Influence of branching on melt viscosity of polydisperse polymers

Summary The relation of melt viscosity to weight-average molecular weight and branching index has been derived for polydisperse polymers, with the most probable distribution of primary chains, having randomly distributed tri- or tetrafunctional branch points. The results are obtained by an extension of theKilb treatment for the intrinsic viscosity calculations. Numerical values of the viscosity functions are given for selected branching indices.

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Zusammenfassung Die Beziehung zwischen der Schmelzviskosität, dem mittleren Molekulargewicht und dem Verzweigungsindex wurde für polydisperse Polymere mit der wahrscheinlichsten Verteilung von primären Ketten, die ihrerseits statistisch verteilte tri- oder tetrafunktionale Verzweigungspunkte besitzen, abgeleitet. Die Ergebnisse wurden aus einer Erweiterung der vonKilb für die Berechnung der Grenzviskosität angewandten Methode erhalten. Für ausgewählte Verzweigungsindizes werden numerische Werte der Viskositätsfunktionen angegeben.

     

Mechanical behavior of amorphous polymers in shear

Based on the non-equilibrium thermodynamic theory, a new thermo-viscoelastic constitutive model for an incompressible material is proposed. This model can be considered as a kind of generalization of the non-Gaussian network theory in rubber elasticity to include the viscous and the thermal effects. A set of second rank tensorial internal variables was introduced, and in order to adequately describe the evolution of these internal variables, a new expression of the Helmholtz free energy was suggested. The mechanical behavior of the thermo-viscoelastic material under simple shear deformation was studied, and the “ viscous dissipation induced“ anisotropy due to the change of orientation distribution of molecular chains was examined. Influences of strain rate and thermal softening produced by the viscous dissipation on the shear stress were also discussed. Finally, the model predictions were compared with the experimental results performed by G‘ Sell et al. , thus the validity of the proposed model is verified.     

Effect of the molecular mass on the shear and longitudinal viscosity of linear polymers

The effect of the molecular mass of a polymer sample on the dependence of the stationary viscosity on the velocity gradient upon simple shear and uniaxial tension is studied. The model of the dynamics of a suspension of noninteracting dumbbells in the anisotropic medium is used. The theoretical results show that the asymptotic behavior of the shear viscosity does not depend on the molecular mass and corresponds to experimental data. Polzunov Altai State Technical University, Barnaul 656099. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 154–160, March–April, 2000.     

The viscosity of a polar fluid with suspensions

Summary The apparent viscosity of a polar fluid with suspensions of rigid spherical particles undergoing a prescribed bulk motion is calculated. It is shown that the increased rate of dissipation in a polar fluid with suspensions is greater than that of a Newtonian fluid. It is found that the relationship between the viscosity and the concentration has a same form with that of a Newtonian fluid suspension of which ambient fluid has a shear viscosity multiplied by a factor which is greater than unity.

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Zusammenfassung Die scheinbare Viskosität einer polaren Flüssigkeit mit suspendierten steifen, kugelförmigen Teilchen, die eine vorgeschriebene Bewegung ausführen, wird berechnet. Es wird gezeigt, daß die anwachsende Dissipationsgeschwindigkeit in einer polaren Flüssigkeit mit suspendierten Teilchen größer ist als die einerNewtonschen Flüssigkeit. Es zeigt sich, daß die Beziehung zwischen der Viskosität und der Konzentration die gleiche Form hat wie die einerNewtonschen Flüssigkeitssuspension, bei der die umgebende Flüssigkeit eine Scherviskosität besitzt, multipliziert mit einem Faktor größer als 1.

     

Rheological behavior of fiber-filled polymers under large amplitude oscillatory shear flow

Small and large amplitude oscillatory shear measurements (SAOS and LAOS) were used to investigate the rheological behavior of short glass fibers suspended in polybutene and molten polypropylene. Raw torque and normal force signals obtained from a strain-controlled instrument (ARES rheometer) were digitized using an analog to digital converter (ADC) card to allow more precise data analysis. The fiber concentration did not affect the torque signal in the SAOS mode, except for its magnitude, whereas the normal force signal was too low to be measurable. With increasing strain amplitude, the magnitude of the torque became a function of time. Depending on the applied frequency and strain rate, the stress in the filled polybutene increased with time, whereas for reinforced polypropylene (viscoelastic matrix), the behavior was opposite, i.e. the stress decreased with time. These effects were more pronounced at high fiber content. In addition the primary normal stress differences were no longer negligible at large deformation amplitude and exhibited a non-sinusoidal periodic response. Fast Fourier transform (FFT) analysis was performed and the resulting spectra, along with Lissajous figures of the shear stress and the primary normal stress differences, are explained in terms of fiber orientation. The experimental results for the suspensions in polybutene are well predicted by the Folgar-Tucker-Lipscomb (FTL) model.     

A study of the shear viscosity of human whole saliva

Summary 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, , whereµ is the shear viscosity at shear rate 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.

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Zusammenfassung Mit Hilfe eines Weissenberg-Rheogoniometers (Typ R-18) wurden bei stationärem Betrieb Scherviskositätskurven in Abhängigkeit von der Schergeschwindigkeit für den Speichel von Männern und Frauen gemessen. Man fand, daß sich die Meßwerte hinreichend genau durch ein Sisko-Modell, , beschreiben lassen, woµ die Scherviskosität bei der Schergeschwindigkeit die asymptotische Scherviskosität bei unendlich großer Schergeschwindigkeit sowieK undn weitere Konstanten bedeuten. Diese Messungen verfolgten die Wirkung von Nahrung, Kaffee, Coffein und Aspirin als Funktion der Zeit. Untersucht wurde weiterhin der Einfluß von emotionaler Spannung, sowie Geschlecht und Alter der Spender.Die Speichelviskosität stieg bei den meisten eingenommenen Stoffen mit der Zeit zuerst an, um danach wieder auf den Normalwert abzusinken. Ebenso fand man, daß emotionale Spannung eine Viskositätserhöhung hervorruft. Dagegen wurden bei Gruppen von Männern und Frauen keine signifikanten Unterschiede gefunden, und ebenso wurde kein gesicherter Einfluß des Alters festgestellt.

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With 4 figures and 6 tables     

Measurement of the shear viscosity using a newly developed GRLDA-viscometer

A two-point laser-Doppler anemometer is used to determine velocity gradients. Measuring additionally the pressure drop in channel flow allows one to use this instrument as a viscometer. This is demonstrated by measuring two polymer solutions as well as water. Besides the velocity gradient, the system also furnishes the velocity as well as velocity fluctuations. For surfactant solutions the sudden increase in these fluctuations go hand-in-hand with the sudden shear thickening reported. This behavior thus seems to be caused by a change in type of flow field (structural turbulence) rather than a change in the rheology of the surfactant solutions.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

Nonlinear shear behavior and interlaminar shear strength of unidirectional polymer matrix composites: A numerical study

Detailed finite element implementation is presented for a recently developed technique (He et al., 2012) to characterize nonlinear shear stress–strain response and interlaminar shear strength based on short-beam shear test of unidirectional polymeric composites. The material characterization couples iterative three-dimensional finite element modeling for stress calculation with digital image correlation for strain evaluation. Extensive numerical experiments were conducted to examine the dependence of the measured shear behavior on specimen and test configurations. The numerical results demonstrate that consistent results can be achieved for specimens with various span-to-thickness ratios, supporting the accurate material properties for the carbon/epoxy composite under study.     

Tangential discontinuities of parameters of a polar fluid under shear strain

Possible formation of tangential discontinuities of parameters of a deformable polar fluid is examined by the example of glycerin. It is experimentally established that glycerin under weak shear loads possesses the properties of a non-Newtonian elastoviscoplastic fluid, and formation of tangential discontinuities in viscosity is possible. In the discontinuity region, glycerin has the properties of a low-viscosity fluid, and the structure of the medium is reconstructed after unloading. A rheological equation of the examined fluid is derived, which allows one to analyze the behavior of the medium in different modes of its deformation, including the formation of a local region with reduced viscosity and a tensile stress field. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 41–49, May–June, 2005.     

Influence of aspect ratio and arrangement direction on the shear behavior of ellipsoids

This work studies the macroscopic and microscopic behaviors of ellipsoids under triaxial tests using 3D discrete element method (DEM) simulation. To avoid the boundary effect, a novel stress servo-controlled periodic boundary condition is proposed to maintain the confining pressure of samples during testing. The shape features of ellipsoids are investigated, including the aspect ratio of elongated/oblate ellipsoids and the initial arrangement directions of ellipsoids. The macroscopic properties of ellipsoidal particle samples, such as the deviatoric stress, volumetric strain, internal friction angle, as well as dilatancy angles are explored. Elongated and oblate ellipsoids with varying aspect ratios are investigated for the occurrence of stick-slips. In addition, it is demonstrated that the initial arrangement direction has a significant impact on the coordination number and contact force chains. The corresponding anisotropy coefficients of the entire contact network are analyzed to probe the microscopic roots of macroscopic behavior.     

Influence of medium viscosity and adsorbed polymer on the reversible shear thickening transition in concentrated colloidal dispersions

The influence of medium viscosity on the onset of shear thickening of silica dispersions is investigated with two different methods. In the first method, the sample temperature is varied over a narrow range for two different suspensions. For the first suspension, the stress at the onset of shear thickening, or the critical stress, was found to be independent of sample viscosity, and the shear viscosity scaled with Peclet number, as expected. The critical stress for the second suspension was not independent of sample viscosity, and the Peclet number scaling was only moderately successful. The differences were attributed to changes in particle interactions with temperature. In the second method, the molecular weight of an oligomeric silicone oil medium is varied. In principle, this method should maintain constant chemical interactions as medium viscosity varies; however the polymer is found to adsorb onto the silica surface and delay shear thickening to higher stresses with increasing molecular weight. The critical stress for the highest molecular weight systems, which is highly dependent on particle loading, overlays with an effective volume fraction based on the hydrodynamic diameter of the polymer-stabilized colloids. The results of both methods suggest that if all other properties of the dispersion are held constant, critical stress is independent of medium viscosity.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 2. High shear limit behavior

It is shown that in a truly bimodal coal-water slurry the hydrodynamic interactions between the coarse particles impose on the fine fraction a shear rate higher than that applied externally by the viscometer walls. A semi-empirical function of the coarse volume fraction is obtained for this correction factor to the applied shear rate. The derivation of this shear correction factor is based on lubrication concepts and introduces the maximum packing fraction,ø _m, at which flow can take place.ø _m is obtainable from a simple dry packing experiment. It is shown that the contribution of the coarse particles to the viscosity rise can be successfully described by a viscosity model employing the same concepts used to derive the shear correction factor. The bimodal model is applied in the high shear limit to polymodal coal slurries with a continuous particle size distribution. In the model, the contribution of the coarse particles to the viscosity rise is taken from separate viscosity measurements for the coarse coal particles, while the contribution to the viscosity of the fine coal particles is taken to be that given by the measured viscosity of colloidal suspensions of monomodal rigid spheres. It is shown that there is a ratio of coarse to fine fraction volumes in the continuous size distribution, corresponding to a specific separating particle size, for which the measured viscosities of the polymodal slurries match almost perfectly over the whole solids volume fraction range with the viscosity values obtained using the bimodal approach. The match is found to be relatively insensitive to the precise value of the separating particle size.     

Research on viscosity of metal at high pressure

A new experimental technique, the flyer-impact method, is proposed in this article to investigate the viscosity coefficient of shocked metals. In this technique, a shock wave with a sinusoidal perturbation on the front is induced by the sinusoidal profile of the impact surface of the sample by use of a two-stage light-gas gun, and the oscillatory damping process of the perturbation amplitude is monitored by electric pins. The damping processes of aluminum at 78 and 101 GPa and iron at 159 and 103 GPa are obtained by this technique, which supplement the existing data by measuring the viscosity coefficient via a dynamic high-pressure method. Applying the formula of Miller and Ahrens to fit the experimental data, the shear viscosity coefficients of aluminum at 78 and 101 GPa are \(1350\,\pm \,500\) and \(1200\,\pm \,500~\hbox {Pa}\,\hbox {s}\), respectively, and those of iron at 159 and 103 GPa are \(1150\,\pm \,1000\) and \(4800\,\pm \,1000~\hbox {Pa}\,\hbox {s}\), respectively. The values measured by the flyer-impact method, approximately \(10^{3}~\hbox {Pa}\, \hbox {s}\), are consistent with those measured by Sakharov’s method, while still greatly differing from those measured by static high-pressure methods. In dynamic high-pressure experiments, the shear viscosity is related to dislocation motion in the solid material, while that in static high-pressure experiments is related to the diffusion motion of atoms or molecules in liquids. Therefore, there are different physical meanings of shear viscosity in dynamic and static high-pressure experiments, and there is no comparability among these results.     

The shear viscosity dependence on concentration,molecular weight,and shear rate of polystyrene solutions

The solution viscosity of narrow molecular weight distribution polystyrene samples dissolved in toluene and trans-decalin was investigated. The effect of polymer concentration, molecular weight and shear rate on viscosity was determined. The molecular weights lay between 5 10⁴ and 24 10⁶ and the concentrations covered a range of values below and above the critical valuec ^*, at which the macromolecular coils begin to overlap. Flow curves were generated for the solutions studied by plotting log versus log . Different molecular weights were found to have the same viscosity in the non-Newtonian region of the flow curves and follow a straight line with a slope of – 0.83. A plot of log ₀ versus logM _w for 3 wt-% polystyrene in toluene showed a slope of approximately 3.4 in the high molecular weight regime. Increasing the shear rate resulted in a viscosity that was independent of molecular weight. The sloped (log)/d (logM _w ) was found to be zero for molecular weights at which the corresponding viscosities lay on the straight line in the power-law region.On the basis of a relation between _sp and the dimensionless productc · [], simple three-term equations were developed for polystyrene in toluene andt-decalin to correlate the zero-shear viscosity with the concentration and molecular weight. These are valid over a wide concentration range, but they are restricted to molar masses greater than approximately 20000. In the limit of high molecular weights the exponent ofM _w in the dominant term in the equations for both solvents is close to the value 3.4. That is, the correlation between _sp andc · [] results in a sloped(log _sp)/d(logc · []) of approximately 3.4/a at high values ofc · [] wherea is the Mark-Houwink constant. This slope of 3.4/a is also the power ofc in the plot of ₀ versusc at high concentrations. a Mark-Houwink constant - B ₁,B ₂,B _n constants - c concentration (g · cm^–3) - c ^* critical concentration (g · cm^–3) - K, K constants - K _H Huggins constant - M molecular weight - M _c critical molecular weight - M _n number-average molecular weight - M _w weight-average molecular weight - n sloped(log _sp)/d (logc · []) at highc · [] - PS polystyrene - T temperature (K) - shear rate (s^–1) - critical shear rate (s^–1) - viscosity (Pa · s) - ₀ zero-shear viscosity (Pa · s) - _s solvent viscosity (Pa · s) - _sp specific viscosity - [] intrinsic viscosity (cm³ · g^–1) - dynamic viscosity (Pa · s) - | ^*| complex dynamic viscosity (Pa · s) - angular frequency (rad/s) - density of polymer solution (g · cm^–3) - ₁₂ shear stress (Pa) Dedicated to Prof. Dr. J. Schurz on the occasion of his 60^th birthday.Excerpt from the dissertation of Reinhard Kniewske: Bedeutung der molekularen Parameter von Polymeren auf die viskoelastischen Eigenschaften in wäßrigen und nichtwäßrigen Medien, Technische Universität Braunschweig 1983.     

Effects of viscosity ratio on deformation of a viscoelastic drop in a Newtonian matrix under steady shear

Deformation of an Oldroyd B drop in a Newtonian matrix under steady shear is simulated using a front tracking finite difference method for varying viscosity ratio. For drop viscosity lower than that of the matrix, the long-time steady deformation behavior is similar to that of the viscosity matched system—the drop shows reduced deformation with increasing Deborah number due to the increased inhibiting viscoelastic normal stress inside the drop. However for higher viscosity ratio systems, the drop response is non-monotonic—the steady drop deformation first decreases with increasing Deborah number but above a critical Deborah number, it increases with further increase in Deborah number, reaching higher than the viscous case value for some viscosity ratios. We explain the increase in deformation with Deborah number by noting that at higher viscosity ratios, strain rate inside the drop is reduced, thereby reducing the inhibiting viscoelastic stress. Furthermore, similar to the viscosity matched system, the drop inclination angle increases with increasing Deborah number. A drop aligned more with the maximum stretching axis at 45 degree of the imposed shear, experiences increased viscous stretching. With increased ratio of polymeric viscosity to total drop viscosity, the drop deformation decreases and the inclination angle increases. Our simulation results compare favorably with a number of experimental and computational results from other researchers.     

Exploratory study of turbulent structure of a compressible shear layer using fluctuating pitot pressure measurements

An experimental study has been conducted to determine if two-point fluctuating pitot pressure measurements can be used to detect and quantify the large-scale structures in a two-dimensional, high Reynolds number, supersonic, turbulent shear layer. There is evidence from the two-point correlations of fluctuating pitot pressures and from the VITA analysis that large-scale structures exist and span the thickness of the shear layer. Because the shear layer exhibits a wake-like character, the large-scale structure in the lower part of the shear layer is essentially normal to the flow direction. Power spectra measured at about 25 initial shear layer thicknesses downstream of the origin are broadband, which suggests that the large-scale structures are not yet highly organized.A version of this paper was presented at the 12^th Symposium on Turbulence at the University of Missouri-Rolla     

Meltblown fibers: Influence of viscosity and elasticity on diameter distribution

Both melt viscosity (η_o) and elasticity (correlated here with the longest melt relaxation time λ₁) were found to control the diameter distribution of meltblown fibers. Fibers were formed by melt blowing binary polystyrene (PS) blends containing widely differing component molecular weights using a custom-built laboratory apparatus. Varying the concentration and molecular weight of a high molecular weight PS provided independent control over η_o and λ₁. These rheological parameters influence the average diameter (d_av) and the distribution of diameters (coefficient of variation, CV) of meltblown fibers in different ways. Increasing η_o leads to an increase in d_av but has little impact on CV. On the other hand, increasing λ₁ beyond a threshold value reduces CV while simultaneously increasing d_av. A one-dimensional slender-jet theoretical model with both upper convected Maxwell and Phan–Thien and Tanner constitutive equations was developed to investigate the influence of viscoelasticity and processing parameters on the properties of meltblown fibers. This model predicts a strong dependence of fiber diameter on the air shear stress and variations in fiber diameter with viscoelasticity that are in qualitative agreement with the experimental results. We believe these results suggest that carefully controlling the viscoelastic profile of polymers used in melt blowing is a viable approach for producing nanofibers with narrow fiber diameter distributions using current commercial equipment.