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Dynamic Theory of die swell for Entangled Polymeric Liquids in Tube Extrusion： Correlations of Total and Ultimate Extrudate swell Effects to Growth Time, Shear Stress and Aspect Ratio Under the Free States

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Chinese Journal of Chemical Physics 2008年第1期21卷 55-68页

作者： Jing Zhao Ming-shi Song Chang-wei Zhu Gui-xian Hu Ke-jian Wang Da-ming Wu School of Mechanical and Electrical Engineering Belting University of Chemical and TechnologyBeijing 100029 China School of Materials Science and Engineering Beifing University of Chemical and TechnologyBeijing 100029 China

The dynamic theory of die swell deduced in a previous paper was extensively applied to study the extrudate swelling behaviors of two entangled polymeric liquids （HDPE and PBD） in a simple shear flow at steady shear stress. The mechanism and dynamics for the recoils and the recoveries of viscoelastic strains in the extrudate were investigated under the free recovery and dynamic states. It was found that in the course of recovery the free recoil and the growth of die swell in the extrudate may be divided into two recovery regions （instantaneous and delayed regions） and three growth stages （instantaneous, delayed, and ultimate extrudate swelling stages）. The free recoil and the extrudate swelling behaviors may be expressed as a function of shear stress. The correlations of instantaneous, delayed, total and ultimate extrudate swell effects to the molecular parameters and the operational variables in the simple shear flow at steady shear stress were derived from the dynamic theory of die swell. Also, two sets of new universal equations on the total extrudate swelling effect （TESE） and ultimate extrudate swelling effect （UESE） were deduced. The first is the universal equation of the logarithmic correlation between the TESE and the growth time under the free and dynamic states; the second is the universal equation of the logarithmic correlation between the UESE and the operational variables under the free and equilibrium states. The first equation was verified by experimental data of PBD with different molecular weights at different operational variables. The second equation was verified by experimental data of HDPE at two temperatures and different operational variables. An excellent agreement result was obtained. The excellent agreement shows that the two universal equations can be used directly to predict the correlations of the TESE and UESE to the growth time, the molecular parameters, and the operational variables under the dynamic and equilibrium states.

关键词： die swell Entanglement Viscoelastic recoil

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Dynamics of Polymeric Fluids：Part Ⅱ The Molecular Theory of die swell： Correlation of Ultimate die swelling Effect to the Molecular Parameters and the Operational Variables

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Journal of Materials Science & Technology 2006年第5期22卷 664-676页

作者： Mingshi SONG Qiang XU Guixian HU Sizhu WU Key Laboratory of Science and Technology of Controlled Chemical Reactions Beijing University of Chemical TechnologyBeijing 100029 China

A general expression for the correlation of the simple shear （tanφ） to the molecular parameters and the shear rate （·↑γ） was deduced. It shows that the simple shear （tanφ） may be resolved into free recoil （recoverable strain） and viscous heating （unrecoverable strain）. The magnitudes of the simple shears for recoil （tanφE） and （tanφv） for viscous heating not only depended on the molecular parameters and the operational variables, but also on the exponential fractions of the recoverable （1--↑W·↑γ） and unrecoverable （-↑W·↑γ） conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears （tanφE） for recoil and （tanφv） for viscous heating are, respectively, expressed as the partition function to the （1--↑W·↑γ）th power and the partition function to the （-↑W·↑γ）th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [n′, α, η0, GN^0 and （1--↑W·↑γ）] and the operational variables （·↑γ, （L/D） and tr） were deduced respectively, which show that at very different shear rates （0≤·↑γ≤∞） the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=（L/D）], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [n′, α, η0, GN^0 and （1--↑W·↑γ）] and the operational variables （·↑γ, （L/D） and tr） were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene （HDPE） which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.

关键词： die swell Viscoelastic recoil Entanglement

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Dynamics of Polymeric Fluids 1. The Molecular Theory of die swell:A Set of Equation on swelling Ratio in Extrudates

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Journal of Materials Science & Technology 2006年第1期22卷 93-107页

作者： Mingshi SONG Guixian HU Zhihong YANG Qiang xu Sizhu WU Key Laboratory of Science and Technology of Controlled Chemical Reactions Beijing University of Chemical TechnologyBeijing 100029 China

The structural model of the multiple-transient networks and the mechanism of the multiple-reptation entangled chains due to the dynamic reorganization in the entangled sites were extensively applied on the die swell of polymeric liquids in the steady simple shear flow. The total （recoverable and unrecoverable） viscoelastic free energy of deformation and flow, the constitutive equation and the expression of the simple shear （tanψ） were deduced from the conformational probability distribution function of the entangled polymer chains. It found that：（1） the magnitudes of simple shear （tanψ） depended not only on the free recoil （or recoverable strain） but also on the viscous heating （or unrecoverable strain）; （2） the total recoil may be resolved into the instantaneous and delayed recoil. Based on these facts, the functions of the partition and two experiential fractions of the recoverable （1-Wγ） and the unrecoverable （Wγ） conformations for the recoil and viscous heating of polymeric liquids were defined correspondingly. Then the correlation of the instantaneously and ultimately （or total） recoverable strains to the （N1/T12）w and the fraction of trans-form conformation was obtained. After introducing the condition of uniform two-dimensional extension （αx=αy=α, αz=α^-2） and the swell ratio （B=α）, two sets of equations on the instantaneous and ultimate swelling ratios （BE, BEVT） were obtained, and a method to determine the fraction of the recoverable transform conformation were proposed, The equations of BE and BE5 were verified by the experimental data of HDPE （high denisity polyethylene） at two different high temperatures. It shows that the molecular theory of die swell can be used to predict the correlation of the swelling to the （NI/TI2）w and the fraction of trans-form conformation.

关键词： die swell Entanglement Viscoelastic recoil

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A mixed finite element scheme for viscoelastic flows with XPP model

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Acta Mechanica Sinica 2008年第6期24卷 671-680页

作者： Xianhong Han Xikui Li State Key Laboratory of Structural Analysis of Industrial Equipment Dalian University of Technology 116023 Dalian China National die and Mold CAD Engineering Research Center Shanghai Jiao Tong University 200030 Shanghai China

A mixed finite element formulation for viscoelastic flows is derived in this paper, in which the FIC （finite incremental calculus） pressure stabilization process and the DEVSS （discrete elastic viscous stress splitting） method using the Crank-Nicolson-based split are introduced within a general framework of the iterative version of the fractional step algorithm. The SU （streamline-upwind） method is particularly chosen to tackle the convective terms in constitutive equations of viscoelastic flows. Thanks to the proposed scheme the finite elements with equal low-order interpolation approximations for stress-velocity-pressure variables can be successfully used even for viscoelastic flows with high Weissenberg numbers. The XPP （extended Pom-Pom） constitutive model for describing viscoelastic behaviors is particularly integrated into the proposed scheme. The numerical results for the 4：1 sudden contraction flow problem demonstrate prominent stability, accuracy and convergence rate of the proposed scheme in both pressure and stress distributions over the flow domain within a wide range of the Weissenberg number, particularly the capability in reproducing the results, which can be used to explain the ＂die swell＂ phenomenon observed in the polymer injection molding process.

关键词： Viscoelastic flow XPP model Low-order finite elements Iterative procedure die swell

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Coaxial liquid-liquid flows in tubes with limited length

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第3期7卷 347-351页

作者：胡影影黄争鸣 School of Aerospace Engineering and Applied Mechanics Tongji University Shanghai 200092 China

Coaxial liquid-liquid flows were numerically studied in a nesting two-tube system. Calculations were carried out when various exit-lengths (meaning length differences between the two tubes) were used. Numerical results indicated that there exists a certain range of exit-length for the liquid-liquid flows to form stable and smooth interfaces, which requires that the exit-length should roughly be less than 5.6 times the outer tube diameter. In this range, interface instability is effectively restrained and the core fluid shows a phenomenon of die swell. When the exit-length is about 1.6 times the outer tube diameter, the core fluid has the greatest diameter size in the shell fluid. Velocity distributions at the outer tube exit favor formation of a continuous and stable core-shell structure.

关键词： Coaxial liquid-liquid flow Exit-length Instability die swell

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On the elasticity of polymer fluids

On the elasticity of polymer fluids

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2014年全国高分子材料科学与工程研讨会

作者： WU Qiye Department of Polymer Science and Engineering Qingdao University of Science and Technology

It was showed in literatures that polymer fluids(as melts or solutions)which have similar viscosity but different elasticity,their rheological and processing behaviors were widely *** measure method and norm for fluid elasticity are not a circumstance to fluid *** physical quantities to describe of fluid elasticity in literatures were *** are distinguished about three classes:1)a class of elastic modulus,includes melts strength,extensional viscosity,inlet pressure drop,etc.2)a class of resiliency,includes recoverable strain,die swell,compliance,pressure at die exit,exc.3)the normal stress differences,they have scientific significance but are difficult to *** tests showed that,although the quantities of first two classes have close interrelation,but they are not *** example although the inlet pressure drop is a reason of die swell,and the die swell is a result of elastic recovering,but they both showed not always the same regularity in *** test the die swell and the inlet pressure drop differ sometimes,therefore it is needed to take notice of the difference of these quantities,in order to proper select one to character the fluid *** Fig.l the measure results of die swell B and inlet pressure drop PO of samples of SSBRT2003/CB-N330 composites with different CB(carbon black)amounts were provided by a double capillary rheometer *** is indicated that along with increase of CB amounts,the B decrease but the PO magnify,they both display different variety *** man want ask,which quantity shows a correct description of melts elasticity?And why the both quantities are disparate?By means of the comparison of extrudate appearances photos(Fig.2)it was informed,that melts flow instability was improved and the melts elasticity weakened obviously with increase of CB *** was the same law of die *** by means of measure of dynamic modulus,extensional viscosity and the content of CB network in samp

关键词： fluid elasticity polymer fluids die swell inlet pressure drop

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