摘要:

Extension of flat films uneven in thickness and lying on the (x,y) plane is analyzed mathematically. Constitutive models assumed are isothermal Newtonian fluids and rubber‐like elastic solids. Governing equations reduce to the Cauchy–Riemann equations when the material is Newtonian fluid and the film is uniform in thickness. Many unusual modes of extension exist in this case. In both cases of Newtonian fluids and rubberlike elastic solids, governing equations reduce to readily solvable ordinary differential equations when the extension is axisymmetrical. Conditions of wrinkle free extension are introduced. Numerical solutions are obtained for the general extension of the films of rubber‐like elastic solids.

ISSN:0148-6055    

DOI:10.1122/1.550489

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

The stress relaxation and simultaneous birefringence variation were measured for bisphenol A polycarbonate over the glassy to the rubbery plateau regions. The measurements were performed at various temperatures of 142–156 °C over the time range of 0.4 to 2000 s. Results of relaxation measurements were consistent with those of dynamic measurements with respect to the birefringence as well as the stress in the framework of linear viscoelasticity. A modified stress‐optical rule was applied to the results of relaxation measurements. This rule was earlier proposed to replace the stress‐optical rule which was suitable only in the rubbery and the terminal flow regions. The relaxation modulus,E(t), was separated into two component functions,ER(t) andEG(t). In constructing master curves ofER(t) andEG(t) with the method of reduced variables, their shift factors were found to have different temperature dependence. This result can account for the break down of time‐temperature superposition principle forE(t) reported by several investigators. The present modified stress‐optical rule was more convenient in several ways compared with the similar modifications proposed earlier by Priss et al. and Read.

ISSN:0148-6055    

DOI:10.1122/1.550491

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

Effects of process variables and material properties on melt spinning of pitches have been studied based on simulation using governing equations by Kase and Matsuo. It is shown that the tensionFin a filament depends on spinning conditions as well as viscosity of pitch in the form ofF∝μ0W1/6f1(v0,vL,vA)/f2(T0,TS,TA,E). Here,W,v0,vL, andvAare mass flow rate, velocity at the spinnerette, winding speed and cross‐flow air velocity respectively, andT0,TS, andTAdenote temperatures at the spinnerette, at the solidification point and of air. Temperature dependence of viscosity is simplified by an Arrhenius type equation with a pre‐exponential factor μ0and a flow activation energyE. To improve spinnability, the maximum tensile stress σLshould be decreased by increasingW,T0andTAor by decreasingvL,vA,TS, μ0andE. In other words, slower cooling of the filament with larger diameter for a pitch with smaller activation energy is preferable to better spinnability. Effects of these factors on diameter, temperature and strain rate of the spinning filament are also discussed.

ISSN:0148-6055    

DOI:10.1122/1.550492

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

Pulse Strain Method for viscoelastic measurements is presented, which is based on the Raised Cosine Pulse Method (RCP Method). According to the RCP Method, frequency dependence of complex shear modulus is given by the Fourier transform of shear stress as the response to a pulse strain of cosine type. However, frequency range of observation is limited to only 1 or 2 decades in lower region of fundamental frequency of applied pulse strain. To expand the frequency range, we have modified the RCP Method using Rectangular Pulse Strain, which includes high‐frequency components (RAP Method). Comparison among the RCP Method, RAP Method and conventional dynamic methods was made on a 20% polystyrene solution in diethylphthalate. In the case of the RAP Method, frequency range was expanded to higher frequencies of fundamental frequency of applied pulse strain compared with the RCP Method. Computer simulation of Pulse Strain Method was made to know the requirements for further expansion of frequency range. The shear stress as the response to pulse strain was calculated for a Maxwell model using the Boltzmann superposition principle, and then complex shear modulus was calculated from Fourier transform of pulse strain and shear stress. The obtained shear modulus from simulation was compared with the theoretical value. It has been shown that resolution and response time of a torque transducer are important to make the best use of Pulse Strain Method. The requirements for a torque transducer are as follows, resolution is 1/10000, and response time is 0.1 ms.

ISSN:0148-6055    

DOI:10.1122/1.550493

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

A mechanism of chain slippage across the entanglement link is adopted to describe the early stage behavior in the stress relaxation of concentrated polymer systems. The chain slippage in the postulated mechanism occurs due to the equilibration of natural monomer (Rouse bead) densities between the primitive segmental units. It is shown that the processXintroduced by Lin can be confirmed theoretically and that it partially contributes to the reduction of stress discrepancy between the processesAandBof Doi.

ISSN:0148-6055    

DOI:10.1122/1.550569

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

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.

ISSN:0148-6055    

DOI:10.1122/1.550570

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

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 subelements 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 We simulation.

ISSN:0148-6055    

DOI:10.1122/1.550571

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

This paper reports shear rate dependence of the viscosity and relative viscosity of highly concentrated nonaqueous and aqueous slurries used for tape casting of the alumina sheet by a doctor blade method. The nonaqueous 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, log ηr=αφ and log ηr=αφ+(α/2φm)φ2, are both fitted to the data measured quite well.

ISSN:0148-6055    

DOI:10.1122/1.550572

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

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 viscoelastic 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.

ISSN:0148-6055    

DOI:10.1122/1.550574

出版商:The Society of Rheology    

年代:1994

数据来源: AIP

摘要:

Flow behavior 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 behavior in packed beds of particles and yields the excess pressure loss for the PAA solutions.

ISSN:0148-6055    

DOI:10.1122/1.550576

出版商:The Society of Rheology    

年代:1994

数据来源: AIP