Evaluation of rheological properties of non-newtonian fluids in internal mixers: An alternative method based on the power law model

A new method was developed to evaluate rheological properties of polymer melts such as shear stress, shear rate, apparent viscosity and other rheological parameters in internal mixers. It is based on the classical power law model where the power law index n is directly evaluated from a set of data containing speed S, torque M, and the consistency index m is indirectly determined by an empirical relation. The method is based on a model with only one geometrical parameter (α), which involves a chamber radius R₂ and an equivalent radius R_e. It is assumed that the measuring head consists of two adjacent sets of coaxial cylinders. This method has advantages over previously reported models that use two parameters and do not propose a straightforward method to evaluate m. The pseudoplastic nature of the polymer melt decreases as the rate of loss of structural points, i.e., molecular entanglements and network junctions, increases, which produces greater mobility of the melt. A relationship between α and C(n) is found, which is simpler than other models previously reported. These results further demonstrate the feasibility of evaluating rheological properties of polymer melts in internal mixers.     

Evaluation by torque-rheometer of suspensions of semi-rigid and flexible natural fibers in a matrix of poly(vinyl chloride)

The flow properties of three different PVC-natural fiber suspensions were evaluated using a torque-rheometer. The fibers used were extracted from henequen leaves, coconut husk, and bovine leather. They have distinct mechanical properties that produce suspensions with different flow behaviors. Nevertheless, the experimental results show that, at the rates employed, the behavior of the suspensions can be described by a power-law ($ \sigma = m\dot \gamma ^n $). The flow (n) and consistency (m) indexes of each suspension were evaluated using an approximate technique previously developed. The evolution of these indexes as a function of the volume fraction of fibers (Φ) are studied and discussed. It was found that, at diluted concentrations, the value of the flow index unexpectedly increases with the concentration of fibers, especially in those suspensions containing the more flexible fibers. However, at elevated concentrations it substantially diminishes. To model this behavior an empirical function for n(Φ) is proposed. The index of consistency (m) presents a continuous increment with the concentration of fibers. To model the evolution of this parameter with the content of fibers, we have defined a relative consistency index m_r(m_r = m_s/m_o, where m_s and m_o are the suspension and matrix indexes) in a similar form to that established for the relative Newtonian viscosity. The function m_r(Φ) is modeled using several equations used to describe the behavior of this last viscosity (Maron and Pierce, Mooney, Thomas, Sudduth and Polynomial models). Among them, the Sudduth and Polynomial equations were those that better fit the behavior of these type of suspensions. Finally, to test the previous methodology, the theoretical torque values obtained were compared with experimental data for each suspension. Excellent agreement among them was found.     

Effect of nanosize CaSO4 and Ca3(PO4)2 particles on the rheological behavior of polypropylene and its simulation with a mathematical model

Nanosize CaSO₄ and Ca₃(PO₄)₂ fillers were synthesized with an in situ deposition technique, and their sizes were confirmed by X‐ray diffraction. CaSO₄ was prepared in 12‐ and 22‐nm sizes, and Ca₃(PO₄)₂ was prepared in 13‐ and 24‐nm sizes. Experimental variables, such as torque, shear viscosity, shear stress, and shear rate, of the nanofilled polypropylene (PP) composites were measured with torque rheometry and melt flow index (MFI) measurements. Torque versus time, shear viscosity versus weight percentage, and MFI versus weight percentage were plotted to investigate the rheological behavior of the nanofilled composites. The Cross–Williamson (CW) model was simulated with the MATLAB simulation package to study the thinning behavior of the PP composites. The experimental results show a decrease in the shear viscosity with increasing weight percentage of filler. Shear thinning in the molten PP composites was comparatively greater with decreasing nanosize of CaSO₄ and Ca₃(PO₄)₂. This kind of behavior was confirmed by the N parameter as determined from the CW model. The simulation of experimental data also showed similar trends as the theoretical data. At a certain stage, a violation of theoretical data was observed. This was because of practical limitations of the equation, as the equation does not include consideration of the physical situation of chain entanglements. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4190–4196, 2006     

Flow properties of molten ethylene–vinyl acetate copolymer and melt fracture

In an investigation of the behavior and formation mechanism of melt fracture the flow properties of molten ethylene–vinyl acetate (EVA) copolymer in the region of high shear rate were measured with a capillary-type rheometer. EVA copolymer differs slightly in flow curve from low-density polyethylene (LDPE); it seems, however, that the difference is due to the difference in molecular weight distribution (MWD) rather than to the materials themselves. The fluidity of molten EVA copolymer having a narrow MWD is equivalent to that of LDPE having a broad MWD and, generally, EVA copolymer has a higher fluidity than LDPE. It is expected that the fluidity increases with incorporation of vinyl acetate at the same MWD and the same M?_w. The critical shear rate increases with melt index and temperature. It cannot be found that the materials themselves and the MWD directly influence the critical point of melt fracture formation when the melt index is taken as a parameter. The critical viscosity (η_c) at which melt fracture forms decreases in an almost straight line with an increase of melt index. It was found from the studies of end correction and behavior of melt fracture formation that melt fracture occurs at the inlet of the die, and it is supposed that the melt fracture formation is caused by the elastic turbulence in the flow pattern due to a failure of recoverable shear strain at the die inlet.     

Pipe flow of a dense emulsion: Homogeneous shear‐thinning or shear‐induced migration?

The flow field of a 70% concentrated noncolloidal o/w emulsion in a pipe has been investigated by means of Particle Image Velocimetry in a matched refractive index medium. At steady state and in laminar regime, the shape of axial velocity profiles is not parabolic and exhibits a shear‐thinning behavior of the dense emulsion, with a flow index of 0.5 and a negligible yield stress (less than 1 Pa). However, instead of a square root law, the pressure drop increases linearly with U_m. To explain this apparent inconsistency, two mechanisms of different nature are considered. The first originates from a possible relation between the consistency factor and the drop mean diameter. The second mechanism is shear‐induced migration and leads to the development of a concentration gradient in the pipe cross section. Both mechanisms considered reconcile the experimental data, the apparent local shear‐thinning behavior and the linear evolution of the pressure drop with the flow rate. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Rheology of thermoplastic starch: Effects of temperature,moisture content,and additives on melt viscosity

The melt viscosity of thermoplastic starch has been investigated as a function of temperature, moisture content, and processing conditions. The effects of various low molecular weight additives have also been studied. Starch melts exhibit power law behavior over the range of shear rates studied. Melt viscosity decreased with increasing temperature and moisture content (MC). The power law index m increased with increasing temperature. The consistency K decreased with increasing temperature and increasing moisture content. Moisture content during the pelletizing step influenced melt viscosities measured after equilibration to different MCs. All additives studied except glycerol monostearate (GMS) significantly lowered the melt viscosity of starch, some more effectively than water relative to starch with 15% MC. Starch with GMS had viscosities essentially the same as, or slightly higher than, starch/water. This behavior may be due to the presence of unmelted helical inclusion complexes of starch and GMS. Starch formulations at 160°C exhibited melt visocosities similar to an LDPE of melt index 1.8.     

Rheological analysis of the degradation of HDPE during consecutive processing steps and for different processing conditions

Using a twin‐screw extruder, HDPE has been processed six times consecutively under a range of processing conditions (changing barrel temperature, screw speed, and feed rate). After each pass, the product has been analyzed in terms of the melt flow index (MFI) and G_C(ω_C), the crossover point of the viscoelastic moduli as a function of the angular velocity at which it occurs. MFI data show changes in the structure of the HDPE after each processing step, but this information is limited in quality and quantity. G_C data show the mechanism for degradation (side‐chain branching and chain scission) and allow us to track relative changes in mean molecular weight (MMW) and molecular weight distribution (MWD). MMW and MWD both increase as a result of continued reprocessing. The apparent changes in MWD are substantial indicating significant chain scission initially, accompanied and followed during subsequent processing by a combination of side‐chain branching and further chain scission. A relative measure of the polydispersity index (PI) of the melt is calculated and the PI increases as the HDPE is further reprocessed. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Rheological and thermal properties of thermoplastic natural rubbers based on poly(methyl methacrylate)/epoxidized‐natural‐rubber blends

Epoxidized natural rubbers (ENRs) with epoxide levels of 10, 20, 30, 40, and 50 mol % were prepared. The ENRs were later blended with poly(methyl methacrylate) (PMMA) with various blend formulations. The mixing torque of the blends was observed. The torque increased as the PMMA contents and epoxide molar percentage increased in the ENR molecules. Furthermore, the shear stress and shear viscosity of the polymer blends in the molten state increased as the ENR content and epoxide molar percentage increased in the ENR molecules. Chemical interactions between polar groups in the ENR and PMMA molecules might be the reason for the increases in the torque, shear stress, and viscosity. All the ENR/PMMA blends exhibited shear‐thinning behavior. This was observed as a decrease in the shear viscosity with an increase in the shear rate. The power‐law index of the blends decreased as the ENR contents and epoxide molar percentage increased in the ENR molecules. However, the consistency index (or zero shear viscosity) increased as the ENR contents and epoxide molar percentage increased. A two‐phase morphology was observed with scanning electron microscopy. The small domains of the minor components were dispersed in the major phase. For the determination of blend compatibility, two distinct glass‐transition‐temperature (T_g) peaks from the tan δ/temperature curves were found. Shifts in T_g to a higher temperature for the elastomeric phase and to a lower temperature for the PMMA phase were observed. Therefore, the ENR/PMMA blends could be described as partly miscible blends. According to the thermogravimetry results, the decomposition temperatures of the blends increased as the levels of ENR and the epoxide molar percentage increased. The chemical interactions between the different phases of the blends could be the reason for the increase. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3561–3572, 2004     

Identification of transient responses of a plasticating twin screw extruder due to excitation in feed rate

A corotating plasticating twin screw extruder (TSE) was excited by changing feed rate according to predesigned random binary sequence (RBS) and stair type excitation. A high density polyethylene was used as processing material in this study. Empirical models were developed relating two output variables, melt pressure at die (P_m), and melt temperature at die (T_m), with feed rate (F). Classical linear system identification technique was used to develop models. Models were developed using a data set obtained from RBS excitation. Stair type excitation data were used to validate the developed models. The structure of the obtained models was autoregressive moving average with exogenous input (ARMAX). Models with ARMAX structure and order of 2 were found to be sufficient to capture the dynamic behaviors of P_m and T_m when F was changed. A delay‐gain model was proposed for P_m and was found to capture the response quite satisfactorily. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers     

Modifications of the weissenberg rheogoniometer for measurement of transient rheological properties of molten polyethylene under shear. Comparison with tensile data

Improvements to the Weissenberg rheogoniometer are necessary in order to measure the transient rheological properties of polymer melts correctly. The improvements reported concern the mechanical design, a new heating system, a new normal force measuring system, and additional equipment for the relaxation test. Reliable short-time results require sufficiently stiff torque and normal force springs, and a small radius and relatively large angles of the cone-and-plate gap. The behavior of the LDPE melt under test is “linear viscoelastic,” if shear rate or total shear are small: The relaxation modulus, the stress growth at the onset of constant shear rate, the stress relaxation after cessation of steady shear flow, and, in addition, dynamic shear data (from an oscillation viscometer) all show consistent results when correlated by means of formulae from the theory of linear viscoelasticity. Shearing in the nonlinear range with constant shear rate leads to pronounced maxima of the shear stress p₁₂ and of the first normal stress difference p₁₁ ? p₂₂ which occur at constant total shear, almost independent of shear rate. Comparison of shear and tensile data (from extensional rheometer) confirms the Trouton relation in the linear-viscoelastic case. In the nonlinear case, there is a “work softening” in shear and a “work hardening” in extension.     

Characterization of drag reduction and degradation effects in the turbulent pipe flow of dilute polymer solutions

Turbulent drag reduction data were obtained at Re = 9000 in a 0.62-cm-I.D. pipe for five Polyox compounds covering a wide range of molecular weights. The concentration dependence of drag reduction was shown to obey an improved form of Virk's drag reduction equation, which was previously applied only to flows in capillary tubes. The efficiency of the drag-reducing polymer additives on a unit concentration basis at infinite dilution was determined by using a characteristic parameter, DR_m/[c], for each compound. A linear relationship was found to exist between this parameter and polymer molecular weight. The polymer degradation data were analyzed through use of a variable related to the dissipated energy in the wall region. The polymer molecular weight was found to decrease as a hyperbolic function of the dissipated energy function. By examining the change of molecular weight with respect to this function, a degradation index characteristic of the entire Polyox polymer family was established. This index may be of general application and provide a method by which the shear stability of various species of drag-reducing polymers may be meaningfully compared.     

The second ACTRIS inter-comparison (2016) for Aerosol Chemical Speciation Monitors (ACSM): Calibration protocols and instrument performance evaluations

This work describes results obtained from the 2016 Aerosol Chemical Speciation Monitor (ACSM) intercomparison exercise performed at the Aerosol Chemical Monitor Calibration Center (ACMCC, France). Fifteen quadrupole ACSMs (Q_ACSM) from the European Research Infrastructure for the observation of Aerosols, Clouds and Trace gases (ACTRIS) network were calibrated using a new procedure that acquires calibration data under the same operating conditions as those used during sampling and hence gets information representative of instrument performance. The new calibration procedure notably resulted in a decrease in the spread of the measured sulfate mass concentrations, improving the reproducibility of inorganic species measurements between ACSMs as well as the consistency with co-located independent instruments. Tested calibration procedures also allowed for the investigation of artifacts in individual instruments, such as the overestimation of m/z 44 from organic aerosol. This effect was quantified by the m/z (mass-to-charge) 44 to nitrate ratio measured during ammonium nitrate calibrations, with values ranging from 0.03 to 0.26, showing that it can be significant for some instruments. The fragmentation table correction previously proposed to account for this artifact was applied to the measurements acquired during this study. For some instruments (those with high artifacts), this fragmentation table adjustment led to an “overcorrection” of the f44 (m/z 44/Org) signal. This correction based on measurements made with pure NH₄NO₃, assumes that the magnitude of the artifact is independent of chemical composition. Using data acquired at different NH₄NO₃ mixing ratios (from solutions of NH₄NO₃ and (NH₄)₂SO₄) we observe that the magnitude of the artifact varies as a function of composition. Here we applied an updated correction, dependent on the ambient NO₃ mass fraction, which resulted in an improved agreement in organic signal among instruments. This work illustrates the benefits of integrating new calibration procedures and artifact corrections, but also highlights the benefits of these intercomparison exercises to continue to improve our knowledge of how these instruments operate, and assist us in interpreting atmospheric chemistry.     

Effect of bark flour on melt rheological behavior of high density polyethylene

The melt rheological behavior of neem bark flour (BF) filled high density polyethylene (HDPE) has been studied at varying volume fraction (?_f) from 0 to 0.26 at 180, 190, and 200°C in the shear rate range from 100 to 5000 s^?1 using extruded pellets of the composites. The melt viscosity of HDPE increases with ?_f because the BF particles obstruct the flow of HDPE. With the incorporation of the coupling agent HDPE‐g‐MAH, the viscosity decreased compared to the corresponding compositions in the HDPE/BF systems due to a plasticizing/lubricating effect by HDPE‐g‐MAH. The composites obeyed power law behavior in the melt flow. The power law index decreases with increase in the filler content and increases with temperature for the corresponding systems while the consistency index showed the opposite trend. The activation energy for viscous flow exhibited inappreciable change with either ?_f or inclusion of the coupling agent, however, the pre‐exponential factor increased with filler concentration. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

A study of gas hold-up,liquid velocity,and mixing time in a complex high viscosity,fermentation fluid in an airlift bioreactor

Whole mean gas hold-up ε_g, liquid recirculation velocity U_1d and mixing time t_m were measured in a 0.12 m³ airlift reactor, with an external recirculation loop (ALR-EL), which was used for the production of the exopolysaccharide, Scleroglucan, by cultivation of the filamentous fungus, Scleroticum glucanicum. Under identical fermentation conditions, the effects of air flowrate and the viscosity of the culture fluid on ε_g, U_1d, and t_m were investigated. In the range studied, empirical correlation for ε_g, U_1d and t_m with both superficial velocity U_gr and consistency coefficient K were obtained and expressed separately.     

Rheological properties of glass bead-filled low-density polyethylene composite melts in capillary extrusion

The melt flow of glass bead-filled low-density polyethylene composites in extrusion have been observed by using a capillary rheometer to investigate the effects of temperature, shear rate, and filler content on the rheological properties of the melts. The results show that the melt shear flow obeys a power law, and the dependence of the apparent shear viscosity, η_app, on temperature is in accord with an Arrhenius equation. At the same temperature and shear rate, η_app increases slightly with increasing the volume fraction of glass beads, but the flow behavior index decreases with increasing filler content. In addition, the first normal stress difference of the melts linearly increases with increasing wall shear stress. Good agreement is shown with the N₁ calculated with the equation presented in this article and the pressured data from the sample melts. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 1451–1456, 1999     

Effects on the melt rheology of systems of Nd‐Fe‐B particles suspended in a poly(phenylene sulfide) and liquid crystalline polymer blend

The melt rheology of blends of a liquid crystalline polymer (LCP) and poly(phenylene sulfide) (PPS) and their composites with ferromagnetic Nd‐Fe‐B particles (MQP) was studied. We investigated the effects of LCP concentration, Nd‐Fe‐B particle volume fraction and size, distribution, and shear rate on the rheological properties of these composites. Enthalpy of fusion changes that were observed resulted from the addition of the LCP and Nd‐Fe‐B particles to the polymer blends/composites. The shear rate and frequency dependencies of the materials revealed a viscosity reduction at low (1–3 wt%) and moderate (10–15 wt%) LCP concentrations, and strong effects on the shear‐thinning characteristics of the melt. The suspensions of polydispersed Nd‐Fe‐B particle configurations in PPS that were of lower size ratios gave better processability, which is contradictory to previously reported behavior of suspensions containing spherical particles. Specifically, the compositions with unimodal and a bimodal distribution of Nd‐Fe‐B particles gave the lowest viscosities. The experimental data were correlated with semi‐empirical viscosity model equations of Maron‐Pierce, Krieger‐Dougherty, Eilers, and Thomas and were found to be consistent with the data. The maximum packing fraction, ϕ_m, of the MQP particles was estimated to be within the range of 0.78 ϕ ≤_m ≤ 1.0 through graphical and parametric evaluation methods.     

Melt flow behavior of blends from poly(vinyl chloride) and epoxidized natural rubber

Blends from poly(vinyl chloride) (PVC) and epoxidized natural rubber (ENR) were prepared in a Brabender plasticorder by the melt blending technique. The melt flow behavior of these blends with respect to blend ratio and temperature has been examined using a melt flow indexer and capillary rheometer. ENR decreases the Brabender torque, increases the melt flow index (MFI), and decreases the melt viscosity of PVC in the blends. Arrhenius plots were used to study the effect of temperature on melt flow index (MFI) and viscosity. Moreover, the flow behavior index (n′) obtained from capillary rheometer data was found to be dependent on temperature and blend ratio.     

Shear stress at polymer/metal interface during melting in extrusion

Prediction of the screw horsepower requirement involves, among many others, the calculation of the shear stress (τ_s) between the solid polymer and the barrel surface during melting. Prediction of the solid bed down-channel velocity also requires the calculation of τ_s. However, the pseudoplastic nature and strong temperature dependence of melt viscosity make the mathematics of calculating τ_s extremely difficult. As a first step of developing a reasonable mathematical model for calculating τ_s, experimental measurements of τ_s were made over a wide range of metal temperature and sliding speed for five commercial polymers using molded, block samples. Although dependences of τ_s on metal temperature and sliding speed were found to have similar functionality to those of the dependences of melt viscosity on melt temperature and shear rate, this study showed that τ_s could not be expressed as a sole function of the melt rheological properties. Our subsequent study, to be reported in a follow up paper, will show that τ_s must be expressed as a function of the thermodynamic properties and melt density of the polymer as well as the melt rheological properties and the melting conditions.     

Novel Gas Dispersion in Highly Viscous Fluids Using a Plasticating Extruder. II. Gas Dispersion Model

The process of gas dispersion in the mixing zone of an extruder employing on-line injection into a viscous polymeric melt, has been analyzed. In the model system considered, the gaseous component was injected into a non-Newtonian melt (LLDPE) via a permeable wall, during which a shear field was imposed at right angles to the direction of flow of the melt. The dispersion of the injectant has been quantified in terms of the spatial coordinate positions of the microvoids as they travel through the melt. Computer simulation was performed to ascertain the trajectories, radial velocities, and times of traverse of the particles migrating from the injection orifice under the imposed shear field. Numerical solutions have been obtained for system angular velocity from 6 to 10 rad/s, melt viscosity from 6 to 6.5 kPa ^. s, particle diameter/ annular gap ratio of 0.20, injectant/melt density ratio of 0.032, and power law index of 0.51. The computed trajectories were found to be consistent with previously recorded visual observations. The analytical results on the time of traverse (～0.5–1.0 s) indicated that dispersion by on-line shear injection was viable. The latter results, however, need experimental verification.     

On the rheology of molten binary blends of polyolefins. X. Homogeneity and high shear (Poiseuille's) melt flow of polypropylene–polyethylene blends

Statistical analysis of inherent viscosities (LVN), shear modulus (G^*), and melting temperature (T_m) interval data for isotactic polypropylene–linear polyethylene (HDPE) blends was performed in order to verify their microheterogeneity. High shear measurements in viscometric (Poiseuille's) flow were carried out on four replicated compositions of the blends. Least-squares treatment of the results yielded power law parameters for the blends differing in composition. The significance of differences between the blends of various HDPE content was tested using the multiple-range (Duncan's) test, and tentative conclusions are drawn on the composition dependence of the melt flow viscosities of the blends.