. Soc. 1959, 58: 470-484.
[112] Boek E S, Padding J T, Anderson V J, et al. Constitutive equations for extensional flow of wormlike micelles: stability analysis of the Bautista–Manero model[J]. Journal of Non-Newtonian Fluid Mechanics. 2005, 126: 39-46.
[113] Liang J Z. Estimation of entry natural converging angles during capillary extrusion flow of carbon black filled NR/SBR compound[J]. Polymer Testing. 2005, 24(4): 435-438.
[114] Ma C Y, White J L, Weissert F C, et al. Flow patterns in carbon black filled polyethylene at the entrance to a die[J]. Journal of Non-Newtonian Fluid Mechanics. 1985, 17: 275-287.
[115] Martyn M T, Nakason C, Coates P D. Flow visualisation of polymer melts in abrupt contraction extrusion dies: quantification of melt recirculation and flow patterns[J]. Journal of Non-Newtonian Fluid Mechanics. 2000, 91: 109-122
[116] White S A, Gotsis D A, Baird D G, Review of the entry flow problem: experimental and numerical[J]. Journal of Non-Newtonian Fluid Mechanics. 1987, 24: 121-160
[117]梁基照. LDPE熔体在挤出口模流动时入口区流型的观测[J].合成树脂及塑料. 2003, 20(1): 53-56.
[118] Baldi F, Franceschini A, Ricco T. Determination of the elongational viscosity of polymer melts by melt spinning experiments: A comparison with different experimental
[119] Baldi F, Franceschini A, Bignotti F. Rheological behaviour of nano-composites based on polyamide 6 under shear and elongational flow at high strain rates[J]. Rheologica Acta. 2009, 48(1): 73-88.
[120] Munstedt H, Laun H M. Elongational behaviour of a low density polyethylene melt[J]. Rheologica Acta, 1979, 18:492-504.
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