The viscoelastic flow in a planar abrupt contraction was analyzed including the inertia effect, and the effects of inertia and viscoelasticity on the flow were studied. The Galerkin finite element method was employed as the numerical method. The constitutive model was the simplified Criminale-Ericksen-Filbey (CEF) model which expressed the extra stresses as an explicit function of velocity and deformation rate. We studied the effects of the Reynolds number, the Weissenberg number (the primary normal stress difference) and the elongational viscosity individually on the re-entrant corner vortex and the entrance pressure drop. As a result, we found the following; 1) as the primary normal stress difference increases, the corner vortex grows up but the entrance pressure drop slightly decreases. 2) The inertia effect reduces the corner vortex produced by the viscoelasticity and increases the entrance pressure drop. 3) The flow fields are significantly influenced by the viscoelasticity in the low flow rate region but become to be dominated by the inertia with increasing flow rate. 4) Both the vortex intensity and the entrance pressure drop for the fluid with strain-thickening elongational viscosity are larger than those for the fluid with strain-thinning elongational viscosity.
In order to predict the die swell seen in the actual polymer processing, the planar, the capillary and the annular die swell simulations have been performed by the streamline-upwind finite element method with the sub-elements for stress components, which was shown effective to calculate up to high Weissenberg number (We) for the entry flow simulation in an earlier study. The calculation using the Giesekus model, which is the differential type viscoelastic model, was found feasible over hundreds of We in the planar and the capillary die swell simulations as long as the primary normal stress difference was not so large. The shape of free surface at high We under the condition of no gravitation once showed the maximum swell and became an equilibrium one after shrinking back a little. This tendency became remarkable for the model with larger We and larger primary normal stress difference. Through the examination of the velocity profile, it was found that the velocity near the free surface was accelerated during the swell after extrusion and was larger than the inside velocity in the neighborhood of the position which showed the maximum swell. Since the accelerated outer fluid dragged the inside fluid, the swelling ratio was supposed to take an equilibrium value after shrinking back a little. Also, as the primary normal stress difference became larger, the axial position of the maximum swell approached the die. This may be due to that the model with the large primary normal stress difference predicts faster swell, because the elastic recovery force after extrusion is large. The axial position of the maximum swell became distant from the die with increasing We. We interpreted that the axial position of the maximum swell shifted downstream as the representative relaxation time was longer, or the velocity became larger. On the other hand, the calculation became impossible for We>3 in the annular die swell simulation. In order to examine this reason, we performed the calculation for the planar die swell in two different analysis regions i. e. one being the whole flow region with two singular points and the other, the half flow region with one singular point in consideration of flow symmetry. The calculation in the whole flow region with two singular points was unsuccessful at high We. It seems that the presence of two singular points in the analysis region made it impossible to perform the annular die swell up to high Wesimulation.
This paper reports shear rate dependence of the viscosity and relative viscosity of highly concentrated non-aqueous and aqueous slurries used for tape casting of the alumina sheet by a doctor blade method.The non-aqueous and aqueous slurries containing 28-35 vol% and 24-29 vol%alumina, respectively, were prepared by ball milling for this work.Approximate equations, derived from the Dougherty-Krieger-equation, logηr,=αφand logηr=αφ+(α/2φm)φ2, are both fitted to the data measured quite well.
Flows of non-Newtonian fluids passing a flat external surface with zero incidence angle was studied theoretically. The constitutive equation used in the present study is the Phan Thien-Tanner (PTT) type with the network theory, and the simple power law is used for comparison. The thickness of the boundary layer and the friction coefficient are calculated in order to examine the effects of the breakage index and the slip parameter in the shear behavior. The Von Karman integral equation is solved numerically with a similar solution of the velocity profile using the newly defined shape factor. The calculation results for shear thinning liquids indicate that the thickness of the boundary layer and the friction coefficient are dependent upon the slip parameter and the breakage index, where a choice of non-zero breakage index without the effect of the normal stress terms yields similar results to the power law case. It is revealed that the friction coefficient (wall shear stress) has a peak value at the entrance region of the plate, whereas such a symotom is not seen in the case of the power law and the Newtonian flows.
A simulation system is developed for evaluating viscoelastic properties of polymer melts with arbitrary polydispersity in molecular weight, starting from the known chemical structure of the polymers. The critical molecular weight for entanglement and molecular weight dependence of zero shear viscosity are evaluated based on theories of van Krevelen and Berry-Fox by optimizing parameters associated with chain flexibility, chain length and effective molar weight per repeating unit. In the evaluation of viscoelastic properties of polymer melts, simple and reasonable shape of relaxation spectrum is assumed for polydisperse systems. Using molecular parameters evaluated above, frequency dependence of viscoleastic functions is calculated from the relaxation spectrum. This method is shown to be superior to the usual way of calculation of viscoelasticity based on blending rules: The time needed for the calculation is very short and does not depend on the polydispersity in molecular weight. Combination of the present method with an appropriate constitutive equation gives a system for evaluating nonlinear viscoelastic properties of polydisperse polymers.
Dry gel films of ultrahigh molecular weight poly(acrylonitrile) homopolymer, having strong intermolecular forces, have been drawn by solid-state coextrusion in the temperature range from room temperature to 260°C. The effects of solution concentration from which gel was made and extrusion temperature on the extrusion behavior and the structure and properties of drwan films have been studied. The draw-ability of each gel increased with extrusion temperature above the Tg(80°C), reached a maximum at 160°C, and then decreased rapidly above 160°C. The draw-ability of gel also increased with decreasing the solution concentration from which gel was generated. This indicates that the ductility of poly(acrylonitrile), which has strong intermolecular forces and exhibits no crystalline relaxation, is also controlled by the entanglement density, like polyethylene having weak intermolecular interactions. Gel prepared from the lowest concentration of 2 wt% in this work could be extrusion-drawn to draw ratios ≤82 at 160°C. Extrusion temperature markedly affected not only the ductility of gel, but also the efficiency of draw and the formation of flaws at high draw ratios. Thus, the maximum tensile modulus and strength achieved in this work were 20 and 1.0 GPa, respectively.
Flow behaviour of polymer solutions through packed beds of particles, which are used as a model of porous media, is experimentally examined. Two packing patterns are prepared and the test fluids used here are aqueous solutions of polyacrylamide(PAA) at three different concentrations. In the measurement of pressure loss, it is observed that the curve of pressure loss makes a sudden change at the critical flow rate. Below the critical flow rate, the pressure loss depends on the shear property of the fluids and can be expressed by the modified Darcy's law applying the power law model to the shear viscosity of fluids. Beyond the critical flow rate, however, the transient elongational property of the fluids dominates the flow behaviour in packed beds of particles and yields the excess pressure loss for the PAA solutions.
An experimental study for petroleum liquid crystalline pitch materials has been carried out to clarify the relationship between rheological properties and melt spinning process. The softening temperature, specific heat, viscosity, and dynamic moduli were measured. The flow activation energy was obtained to be 55 kcal/mol from the viscoelastic measurements. The attenuation process in melt spinning occurred only close to the spinneret. The stress growth of the running filaments was calculated by using the Bogue-White constitutive model. The experimental data were explained well with a single relaxation time of 0.01 sec and non-linear parameter of 0.5. Spinnability was inversely correlated to the relaxation time for the liquid crystalline pitch.
A computer program to simulate three dimensional flow in injection molding process has been developed. To investigate numerical methods of moving free surfaces of the flow, the flow in injection molding process is regarded as isothermal, incompressible, high viscous flow of a Newtonian fluid with free surfaces. Generally, many computing times and computer memories are spent for numerical calculation of high viscous flow with free surfaces. Therefore, an effective combined calculation method was developed by using the two-stages rational Runge-Kutta scheme for time integration, the pseudo concentrations method for calculation of the moving free surfaces and the donor-acceptor scheme for an advection equation of the pseudo concentrations to reduce the computational effort in the computer program. A numerical calculation was carried out for the mold filling simulation in a cavity composed of a plate and a cylinder. This calculated result was compared with the experimental result which was obtained by an observation of filling flow of silicone oil in a visible cavity. As a result, the calculated flow patterns agreed with the observed ones.
Dynamic viscoelasticity of the systems having yield stress was measured using the raised cosine pulse (RCP) method by means of a cone-plate type rheometer. The systems employed were mayonnaise and ketchup which are typical plastic materials. Influence of the amplitude of RCP strain on the convergence of the response stress was investigated. The response stress for a large RCP strain does not converge to zero. That is, the stress has a finite negative value still after a long time. In this case, the Fourier transformation of the response stress cannot be performed with a satisfied accuracy. On the other hand, the response stress converges to zero within a very short time for a small RCP stain and the frequency dependences of the dynamic moduli can be obtained, which are sufficiently congruent to them by the usual dynamic measurement.