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

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. Experimentsshow 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 twoexponential 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 freestate were deduced. After introducing the condition of uniform two dimensional extensions, the definition ofswell 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.     

Effect of titanium dioxide nanoparticles on polymer network formation

This work presents a study of the effect of nanoparticles on polymer composites to develop a powerful polymer dispersed liquid crystal materials. Tri propylene glycol diarcrylate/titanium dioxide nanocomposites were produced at various titanium dioxide fractions ranging between 0 and 1?wt%, through ultraviolet curing technique during 30?min. Different technics such as polarized optical microscopy, Fourier transform infrared spectroscopy, differential scanning calorimetry, and thermal gravimetric analysis were used to characterize the samples. A dynamic swelling of polymer network was also investigated. The evolution of the acrylic double-bond conversion shows a decrease in the absorption intensity at 1637?cm^?1. It is noted that the conversion rate decreases from 0.1 to 1?wt% of titanium dioxide nanoparticles. An increase in glass transition temperature is observed by differential scanning calorimetry. The thermogravimetric analysis results reveal a highly improved thermal stability upon the addition of the reinforcing phase. The follow of kinetics swelling of polymer network shows a decrease of the swell ratio with the inclusion of titanium dioxide nanoparticles.     

Viscoelastic simulations of stick‐slip and die‐swell flows

Numerical solutions of viscoelastic flows are demonstrated for a time marching, semi‐implicit Taylor–Galerkin/pressure‐correction algorithm. Steady solutions are sought for free boundary problems involving combinations of die‐swell and stick‐slip conditions. Flows with and without drag flow are investigated comparatively, so that the influence of the additional component of the drag flow may be analysed effectively. The influence of die‐swell is considered that has application to various industrial processes, such as wire coating. Solutions for two‐dimensional axisymmetric flows with an Oldroyd‐B model are presented that compare favourably with the literature. The study advances our prior fixed domain formulation with this algorithm, into the realm of free‐surface viscoelastic flows. The work involves streamline‐upwind/Petrov–Galerkin weighting and velocity gradient recovery techniques that are applied upon the constitutive equation. Free surface solution reprojection and a new pressure‐drop/mass balance scheme are proposed. Copyright © 2001 John Wiley & Sons, Ltd.     

Melt rheology and morphology of thermoplastic elastomers from polyethylene/nitrile‐rubber blends: The effect of blend ratio,reactive compatibilization,and dynamic vulcanization

A study of the melt‐rheological behavior of thermoplastic elastomers from high‐density polyethylene and acrylonitrile butadiene rubber (NBR) blends was carried out in a capillary rheometer. The effect of the blend ratio and shear rate on the melt viscosity reveals that the viscosity decreases with the shear rate but increases with NBR content. Compatibilization by maleic anhydride modified polyethylene has no significant effect on the blend viscosity, but a finer dispersion of the rubber is obtained, as is evident from scanning electron micrographs. The melt‐elasticity parameters, such as the die swell, principal normal stress difference, recoverable shear strain, and elastic shear modulus of the blends, were also evaluated. The effect of annealing on the morphology of the extrudate reveals that annealing in the extruder barrel results in the coalescence of rubber particles in the case of the incompatible blends, whereas the tendency toward agglomeration is somewhat suppressed in the compatibilized blends. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1104–1122, 2000     

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

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     

A finite difference analysis of the extrudate swell problem

The extrudate swell phenomenon of a purely viscous fluid is analysed by solving simultaneously the Cauchy momentum equations along with the continuity equation by means of a finite difference method. The circular and planar jet flows of Newtonian and power-law fluids are simulated using a control volume finite difference method suggested by Patankar called SIMPLER (semi-implicit method for pressure-linked equations). This method uses the velocity components and pressure as the primitive variables and employs a staggered grid and control volume for each separate variable. The numerical results show good agreement with the analytical solution of the axisymmetric stick-slip problem and exhibit a Newtonian swelling ratio of 13.2% or 19.2% for a capillary or slit die respectively in accordance with previously reported experimental and numerical results. Shear thinning results in a decrease in swelling ratio, as does the introduction of gravity and surface tension.     

A mixed finite element scheme for viscoelastic flows with XPP model

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.     

Numerical simulation of the extrusion of strongly compressible Newtonian liquids

The axisymmetric and plane extrusion flows of a liquid foam are simulated assuming that the foam is a homogeneous compressible Newtonian fluid that slips along the walls. Compressibility effects are investigated using both a linear and an exponential equation of state. The numerical results confirm previous reports that the swelling of the extrudate decreases initially as the compressibility of the fluid is increased and then increases considerably. The latter increase is sharper in the case of the exponential equation of state. In the case of non-zero inertia, high compressibility was found to lead to a contraction of the extrudate after the initial expansion, similar to that observed experimentally with liquid foams and to decaying oscillations of the extrudate surface. The time-dependent calculations show that the oscillatory steady-state solutions are stable. These steady-state oscillatory solutions are not affected by the length of the extrudate region nor by the boundary condition along the wall.     

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

The dynamic theory of die swell deduced in a previous paper was extensively applied to study the xtrudate 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.     

On the stretching and swelling of an elastic liquid extruded from a capillary die

A theoretical model for calculating the profile of a polymer jet extruded from a circular die and stretched by an axial force is elaborated. The model exploits the idea of matching the solutions for the polymer flow inside and outside the capillary by equating the elastic energy flux at the die outlet. The rheological equations used to obtain the two solutions have been previously tested in many situations. Comparison of the results of computations made according to the theoretical model with those of some special experiments revealed satisfactory agreement.