A rheometer for measuring the viscoelastic response of polymer melts in arbitrary planar and biaxial extensional flow fields

In this paper we describe the operation of a rheometer that is capable of measuring the viscoelastic response of a polymer melt in a biaxial or planar extensional flow field under circumstances wherein the deformation history can be varied in an arbitrary manner. The principal feature of this rheometer is the use of a closed loop feedback system to control the inflation of a flat, molten polymer sheet clamped around its periphery. The feedback system is especially designed so that either stress or strain can be used as the reference point, thus permitting the deformation history to be varied arbitrarily. Illustrative data are presented on the viscoelastic response of a molten acrylonitrile-butadiene-styrene copolymer subjected to a planar extensional flow for the following deformation histories: constant stress, constant strain, constant strain rate, oscillatory stress and oscillatory strain.     

Theoretical model for flow of polymer melts in the screw channel

Isothermal and nonisothermal flows of polymer melts in a screw channel are discussed. An exact solution for the isothermal flow of a power law fluid in a rectangular channel including both longitudinal and transverse velocity components is presented. A method to describe the effects of flights and curvature on flow behavior is proposed. The results are extended to deal with various nonisothermal flow conditions. The proposed theory has been numerically verified.     

Elongational flow of polymer melts

A new technique is described whereby the rate of collapse of an air bubble within a molten polymer may be measured without the need for visual observation. The method involves use of a high speed recording dilatometer, From such data it is possible to measure an apparent elongational viscosity of the melt, and such measurements are presented for two polyethylenes (Tennite, a low density PE, and Plaskon, a high density PE), Limitations of the methods are discussed. This is one of a series of papers (1-3) documenting our development of a new experimental technique, and the corresponding mathematical modeling, whereby one may measure the elongational viscosity of polymeric viscoelastic fluids. Previous experimental work was confined to transparent fluids, since the technique depended on high-speed motion picture photography of the collapse of an air bubble within the fluid. In this paper we describe an attempt, largely successful, to develop a new experimental system which permits the study of molten polymers, including opaque fluids. Sample results are presented for both a low and a high density polyethylene.     

Steady‐state viscoelastic flow simulation of polymer melts in a rotational‐type rheometer

Polymer samples in the jigs begins to protrude when the heat is turned up when we measure the rheological characteristics of polymer melts using rotational‐type rheometers, such as parallel and cone‐and‐plate types. To clarify the effects of this protruding part on the obtained rheological data, we tried to evaluate the rotational‐type rheometer by a non‐isothermal viscoelastic flow simulation using the finite element method. The multiple mode Phan‐Thien Tanner (PTT) model was employed as the constitutive equation. As a result, the shear viscosity in the steady state increases with the size of the protruding part of the polymer melt specimen at the same shear rate in case with a parallel plate and a cone‐and‐plate type rheomters. In contrast, the deviation of the primary normal stress difference between the estimated value from the simulation results and the data from the PTT model is almost independent of the size of the protruding part with the cone‐and‐plate type rheometer. In addition, the deviations of the primary normal stress difference with a parallel plate rheometer increase with the protruding part size. However, these deviations are smaller than those of shear viscosity. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Converging flow of polymer melts in extrusion dies

Practical extrusion processes often involve geometrically complex dies. Such dies are usually tapered, or streamlined, to achieve maximum output rate under conditions of laminar flow. These converging flows may be analysed in terms of their extensional and simple shear components to calculate the relationships between volume flow rate, pressure drop, and post extrusion swelling. The analysis can also be extended to cover the free convergence as fluid flows from a reservior into a die. Comparisons between predicted and observed data for a series of coni-cylindrical dies suggest that using this approach the pressure drop/flow rate relationship can be predicted within ±20% and the swell ratio/flow rate relationship within ±10%. Similar treatments have been in use for the last three years in solving such complex flow problems as radial flow in injection moulding and two-dimensional annular convergence in blow moulding dies.     

Capillary flow instability of ethylene polymer melts

The capillary flow instability resulting in extrudate distortion has been studied for ethylene polymer melts using a molecular structure approach. It is found that the instability initiates at a critical value of elastic strain energy independent of (average) molecular weight for linear polyethylene. Once the flow breaks down, a slip interface within the melt is formed near the capillary wall, causing an abrupt increase in volumetric throughput. The velocity gradient within the melt remains continuous through the instability, however. Low molecular weight species present in the molecular weight distribution of linear polyethylene tend to suppress slip. Blends of linear and branched polyethylene exhibit instability behavior characteristic of both components throughout the entire range of composition. Results are discussed in terms of specific molecular mechanisms.     

Development of freeze flow apparatus to study filled polymer melts

A novel method to study the distribution of filler particles and polymer orientation of a polymer melt within a capillary die has been developed. Material within the die is quench‐cooled and then removed to provide information about the flow regime at the instant it was frozen. The equipment has been used to examine calcium carbonate‐filled high density polyethylene under high shear. The samples were examined using Energy Dispersive X‐ray Spectrometry (EDS) as well as being studied using X‐ray Diffraction (XRD). The distribution of filler particles across the radius of the capillary has been studied at high and low wall shear rates using EDS. A constant particle distribution across the radius of the die was observed for both flow regimes. The arrangement of crystalline structures within the specimens was examined by XRD. An increase in crystalline order was noticed with increasing wall shear rate. POLYM. ENG. SCI., 47:1937–1942, 2007. © 2007 Society of Plastics Engineers     

A phenomenological description of the non-linear viscoelastic properties of polymer melts and concentrated solutions

The non-linear stress response of molten polymers and concentrated solutions to an applied strain is formulated in terms of a material response function. The response function is considered to depend explicitly on the resulting stress history and it is shown how many of the non-linear features of these systems can be described both qualitatively and quantitatively. The particular equations used involve one non-linear term in addition to the usual linear response terms. Finally the non-linear equation is interpreted in terms of a plausible model process.     

Numerical study of nonisothermal polymer extrusion flow with a differential viscoelastic model

A numerical study of nonisothermal viscoelastic flow is conducted to investigate the complex flow characteristics of polymer melts in the extrusion process. A general thermodynamic model for the energy conversion related to viscoelastic fluid flow is introduced. The mathematical model for three‐dimensional nonisothermal viscoelastic flow of the polymer melts obeying a differential constitutive equation (Phan‐Thien and Tanner model) is established. A decoupled algorithm based on the penalty finite element method is performed on the calculation. The discrete elastic‐viscous split stress (DEVSS) algorithm, incorporating the streamline‐upwind Petrov‐Galerkin (SUPG) scheme is employed to improve the computation stability. Essential flow characteristics of polymer melts in the extrusion die for hollow square plastic profile is investigated based on the proposed numerical scheme with ignoring the outer thermal resource. The energy partitioning, which quantified the conversion of mechanical energy into thermal energy, is discussed. The effects of volume flow rate and die contraction angle upon the flow patterns are further investigated. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers     

Studies of time effects in the flow of polymer melts using a biconical viscometer

The variation of viscosity of various polymer melts under constant shear rate conditions has been investigated using a biconical viscometer, a cone-plate viscometer, and a capillary rheometer. The validity of the biconical viscometer edge-zone correction was investigated. Comparisons between the three types of viscometer showed that sample fracture at the material boundary contributed to the decrease of viscosity with time of shearing occuring in the cone-plate viscometer. Polymer melts are subjected to hydrostatic pressure within the biconical viscometer and fracture appears to be prevented. Shear stress–shear rate–time relationships were obtained for the materials studied with the biconical viscometer at shear rates up to a few reciprocal seconds. There was good agreement with capillary data at high shear rates and cone-plate data at low shear rates. A recoverable decrease of viscosity with time of shearing was found to occur. Both the fractional decrease in viscosity and the time taken to recover the original viscosity become smaller as the temperature is increased.     

Compensation effects in viscosity-temperature dependence of polymer melts

The thermal dependence of the parameters of the Carreau A model of viscosity has been investigated for 13 polymeric resins. It was shown that the zero-shear viscosity and the time constant obey an Arrhenius-type law and that, for these parameters, compensation effects are exhibited. The shear-thinning index was found to be fairly independent of temperature. An important consequence of a compensation effect is that only one determination of a parameter at a given temperature gives the complete temperature-dependence of this parameter.     

Elongational viscosity of polymer melts: A lubricated skin-core flow approach

Previous work by this research group has shown that the use of a lubricated skin/core flow of polymer melts and a hyperbolic converging die results in an essentially pure elongational flow at a constant elongational strain rate in the core. The previous work was carried out on a laboratory-scale coextrusion system in a planar slit die; tracer particles and an image analysis system were used to confirm the predicted behavior. In this work, the technique was implemented first on the coextruder assembly, as a planar elongational rheometer, and then on a commercial capillary rheometer, as a uniaxial elongational rheometer for polymer melts. The later is achieved by replacing the standard capillary die with a hyperbolic axisymmetric die. A two-laycred billet is prepared for placement in the rheometer barrel by completely encapsulating the core polymer (the polymer to be analyzed) with a low-viscosity polyethylene skin. Commercial grades of polypropylenes, syndiotactic polystyrene, and nylon-66 were analyzed using this technique. Elongational viscosity at high extensional rates can be determined with this method; values in excess of 500 s⁻¹ have already been achieved. © 1996 John Wiley & Sons, Inc.     

Thermomechanical studies of polymer deformation II. A thermodynamic analysis of a viscoelastic material in sinusoidal deformation

In this study, a linearly viscoelastic polyurethane film was subjected to continuous, sinusoidal deformation in a new isothermal deformation calorimeter, whose design details were recently reported (1). Internal energy and entropy of the polymer at each state in the deformation cycle were computed from heat rate and work rate data. This was made possible by using linear viscoelasticity theory to predict the irreversible entropy production. Thermal data were corrected for instrument time lag.     

A single-mode rheological model for steady flows of polymer melts

The steady shear viscosity (η_s), the steady first normal stress coefficient (Ψ₁), the steady second normal stress coefficient (Ψ₂), and extensional viscosity (η_e) are four important parameters for polymer melts during polymer processing. In this article, we propose a stress and rate-dependent function to describe creation and destruction of polymer junctions. Moreover, we also introduce a movement expression to describe nonaffine movement of network junctions. Based on network theory, a nonaffine single-mode rheological model is presented for the steady flow of polymeric melts, and the equations of η_s, Ψ₁, Ψ₂, and η_e are derived from the model accordingly. Furthermore the dependences of η_s and η_e on model parameters are discussed for the model. Without a complex statistical simulation, the single-mode model with four parameters yields good quantitative predictions of the steady shear and extensional flows for two low density polyethylene melts reported from previous literature in very wide range of deformation rates. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Re-analysis of extensional flow data of polymer melts

Extensional flow behaviour is very important in polymer processing operations such as fiber spinning and film blowing but there is scanty experimental data in the literature due to inherent difficulties in measurement of the relevant flow parameters. In the present paper, an attempt has been made to correlate the existing available data on the extensional flow of three generic types of polymer melts through a logarithmic plot of modified extensional viscosity function, η_E · MFI, and a modified extension rate, (ε/MFI)². The method may be extended to other polymeric systems.     

The steady flow shear modulus of polymer melts

Relaxation times of polyethylene melts have been measured by Aloisio, Matsuoka, and Maxwell. One implication regarding their observations is that the elastic properties of polymer melts must be time-dependent. In particular, the steady-flow shear modulus depends on the strain rate. Some interpretations of data in the literature have been based on concepts in rubber elasticity where the steady-flow modulus is an equilibrium value, independent of strain rate. We have used Pao's theory for viscoelastic flow together with measurements of relaxation times to discuss the strain rate dependence of the steady-flow shear modulus of melts. The existence of a strain rate-dependent shear modulus leads naturally to a nonlinear relation between shear stress and recoverable shear strain. The conclusions regarding the molecular weight dependence of the modulus also differ from interpretations based on rubber elasticity.     

微尺度通道中聚合物熔体的黏性耗散效应

以双料筒毛细管流变仪和自行研制的黏性耗散测量装置为实验平台,通过对聚甲醛(POM)和聚苯乙烯(PS)两种聚合物熔体在不同剪切速率下,流经长径比相同的直径/当量直径分别为350 μm和500 μm的圆形及矩形截面微通道出口熔体温升的测量,研究了微尺度通道中聚合物熔体流动时的黏性耗散效应及其对熔体流变行为的影响。结果表明,两种截面微通道中的熔体黏性耗散效应均随剪切速率和微道直径/当量直径的增大而明显增强,其中矩形截面微通道中熔体的黏性耗散作用尤为强烈;且在相同实验条件下,结晶性的POM熔体因黏性耗散效应引起的微通道出口熔体温升值,高于非晶性的PS熔体。