Showing papers in "Rheologica Acta in 1980"

Flow birefringence of dilute polymer solutions in two-dimensional flows

Abstract: Flow birefringence measurements have been obtained on three molecular weight samples (2−8 × 106 M W ,M W /M N = 1.14−1.3) of polystyrene in dilute solution (50–100 ppm) in a viscous polychorinated biphenyl solvent. The flows were generated using a four roll mill which could simulate a wide range of two dimensional flows in which the flow type (i.e. the ratio of the rate of rotation to the rate of strain) could be varied independently of the velocity gradient. The normalized birefringence, corrected for concentration, (Δn/nc), was observed to approach a saturation value at high velocity gradients in purely extensional flow. This saturation value was independent of both the molecular weight and the concentrationc, in agreement with theory. In addition, the magnitude of the saturation value is consistent with nearly fully extended chains and suggests extensions in the range of 20–50 times the rest state size. The data for the birefringence over a wide range of flows was found to be well correlated against the eigenvalue of the velocity gradient tensor in agreement with the results of the “strong/weak” flow theories ofTanner (1976) andOlbricht et al. (1980). The experiments are compared with a simple dumbbell model which incorporates the effects of a nonlinear spring variable hydrodynamic friction, and internal viscosity. It is shown that this simple model can simulate the experimental results surprisingly well if the effects of molecular weight distribution and finite transit times in the flow device are taken into account.

Toward a viscoelastic modelling of the injection molding of polymers

Abstract: By using theLeonov viscoelastic constitutive equation, an idealized problem has been solved for onedimensional, unsteady, non-isothermal flow of polymer between two parallel plates and the subsequent non-isothermal relaxation following cessation of flow. Numerical results are presented for the time dependence of the pressure gradient, the gapwise distribution of linear velocity, shear rate, shear stress and normalstress differences, together with the components of birefringence in different planes. Comparison of the present predictions for the pressure gradient with results based upon an “inelastic” model indicate close agreement whereas the corresponding predictions for normal-stress differences are found to be markedly different from those for the “inelastic” case.

Relation between steady shear flow and dynamic rheology

Abstract: The relationships between steady shear flow and dynamic rheology are investigated at relatively high shear rates and frequencies A useful empirical relationship in this region predicts that the magnitude of the complex dynamic viscosity |η*| should be compared with the shear viscosityη at equal values of frequency and shear rate (Cox-Merz-rule) Polystyrenes (PS) and Polyacrylamides (PAAm) have been investigated over a wide range of concentration and molecular weight Only in case of PAAm/H2O solutions we have found that the results do not coincide with Cox-Merz-rule As far as we know this is the first time that deviations from Cox-Merz-rule were observed in a homogeneous system A molecular interpretation is given

Creeping motion of spheres through shear-thinning elastic fluids described by the Carreau viscosity equation

Abstract: Previous work on the creeping flow of viscoelastic fluids past a sphere is reviewed Theoretical analyses available in the literature were obtained for weakly elastic fluids and therefore they predict only a small influence of fluid elasticity on the drag In this paper, an approximate theoretical analysis is given for the creeping flow past a rigid sphere in an unbounded medium The analysis uses a variational principle to solve the equations of motion and continuity in conjunction with the Carreau constitutive equation The theoretical results are presented in terms of a correction factor to the Newtonian drag coefficient The correction factor is a function of the power law flow behaviour indexn, the ratio of limiting viscosities (η 0 − η∞)/η0 and a dimensionless timeΛ which reflects the elastic nature of the fluids The results are presented in graphical form covering a realistic range of these dimensionless groups In order to verify the theoretical predictions, the drag coefficient of a number of spheres was measured in a series of shear thinning elastic test fluids The flow properties of the test fluids were independently measured with a Weissenberg Rheogoniometer The power law index of the test fluids varied between 10 and 04 Particle Reynolds number based onη 0 was in the range of 4⋅10−6 to 4⋅10−2 The difference between theoretically predicted values of drag coefficient and the experimentally measured values is less than ±75% In addition, it is found that the Carreau viscosity equation can be used to predict the elastic parameter of primary normal stress difference with moderate to good accuracy for all the polymer solutions used in this work

The time temperature position of the glass-rubber transition of amorphous polymers and the free volume

Abstract: Accurate measurements of the shear creep compliance in the glass rubber transition region have been performed by means of a combined torsional pendulum and torsional creep apparatus over a broad experimental window for commercial PS, PMMA and PVC and for two slightly crosslinked rubbers, NR and PU. For the three plastic materials, specific volume vs. temperature curves were obtained by volume dilatometry under different rates of cooling.

The stress relaxation of molten PMMA at large deformations and its theoretical interpretation

Abstract: The stress relaxation behaviour of molten PMMA under large tensile deformations has been studied. Maximum values of the extension ratio were larger than 3.5. Similarly with previous results, the time dependence of the relaxing stress was found to be approximatively the same at all deformations. The deformation dependence was compared with the predictions of a theory byDoi andEdwards as well as with a modification of that theory which proves to agree better with the experimental results.

Rheological properties of agarose-gelatin gels

Abstract: Stress relaxation measurements were made on agarose-gelatin aqueous gels. The results were analysed in terms of a six-element model composed of three Maxwell elements in parallel. The temperature and concentration dependences were examined.E1, the elastic modulus of the Maxwell element with the longest relaxation time, reflects the elasticity of the main network structure. The observed values ofE1 were compared with those calculated by a formula for the composite system. Since the observed values were much smaller than the calculated values, the gelling process of the agarose was considered not to be a simple dispersion of agarose in a gelatin medium, but rather that gelation was hindered by the gelatin. The stress-strain curves for the system were also obtained.

Die Abhängigkeit des Fließverhaltens konzentrierter Kugelsuspensionen von der Strömungsform: Ein Vergleich der Viskosität in Scher- und Dehnströmungen

Abstract: Es wird ein Auslaufviskosimeter mit automatischer Meswertermittlung konstruiert, in dem in guter Naherung eine Dehnstromung realisiert ist. Hiermit werden in Verbindung mit geeigneten Rotationsviskosimetern vergleichende Messungen an konzentrierten Suspensionen von starren Kugeln in newtonschen Flussigkeiten durchgefuhrt, wobei ausgepragte Unterschiede auftreten.

An improved simple version of a nonlinear theory of elasto-viscous polymer media

Abstract: Some rheological equations describing the elastoviscous behavior of concentrated polymer solutions and melts were suggested using a two-parameter elastic potential. These equations, containing a small number of parameters, are based upon a representation involving a set of nonlinear noninteracting relaxators (the Maxwellian models). As examples, shear and extension deformations are considered. The reasons for the choice of rheological constants are given. A comparison between the theory and some experiments for a simplest four-parameter model (two noninteracting nonlinear relaxators) has shown that it describes the tests much better than the simplest three parameter model developed previously.

Propriétés viscoélastiques linéaires de solutions de polybutadiène en régime semi-dilué et concentré

Abstract: L'evolution des proprietes viscoelastiques lineaires de polymeres en solution est caracterisee par l'etude des variations des trois parametres caracteristiques de la viscoelasticite lineaire (viscosite limiteη 0, complaisance limiteJ e 0 et module de plateauG N 0 ) en fonction de la concentration dans differents solvants. Les polymeres etudies sont des polybutadienes lineaires et branches en etoile, a distribution etroite de masses moleculaires. Les solvants etudies ont des temperatures de transition vitreuse inferieure, egale ou superieure a celle du polybutadiene (respectivement le tetradecane, un polybutadiene de faible masse moleculaire et une huile commerciale). Les resultats obtenus (η 0 ∞c 4,0,G 0 ∞c 2,25 etJ 0 ∞c −2,25) sont en desaccord avec le comportement conforme aux modeles de champ moyen generalement admis, et semble partiellement en accord avec les modeles recents de la relaxation et de la thermodynamique des longues chaines flexibles.

Relative viscosities of polymer melts filled with inorganic fillers

Abstract: Viscosities of polyethylene melts filled with natural calcium carbonate (NC), glass fiber (GF), and carbon fiber and polypropylene melts filled with NC, talc, and GF were examined. Constant relative viscositiesηr were obtained on these filled systems if use was made of the definition ofηr suggested in an earlier paper. The relationships betweenηr and the volume fractionφ of the filler were discussed qualitatively in conjunction with earlier data. The magnitude ofηr for the material filled with fiber increases with the increase of the average aspect ratio of the fiber.

On elastic effects in unsteady pipe flows

Abstract: Theoretical consideration is given to two unsteady pipe flows. In the first, a combined steady and oscillatory shear flow is generated by a pulsatile pressure gradient in a stationary pipe. In the second, the pressure gradient is constant, but the pipe wall executes axial vibrations.

The effect of the mixing methods on viscous properties of polyethylene melts filled with fibers

Abstract: The viscous properties of polyethylene melts filled with glass fibers (GF) and carbon fibers (CF) by three different methods were studied. The fiber length and the distribution of the fiber lengths in the samples were examined and were correlated with the viscous properties. The dry blend samples prepared by mixing polyethylene powder and disintegrated fibers behaved somewhat irregular in rheological respect. This was considered to be attributed to the poor dispersion of the fibers in the sample. The samples prepared by a screw extruder (SC) and by an elastic melt extruder (WEX) showed normal rheological behavior. The average aspect ratio of the fibers in the SC-sample is larger for CF than for GF, owing to the higher rigidity of CF. Corresponding to this, the viscosities of CF filled samples were higher than those of GF filled samples. The overall shape of the distribution of the fiber lengths in the WEX-sample was rather broad compared to that in the SC-sample, and also the average aspect ratio of the fibers in the WEX-sample was by far larger than that in the SC-sample. Corresponding to the average aspect ratio and/or the distribution of the fiber lengths, the relative viscosityη r of the WEX-sample is much larger than that of the SC-samples. Results obtained by a parallel plate plastometer supplemented the flow curves in the lower region of shear rate obtained by a cone-plate viscometer. Samples with high fiber content showed a sharp increase of viscosity with decreasing shear rate, especially for the CF filled sample.

Study of the nonlinear response of a polymer solution to various uniaxial shear flow histories

Abstract: A stiffened and automated Weissenberg Rheogoniometer has been used to obtain steady-state and transient stress data on a 12 wt% polystyrene solution While the results agree generally with those previously reported on the same solution, the present data-acquisition system provides a more accurate recording of short-time responses Stress growth and relaxation data were compared with the responses predicted for a finite linear viscoelastic fluid with the same relaxation time spectrum as the test solution Simple generalizations based on such a comparison have been sought

The stick-slip problem for a round jet I. Large surface tension

Abstract: SummaryThe stick-slip problem for a round jet is solved in two ways: by a Wiener-Hopf method and by a direct method in which eigenfunction solutions in the pipe and jet are matched on their common boundary. The same solution is obtained by the two methods, but the eigenfunction method is more direct and converges more rapidly. Reliable graphs are presented for the distributions of the velocity components, stresses and pressures at different axial positions in the pipe and jet. The shape of the free surface for the low speed jet is computed by a perturbation method.ZusammenfassungDas Haft-Gleit-Problem wird für einen runden Strahl auf zwei verschiedene Weisen gelöst: durch die Wiener-Hopf-Methode und durch eine direkte Methode, bei der die Eigenfunktionslösungen für Rohr und Freistrahl an der gemeinsamen Grenze aneinander angeschlossen werden. Mit beiden Methoden erhält man die gleiche Lösung, aber die Eigenfunktionsmethode ist direkter und konvergiert schneller. Glaubwürdige graphische Darstellungen des Verlaufs der Geschwindigkeitskomponenten, der Spannungen und der Drücke für verschiedene axiale Lagen in Rohr und Freistrahl werden mitgeteilt. Die Gestalt der freien Oberfläche für einen mit langsamer Geschwindigkeit austretenden Strahl wird mit Hilfe einer Störungsmethode berechnet.

The free surface on a liquid between cylinders rotating at different speeds. Part III

Abstract: This paper is a further contribution to our work on the Weissenberg effect. One goal of our work is to show how the free-surface deformations on a viscoelastic fluid which is sheared between two concentric rotating cylinders can be used to determine rheological data about the fluid. In this paper we report the results of an experimental program in which free surface shapes have been measured on three viscoelastic fluids undergoing shearing in an apparatus consisting of a stationary outer cylinder and four interchangeable rotating inner cylinders. Experimentally-measured profiles are compared with profiles predicted from second-order theory, and found to be in excellent agreement for STP and TLA-227 in the range of applicability of the second-order theory, but there is some disagreement in the results for a 2% solution of polyacrylamide in 49% water −49% glycerin.

Polypropylene-polyethylene blends

Abstract: Two different model representations are proposed to predict the morphology of the dispersed two-phase binary polyblend flowing through a capillary A blending law has been derived to predict the viscosity of the mixture with a morphology of many continuous fibrils structures as a function of volume ratio and viscosity ratio of the components To test its validity the blends of PP-PE were investigated at different blending compositions and temperatures

New apparatus for the simultaneous measurement of stresses and flow birefringence in biaxial extension of polymer melts

Abstract: A new apparatus is described for the measurement of the viscosity of polymer melts in biaxial extension. Use is made of the method of two impinging fluid streams. The mentioned streams are guided by lubricated trumpet shaped metal walls. The force is measured which tends to separate the trumpets. At the same time, the flow birefringence is measured in the plane of symmetry, which contains the stagnation point. The linear stress-optical relation, which is well-known from shear experiments, turns out to be valid also in the new flow geometry, at least up to the deformation rates applied. Results of the steady state measurements carried out on a polystyrene melt are evaluated. Suggestions for a better performance of the mechanical measurements are given.

About the origin of sharkskin

Abstract: Some new results of experimental study of linear polyethylene melt flow instabilities are given. Two effects, the main flow instability and the sharkskin phenomenon, are presented in terms of relaxation oscillator theory, and permit an understanding of the influence of experimental parameters on the period of the oscillatory flow. Sharkskin is interpreted to be the same phenomenon as the other instability, but to occur in the die entry region rather than in the whole die itself. Various aspects of sharkskin characteristics are considered.

Polypropylene and polyethylene blends

Abstract: The flow behaviour of blends of an isotactic polypropylene (PP) and a high density polyethylene (PE) in the molten state was studied as a function of composition, temperature and shear rate to examine the degree of compatibility under shear. PP and PE were melt blended in a laboratory single screw mixing extruder at the compositions 0, 25, 50, 75 and 100 percentage of PE by weight and shear stress versus shear rate data were obtained using an Instron capillary viscometer at different temperatures. Viscosity-shear rate data of PP-PE blends at different temperatures constitute “master curves” at constant blend composition, when plotted as η/η0 versus $$\dot \gamma $$ η0/T. This type of behaviour is commenly observed for homopolymer systems. Therefore these experimental findings indicate that the PP-PE system forms either a compatible blend in the molten state under shear flow conditions or a morphology which is independent of temperature.

Flows of dilute polymer solutions through packed porous chromatographic columns

Abstract: We have found that diffusion of polystyrene into the micropores of packed porous chromatographic columns of a type used for size separations of macromolecules is strongly influenced by the flow rate of the polymer solution through the column and also by the macromolecular size and internal pore size of the column packing. Dilute polymer solutions (0.05 wt.% polystyrene in THF) were pumped continously through the columns (Dupont SEC). Step changes in flow rate were made and the polymer concentration in the column effluent was monitored continuously. When the flow rate was increased, the partition coefficient for polymer between mobile and stationary phase shifted toward more polymer retention in the column, as evidenced by the drop in outlet concentration for several minutes following the step change. Molecular weight, pore size and solvent effects have all been thoroughly investigated. The conclusion is that polymer molecules diffuse into the internal pores of the column packing at a flow ratedependent rate and moreover, they do so to a greater extent the larger the polymer molecule, provided they are not sterically excluded from the pores. This dynamic diffusional partitioning is clearly important in its effect on resolution characteristics of an SEC column and also sheds some light on qualitatively similar observations in polymer flooding for enhanced oil recovery.

A study of the shear viscosity of human whole saliva

Abstract: A model R-18 Weissenberg Rheogoniometer operating in the continuous shear mode was used to generate shear viscosity vs. shear rate data on male and female human whole saliva. These data were found to accurately follow the Sisko model, $$\mu - \mu _\infty = K\left| {\dot \gamma } \right|^n $$ , whereµ is the shear viscosity at shear rate $$\dot \gamma ,\mu _\infty $$ is the asymptotic shear viscosity at infinite shear rate, andK andn are constants. Data were collected on the effects of food, coffee, caffeine, and aspirin as functions of time. Studies were also made on the effects of emotional stress, donor sex and age. The saliva viscosity increased with time and then decreased to the basal value for most ingested materials. Emotional stress was found to elevate the saliva viscosity. On the other hand, no significant difference was found between the average saliva viscosities of male and female groups. Also, no significant effect of donor age was detected.

Flow enhancement mechanisms of a pulsating flow of non-Newtonian liquids

Abstract: The pipe flow of non-Newtonian liquids under a fluctuating pressure gradient is considered. Adopting a generalized Maxwell model with full relaxation spectrum and considering only weak-sense stationary pressure-gradient noises, it is shown that there are two mechanisms involved in the flow enhancement: an inelastic and a dynamic mechanism. Both depend on the shear-thinning properties of the liquid in steady and oscillatory flows. For one-frequency pressuregradient noises, the flow enhancement increases with increasing frequency of fluctuation if the modulus of the complex viscosity is a decreasing function of the frequency. Since almost all polymeric liquids are shear-thinning in oscillatory shear flows, this investigation serves as a possible explanation for the data collected byBarnes, Townsend andWalters (1971). This, however, does not necessarily ensure that the constitutive model adopted in this study is free of defect in a general flow field.

Automatic apparatus, based upon a nickel-tube resonator, for measuring the complex shear modulus of liquids in the kHz range

Abstract: An apparatus for the measurement of liquid-shear impedance in the frequency range 11–170 kHz using a thin-walled nickel-tube resonator is described. The working principle of the method used has been previously published. Compared with the prototype the most important advances in the design concern the suspension of the resonator and complete automatization of the measurements and data handling. At the cost of not measuring at the fundamental frequency accuracy and ease of operation are greatly improved. Results for Newtonian and viscoelastic liquids are presented. Comparison with other types of apparatus is made.

Study of compressibility in vascular rheology

Abstract: Stresses and strains in vascular tissues are studied in the paper, considering the material to be nonlinearly viscoelastic and compressible. Structural anisotropy is also taken into account. A numerical study of the derived expressions shows that consideration of even a low compressibility for vascular material has got a significant effect on the nonlinear stress-field in vascular walls.

A computer model of hole-pressure measurement in Poiseuille flow of visco-elastic liquids

Abstract: Liquid-filled holes used for pressure measurements of visco-elastic liquids give rise to systematic hole pressure ‘errors’Tanner andPipkin have presented an analysis for flows of a second-order fluid in which they derive a simple relation between the first normal-stress difference and the hole pressure for flow situations where Reynolds numbers are very small Implicit in the analysis is the assumption that the streamlines are symmetric about the hole center line In this paper, using a numerical solution, we investigate the relationship between the hole pressure and the first normalstress difference for a range of Reynolds numbers where inertial effects are not negligible The ratio of hole pressure to first normal-stress difference is found to vary from 025 to 016 as the Reynolds number is varied from 1 to 10 Streamline patterns are presented for Poiseuille flow of a second-order fluid over a slot cut into one wall of an otherwise straight channel Various geometries are considered The results naturally include those for an incompressible Newtonian liquid at non-zero Reynolds numbers

Recoil kinetics of uniaxially oriented polystyrene

Abstract: Recovery experiments aboveTg have been performed on highly oriented polystyrene sheets obtained from extrusion and subsequent hot drawing. A shift procedure has been applied to recoil data using the WLF equation on two different types of commercial polystyrene. A variableλ defined as the fractional distance from equilibrium is able to reduce all the data obtained on sheets drawn at different draw ratios to a single master curve. The change in molecular weight affects only the value of the glass transition and the relaxation kinetics but has no influence on theC1 andC2 constants of the WLF equation. Moreover the molecular orientation does not modify theTg of the drawn polymers.

A Sandwich-Type Creep Rheometer for the measurement of rheological properties of polymer melts at low shear stresses*)

Abstract: A new Sandwich-Typ Creep Rheometer (SCR) is described which is suited for measuring the zero shear viscosityη 0 and the steady-state shear complianceJ e 0 of polymer melts. The range of shear stresses extends from 2 N/m2 to 5000 N/m2. Measurements down to shear rates of 10−5 s−1 and less are possible on high viscosity melts. The agreement between the SCR data and results from a modified Weissenberg rheogoniometer is shown for the viscosities as well as the compliances. Relations are presented which allow to take into account the non negligible influence of the surface tension of the sample on the measurements. From the reverse shear rate of the unloaded sample after total recoil the magnitude of the surface tension can be determined.

A thermodynamical approach to the understanding of slip-phenomena

Abstract: An explanation for wall slip in polymer solutions is given from a thermodynamic point of view. Due to flow induced diffusion, a slip film at the wall consisting of pure solvent can form if a dimensionless number exceeds its critical value. The general conclusions agree qualitatively with experimental findings of others.