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Dynamic Theory of Die Swell for Entangled Polymeric Liquids in Tube Extrusions: New Set of Equations for the Growth and Ultimate Extrudate Swelling Ratios under the Free States
Chang-wei Zhu,Ming-shi Song*,Gui-xian Hu,Da-ming Wu,Jing Zhao
Author NameAffiliationE-mail
Chang-wei Zhu School of Mechanical and Electrical Engineering, Beijing University of Chemical and Technology, Beijing 100029, China  
Ming-shi Song* School of Materials Science and Engineering, Beijing University of Chemical and Technology, Beijing 100029, China songmingshi@mail.buct.edu.cn 
Gui-xian Hu School of Materials Science and Engineering, Beijing University of Chemical and Technology, Beijing 100029, China  
Da-ming Wu School of Mechanical and Electrical Engineering, Beijing University of Chemical and Technology, Beijing 100029, China  
Jing Zhao School of Mechanical and Electrical Engineering, Beijing University of Chemical and Technology, Beijing 100029, China  
Abstract:
A new dynamic theory of die swell for entangled polymeric liquids in a steady simple shear °ow is proposed which can be used to predict the correlation of the time-dependent and time-independent extrudate swelling behaviors to the molecular parameters of polymers and the operational variables. The theory is based on the O-W-F constitutive equation and the free recovery from Poioeuille flow with different ratios. Experiments show that the magnitudes of the simple shear in the steady simple shear flow may be resolved into the free recoil resulting from the recoverable elastic strains and the viscous heating resulting from the unrecoverable viscoelastic strains. For distinguishing the recoil from the viscous heating, a partition function and two exponential fractions of conformation for the recoil and the viscous heating were defined. Thus the instantaneous, delayed and ultimate recoverable strain, and recoil in the free recovery were correlated to the partition function, the fraction of recoverable conformation, the molecular parameters, and the operational variables. Also the dynamics of the growth equation on the delayed viscoelastic strain and the delayed recoil in free state were deduced. After introducing the condition of uniform two dimensional extensions, the definition of swell ratio and the operational variables into the above correlation expressions and growth equations, then the correlations of the delayed extrudate swelling effect and the ultimate extrudate swelling effects to the molecular parameters and the operational variables were derived. Finally, two new sets of equations on the growth variables and ultimate extrudate swelling ratios under the dynamic and equilibrium states were also deduced from this dynamic theory of die swell. The first set of equations on the ultimate extrudate swelling ratio under the free and equilibrium states was verified by HDPE experimental data at two temperatures and different operational variables. The second set of equations on the growth extrudate swelling ratios under free and dynamic states was verified by PBD experimental data with different molecular weights and different operational variables. An excellent agreement is obtained, which shows that the two sets of equations for the growth and ultimate extrudate swelling ratios can be used directly to predict the correlation of extrudate swelling ratios to the molecular parameters and the operational variables.
Key words:  Die swell, Entanglement, Viscoelastic recoil
FundProject:the Beijing Municipal Commission of Education, China (No.2H100100522)
缠结高分子液体在管中挤出胀大动力学理论:一组新的增长和最终挤出胀大比方程
朱常委,宋名实*,胡桂贤,吴大鸣,赵晶
摘要:
基于O-W-F本构方程和自由回复机制,从Poioeuille流出发建立了一种新的缠结高分子液体挤出胀大动力学理论,该理论能有效地预测高分子流体的动静态挤出胀大行为同高分子粘弹性参数和成型条件间的相关性. 基于稳态剪切量可分解为自由“回复线团”和“不可回复热耗”两部分事实,定义了一个稳态剪切下自由“回复线团”和“不可回复热耗”的配分函数和它们两者间分配指数上可回复和不可回复构象分数,从而在理论上得到了瞬时、推迟和最终三者可回复形变量和可回复线团量同配分函数、分配指数上可回复构象分数、分子粘弹性参数和成型条件
关键词:  挤出胀大,缠结,粘弹性线团回复
DOI:10.1088/1674-0068/20/05/563-581
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