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SPE Library content related to rheology
On Experimental and Modeling of the Coupling between Rheological Properties and Diffusion at Polymer/Polymer Interfaces
A new technique has been developed allowing the quantification of self-diffusion and mutual diffusion at polymer/polymer interfaces using rheometry. The technique consists of measuring the dynamic moduli as a function of time for a multilayer sandwich-like assembly in molten state. The technique was tested on PS/PS and PS/PVME systems sheared in oscillatory mode under small amplitudes of deformation for different times of welding. Based on the reptation and double reptation theories [1,2], an analytical expression for the self-diffusion and mutual diffusion coefficients as a function of polymer rheological material functions was derived.
Predicting Pressure Drop in Mixed Shear and Extensional Flow Using Converging Cone Capillary Rheology
No single rheological model is capable of reasonable prediction of observed behavior in cases where shear and extensional flows exit and neither can be neglected. Cogswell's approach was used to determine shear and extensional viscosities using the end-pressure drop method. The data was fitted by the Bird-Carreau model to predict shear and extensional viscosities. An expression for extensional viscosity is postulated based on shear viscosity plus only one other parameter. Determination of all parameters using the converging cone capillary rheometer is demonstrated for two common polymers. The model prediction agrees well with isothermal experimental data. For the first time, to our knowledge, a simple model for extensional viscosity that agrees with experimental data is presented, useful for engineering purposes.
Determination of Optimum Extrusion Conditions for Multilayer, Low Emission Plastic Fuel Line Systems Using Dual Capillay Rheometer Techniques
Multilayer co-extrusion of plastics is fast becoming a very cost effective method of improving the barrier properties of plastic products. In this process individual polymers are melted and conveyed by separate extrusion systems, into a common distribution block and through a forming die where the polymer melts merge to form an integral multilayer structure. Many of these polymers do not form a mutual bond in the melt and so specially formulated tie layers have been developed in order to facilitate melt bonding and so prevent delamination. Multilayer polymer tube structures have recently been developed for use in automotive fuel lines. These multilayer structures are proving difficult to extrude because of their widely different temperature profiles required during extrusion, and the fact that all the melts enter a common die which can only be maintained at one particular temperature. The melt rheological characteristics of a range of commercially available barrier materials, polyvinylidene fluoride (PVDF), a terpolymer of vinylidene fluoride, tetrafluoroethylene and hexafluoropropylene (THV), plasticised Nylons and tie layer materials have been studied using Dual Capillary Rheometric techniques. The relative change in shear viscosity with temperature, up to 270°C and shear rates up to 103 sec-1 have been investigated, for these materials, in order to determine optimum extrusion parameters during manufacture. The findings are confirmed by pilot plant tube extrusion trials using various multilayer structures. Arrhenius flow activation energies are also reported.
Thermal Expansion and its Effect on the Normal Force for a Modified Force Rebalance Transducer
Prior work in this laboratory [Niemiec, et al, J. Rheology, 40, 323-334 (1996)] showed that anomalous normal forces could arise in rotary shear measurements when thermal expansion of the force rebalance transducer (FRT) superimposed a squeezing flow on the shear flow. Transducer heating results from the current to the magnetic coils in the FRT necessary to counteract the applied torque. Partly due to this work, the manufacturer redesigned the transducer by replacing stainless steel components with Invar, an alloy with a very low coefficient of thermal expansion. Tests on the new transducer show that the thermal expansion is significantly reduced. The behavior of the new transducer is described.
A Nonlinear Fluid Standard Reference Material: Progress Report
A new NIST Standard Reference Material (SRM 2490 - Nonlinear Fluid for Rheological Measurements) demonstrates shear thinning and normal stresses typical of polymeric fluids. SRM 2490 consists of polyisobutylene dissolved in 2,6,10,14-tetramethylpentadecane (pristane), giving a stable fluid with a wide temperature range. NIST will certify the linear viscoelastic behavior and the shear-rate dependence of the viscosity and first normal stress difference between 0 °C and 50 °C. NIST will also use the fluid in a round robin to help the polymer community identify sources of variability in rheological measurements. Here we report progress on the project.
Pressure Flow in the Barrel: The Relationship of Fluid Elements in the Cavity to Original Barrel Locations
Pressure-driven flows dominate the injection molding process. A pressure flow is established in the barrel of the injection molding machine initially when the screw moves forward to inject material into the cavity. The laminar shear flow established by this action exhibits a parabolic velocity profile with the highest velocity in the center of the barrel and zero velocity at the barrel walls (Figure 1). With plastic melts the velocity profile is somewhat “flattened” due the non-Newtonian, i.e. nonlinear, rheological behavior of the melt. Such a velocity profile is not only characteristic of the basic flow in the barrel, but it also applies to the pressure-driven shear flows in the nozzle, runners, gates and cavities. The shear flow in the barrel is unique since the origin of the pressure energy is the screw displacement during injection. In order to maintain the highest velocity in the center of the various flow channels, material needs to be constantly added at the pressure source. This occurs in the barrel in the region closest to the screw. As the screw moves down the barrel, slow moving melt adjacent to the screw tip and near the barrel wall, is forced to the fast-moving center region (Figure 2). This sequence continues until the screw bottoms out or until the injection is stopped. Experiments with colored tracers have verified the laminar flow conditions and the volume-element relationship.
Squeeze Flow Rheometer
The squeeze flow rheometer is widely used especially for the rheological characterization of composites and polymer melts. However, since it incorporates both shear and extensional deformations its use is not straightforward. Here the two-dimensional constant-speed squeezing flow of viscoplastic fluids between two approaching surfaces in relative motion is solved using the Finite Element Method. Slip at the wall, a condition generally encountered with viscplastic fluids at solid surfaces, is incorporated in the model. The analysis is applicable to the rheological characterization and testing of parameters of constitutive equations for filled polymers and elatomers that exhibit a yield stress and will expand our understanding of the squeeze flow rheometer. The numerical analysis was focused on the determination of conditions under which 1-D analysis is valid.
Viscoelasticity of Polyethylenes Produced with Single Site Metallocene Catalysis
Linear low density polyethylene (LLDPE) produced using metallocene catalysts is gaining prominence as a class of new polyethylenes with superior performance. Two recently commercialized metallocene-catalyzed linear low density polyethylene resins were characterized in terms of their storage and loss moduli, shear viscosity, shear stress growth, stress relaxation upon cessation of steady shear, and first normal stress difference material functions. Overall the rheological behavior reflects the relatively narrow molecular weight distributions of the resins. The oscillatory shear and relaxation moduli data were employed to determine the parameters of Wagner model. Various material functions, determined on the basis of this model in conjunction with the fitted parameters, agreed reasonably well with the experimental results. The reported data and parameters should facilitate an improved understanding of the processability characteristics of these two new LLDPEs.
Assessment of Particle Migration Effects in Capillary Rheometry of Filled Polymers
It is important to assess the conditions under which the migration of particles becomes important during rheological characterization of filled polymers. Such migrations may become important during nonhomogeneous flow where gradients in shear rate induce particles to move away from high shear rate regions resulting in nonhomogeneous concentration distributions and the blunting of velocity distributions. Using the mathematical model of Phillips et al., a finite difference numerical solution was developed to assess the importance of particle migration effects in pressure-driven viscometric flows.
The Influence of Polymer Rheology on Bubble Penetration in Gas-Assisted Injection Molding
The influence of polymer rheology on the wall thickness and flow dynamics during the filling stage of gas-assisted injection molding is examined. Isothermal experiments are conducted with tailored ideal elastic fluids to isolate the influence of polymer elasticity on the hydrodynamic coating thickness formed during the bubble penetration process. The results indicate that the wall thickness increases with increasing elasticity and extensional viscosity. The results for several tube diameters are scaled onto a single master curve using the Deborah number (De). Flow visualization and particle tracking experiments are conducted to investigate the flow field in the vicinity of the bubble front. It is concluded that the extensional rheology plays an important role in determining the wall thickness in gas-assisted injection molding.
Binary Blends of Ziegler-Natta and Metallocene Catalyzed Polyethylenes: Rheological Properties
The rheological and morphological behaviors of three binary blends of polyethylenes regarding the melt index and density, one component made by Ziegler-Natta and the other by metallocene catalysts, have been investigated to elucidate miscibility and phase behavior. If the comonomer contents are similar, then the melt viscosity is weight average value, otherwise it shows different behavior: the FA+FM blend is miscible, but the RF+EN and RF+PL blends inform immiscible. The microtomed cutting surface indicates that all the blends are not homogenous regardless the density, melt index and cooling processes, and show banded spherulites.
Modification of Thermoplastics for Density and Gas Permeability through Additives and Reactive Processing
Transport properties of thermoplastics such as thermal conductivity and gas permeability are usually controlled through foaming and the formation of lamellar microstructures respectively. Production of low-density foams by extrusion in the presence of physical blowing agents requires materials with particular rheological characteristics. Reactor/post-reactor branching or controlled cross-linking is commonly carried out in the presence of multifunctional additives. Low vapor/gas permeability structures may be formed through the incorporation and subsequent orientation of impermeable lamellar fillers, or the in-situ formation of lamellar microstructures during processing of mixtures of immiscible polymers. Examples of available technologies in both areas and recent research results will be presented.
Constitutive Relationship for Electrorheological Fluids
The Winslow effect in smart-fluids is used in the design of automatic transmission fluid. A configurational distribution function is written and mesoscopic simulations are used to derive the constitutive relation for the stress tensor. The polymer molecule is modeled as an elastic dumbbell connected by a linear spring. Microscopic phenomena and macroscopic behavior are interrelated. Preliminary results reveal that the Bingham or yield stress behavior can be predicted from the first principles. Particle-Particle interactions, Brownian motion induced effect, self-assembly, Marongoni mechanism for particle clustering and their roles in durability, dispersion stability, redispersability and fluidity are explored.
Rheology of Hard-Metal Carbide Compounds
The results of an investigation of steady-state and oscillatory flow properties of hard-metal carbide powder compounds are presented. These highly concentrated compounds are intended for powder injection moulding (PIM) technology. The volume concentrations of powders, containing mainly tungsten carbide and cobalt alloy, differing in particle size distributions, varied up to 57.5 vol. %. The model relations, correlating relative viscosities with volume fraction of filler and shear rate (shear stress), were used in order to attain maximum volume fraction of powder in the compound. At the concentrations near the maximum loading an unstable flow was observed, which has been found to be influenced by the particle size distribution of the powder used as well as its concentration. In some cases, the instabilities were suppressed by repeated extrusion.
Positive and Negative Electrorheological Effect of Poly(Methyl Methacrylate) Dispersions Stabilized by the Block Copolymer Steric Stabilizer
A change of viscosity of the poly(methyl methacrylate) dispersions in decane stabilized with polystyrene-block-poly(ethylene-co-propylene) copolymer after application of an external electric field depends on the character of its original structure. When the mutual particle interactions are low, the organized structure formed in the electric field causes an increase in the viscosity of the dispersion and a positive electrorheological effect appears. If, due to strong interactions, a gel-like network particle structure exists, an application of the electric field causes a breakdown of this structure, the viscosity of the system decreases and negative electrorheological effect occurs. The type of rheological response is thus influenced by composition of dispersions.
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