Biaxial Elongational Viscosity Research Articles

Towards an inline rheometer – A novel approach for assessing biaxial elongational viscosity

Towards an inline rheometer – A novel approach for assessing biaxial elongational viscosity

Textural behavior of gels formed by rice starch and whey protein isolate: Concentration and crosshead velocities

ABSTRACT Fabricated food gels involving the use of hydrocolloids are gaining polpularity as confectionery/convenience foods. Starch is commonly combined with a hydrocolloid (protein our polyssacharides), particularly in the food industry, since native starches generally do not have ideal properties for the preparation of food products. Therefore the texture studies of starch-protein mixtures could provide a new approach in producing starch-based food products, being thus acritical attribute that needs to be carefully adjusted to the consumer liking. This work investigated the texture and rheological properties of mixed gels of different concentrations of rice starch (15%, 17.5%, and 20%) and whey protein isolate (0%, 3%, and 6%) with different crosshead velocities (0.05, 5.0, and 10.0 mm/s) using a Box-Behnken experimental design. The samples were submitted to uniaxial compression tests with 80% deformation in order to determinate the following rheological parameters: Young’s modulus, fracture stress, fracture deformation, recoverable energy, and apparent biaxial elongational viscosity. Gels with a higher rice starch concentration that were submitted to higher test velocities were more rigid and resistant, while the whey protein isolate concentration had little influence on these properties. The gels showed a higher recoverable energy when the crosshead velocity was higher, and the apparent biaxial elongational viscosity was also influenced by this factor. Therefore, mixed gels exhibit different properties depending on the rice starch concentration and crosshead velocity.

Strain and strain rate dependence of gellan, agar and agar–gellan gels as model systems

Gellan, agar and their combination gels (1:1, 2g/100g) as model systems were subjected to strains up to 0.8 while varying the crosshead speed between 0.01 and 10mms−1 to determine different textural characteristics (Young’s modulus, rigidity constant, degree of concavity and apparent biaxial elongational viscosity, ηbe) and fracture characteristics. The compression curves usually consisted of 6 zones, and the gels were sensitive to strain rate and the extent of applied strain. Agar gel showed higher fracture force and energy compared to gellan and agar–gellan samples. However, the fracture strain for gellan was highest (44.6–70.7%) followed by agar (22.8–40.3%) and agar–gellan (24.3–37.3%) gels indicating more brittleness in agar/agar–gellan gels but toughness in gellan samples. The degree of concavity of gellan gel was less than 1 indicating strain-softening characteristics; the agar gel exhibited strain-hardening phenomenon as it was more than 1. However, marginal strain-softening behaviour was observed for gellan–agar combination gel (0.856⩽n⩽0.999). A power law type model linked ηbe and the biaxial extensional rate at fracture. Gellan gels are suitable to prepare chewable fabricated juicy gels, while brittle products resulted from agar/agar–gellan. It is proposed that ηbe at fracture is a good index for characterising gels in relation to product development and compression-spreading.

Evaluation of the Consistency of Low-Fat Mayonnaise by Squeezing Flow Viscometry

Lubricated squeezing flow viscometry was applied for the evaluation of the consistency of mayonnaise samples of 50% w/w oil content. Mayonnaise samples were prepared with the addition of four stabilizers: sodium alginate, xanthan gum, guar gum and carboxymethyl cellulose (CMC). Each stabilizer was added individually at concentrations from 0.5 to 2% w/w. In addition, a series of nine mayonnaise samples was prepared with mixtures of xanthan gum and guar gum in various ratios, at 1.5% w/w total concentration, aiming to determine synergistic effects between the two stabilizers. All samples were characterized as pseudoplastic since flow behavior index was shown to be lower than unity. Biaxial elongational viscosity, expressed as stress growth coefficient, was determined at specimen's compressive deformation 50%, because larger deformations lead to structural breakdown of highly viscous samples. Using the present method, the determination of stress growth coefficient was possible in the range from 40 to 300kPa·s. In all samples, stress growth coefficient was shown to increase with increasing concentrations of stabilizers. At concentrations ranging from 1.0 to 1.5%, CMC provided the most viscous emulsions, followed by those with xanthan gum and sodium alginate, while those with guar gum appeared as the least viscous. Conversely, at concentration of 0.75%, CMC was shown to be unable to form a sufficient network, thus providing a less viscous emulsion than the one by xanthan gum. All mixtures of xanthan gum and guar gum revealed synergistic action, where the highest stress growth coefficient values were observed in samples with xanthan gum/guar gum ratios of 30:70 and 40:60. The above mentioned values were higher by two or threefold (p<0.05) compared to those of samples of equal concentration (1.5%) prepared with the addition of xanthan gum or guar gum alone, respectively.

Measurement of Melt Rheology under Biaxial and Planar Elongations and Rheological Properties of Ethylene-Methacrylic Ionomer Melts

To obtain reproducible, reliable data, the effects of experimental conditions on biaxial and planar elongational viscosities were investigated. It was clarified that a constant area method was preferable rather than a constant volume method. It was concluded that the effects of the viscosity of silicone oil as lubricant were negligible when the constant area method was employed. On the other hand, the effects of ion aggregates on zero shear viscosities η0 for ethylene-co-methacrylic ionomer melts were investigated. Rapid increasing of η0 for Zn ionomers was observed at high neutralization degrees, however, the rapid increase was not observed at all range of the degree neutralization in the case of Na ionomers. The formation of ion aggregates affects on damping functions in both cases of Na and Zn ionomers. This degree of neutralization well corresponds to the onset of strong strain dependence of h(γ) and increasing η0 for EMAA-Zn.

Properties of mLLDPE/LDPE blends in film blowing

We evaluated the inline birefringence of two blend systems in film blowing. The first system consisted of a metallocene catalyzed linear low density polyethylene (mLLDPE-1) and a low density polyethylene (LDPE-1); the second one was made of a metallocene catalyzed polyethylene containing sparse long chain branches (mLLDPE-2) and another low density polyethylene (LDPE-2). Experimental data show that before the crystallization starts, the birefringence of the mLLDPE-2/LDPE-2 blends is a linear function of blend composition, suggesting miscibility of the mLLDPE-2/LDPE-2 blends. However, the birefringence of the mLLDPE-1/LDPE-1 blends shows positive deviations with respect to a linear function of blend composition. This is caused by the existence of form birefringence, suggesting immiscibility of the mLLDPE-1/LDPE-1 blends. The nonuniform biaxial elongational viscosity (NUBEV) at the reference temperature of 175°C for LDPE-1 was evaluated for different operating conditions. The results show that NUBEV is approximately a unique function of the deformation rate, confirming the validity of the assumptions and technique used for the NUBEV calculation. The NUBEV and the nonuniform biaxial Trouton ratio (NUTR) of the mLLDPE-2/LDPE-2 blends was also evaluated using the same technique. The NUBEV of all mLLDPE-2/LDPE-2 blends shows a strain-thinning behavior within the deformation rates investigated. Furthermore, the NUTR results show that LDPE-2 deviates largely from the Newtonian fluid behavior, whereas mLLDPE-2 is quite close to the Newtonian behavior. Nevertheless, the NUTR of the mLLDPE-2/LDPE-2 blends is almost a linear function of blend composition. POLYM. ENG. Sci., 45:343–353, 2005. © 2005 Society of Plastics Engineers

Uniaxial, Biaxial and Planar Elongational Viscosities for lonomers Based on Poly(Ethylene-co-Methacrylic Acid)

The role of ion aggregates in EMAA ionomers on elongational viscosities under uniaxial, biaxial and planar was investigated. Firstly, measurement technique of biaxial and planar elongational viscosities for EMAA ionomers can be optimized due to its difficulties. After optimization, uniaxial, biaxial and planar elongational viscosities of ionomers were obtained. It was considered that effects of ion aggregates can not be appeared under uniaxial deformation in all of strain rates region. On the other hand, it was found that behavior of ion aggregates was changed under biaxial and planar deformations. It was considered that behavior of ion aggregates may be changed by two factors, deformation type and degree of strain rates.

Rheological effects of polyethylenes in film blowing

AbstractThe aim of this work is to correlate the rheological properties and processability of various polyethylenes during the film‐blowing process. The effect of rheology on the kinematics and dynamics of film blowing for five different polyethylene resins has been extensively studied using a fully instrumented laboratory unit. The complex viscosity, shear viscosity, uniaxial elongational viscosity, and non‐uniform biaxial elongational viscosity, as well as the strain rates and stresses during film blowing, have been determined and correlated to the bubble stability. G′ versus G″ plots were found to be virtually independent of temperature for all polymers investigated. The more elastic polymers (larger G′ values) were found to be more stable in film blowing. Also, the more stable polymer melts were found to be those possessing larger elongational properties.

Effects of ABS rubber particles on rheology, melt failure, and thermoforming

AbstractThe rubber particles included in rubber modified polymeric materials such as acrylonitrile‐butadiene‐styrene (ABS) polymer and impact modified polymers play an important role in determining their rheological properties, processing behavior, and mechanical properties. In this study both small strain oscillatory shear viscosity in the frequency range from 10−2 to 102 s−1 and uniaxial elongational viscosity behavior at two elongation rates ( = 0.1 and 1.0 s−1) over the range of temperatures from 140°C to 200°C were measured for commercial ABS polymers with different contents and deformability of rubber particles. The influences of rubber content and deformability on rheological properties such as melt elasticity, elongational viscosity, strain hardening and/or softening, the onset of nonuniform deformation, and thermoforming performance were investigated. The Wagner two‐parameter nonlinear viscoelastic constitutive model was used to describe strain hardening behavior, while the Considère criterion was used to determine the onset point of nonuniform deformation. The part thickness distribution obtained through use of a vacuum snap‐back forming process was simulated to investigate the effects of rheological changes associated with different rubber particles on the thermoforming performance. It was found that ABS polymers with larger contents of hard rubber particles exhibited more melt elasticity, stronger strain hardening, a maximum of biaxial elongational viscosity, onset of nonuniform deformation at later time, and better thermoforming performance. Strain hardening and the Considère criterion provide simple, reliable indicators of the thermoforming performance of ABS polymers.

微分型粘弾性構成方程式の非線形レオロジー特性の予測能力

We propose a kinetics model including extension and anisotropic movement between entangled or branched chains and develop constitutive equations containing the Larson model and the Giesekus model through non-linear parameters. In order to make clear the characteristics of the developed constitutive equations, we examined the predictions of using non-linear parameters and a non-linear stress relaxation modulus. We found that the proposed model shows better predictions of the nonlinear stress relaxation after a double-step shear strain than those of the Larson and the Giesekus models. Furthermore, we found that the proposed model is able to predict the biaxial elongational viscosity and the first planar elongational viscosity comparatively well by fitting the uniaxial elongational viscosity curve.However, the predictions of stress relaxation in the time-strain inseparable region was at most qualitative, and the predictions of the second normal stress difference and the second planar elongational viscosity were lower than experimental results because of the assumptions or crude approximations used in our development.

Rheological properties of low-density polyethylenes produced by tubular and vessel processes

Various rheological properties have been studied for two kinds of low-density polyethylenes (LDPEs): one is produced by tubular process (tubular LDPE) and the other by vessel process (vessel LDPE). The latter shows smaller g′-parameter, the ratio of intrinsic viscosity to that of linear polyethylene. It was found that both LDPEs exhibit marked strain hardening behavior, i.e. upturn departure from the low strain rate asymptote, in both uniaxial and biaxial elongational viscosities, with stronger strain hardening in uniaxial elongation. Further, the vessel LDPE exhibits larger upturn behavior than the tubular LDPE. In the stress relaxation measurement, the vessel LDPE shows larger damping function, while the tubular LDPE shows values similar to those predicted by the Doi–Edwards theory. Furthermore, there is a significant difference in the effect of the shear history on the melt strength. The melt strength of the vessel LDPE decreases more rapidly with the shear history than that of the tubular LDPE. All these differences between the two types of LDPEs are due to the difference in the branch structure. The complex, multi-branched structure of the vessel LDPE gives much more prominent elastic features.

Squeezing flow of a highly viscous incompressible liquid pressed between slightly inclined lubricated wide plates

The theoretical force-height relationships of Newtonian and pseudo plastic liquids compressed between slightly tilted frictionless plates are compared with those produced when the plates are perfectly parallel. It is shown that a very small inclination angle can distort the flow curve to such an extent that a Newtonian liquid will appear as a pseudo plastic fluid, and a pseudo plastic liquid as having a flow index considerably smaller than its true one. The shape of the biaxial elongational viscosity vs biaxial strain rate relationship is also highly sensitive to the plates' inclination angle. Thus, if an experimental force-height relationship is used to determine a material's biaxial elongational viscosity, an unsuspected slight tilt will result in a considerable underestimate of the viscosity. A slight tilt will also produce an apparent strain rate dependency in a Newtonian liquid, which obviously does not exist. The mathematical model developed to reach these conclusions was tested with commercial mayonnaise, a self-lubricating fluid. A reasonable agreement was found between the predicted force-height relationships and those experimentally determined at tilts of 1°, 3°, and 5°.

Effects of rheological properties and processing parameters on ABS thermoforming

AbstractUnderstanding effects of material and processing parameters on the thermoforming process is critical to the optimization of processing conditions and the development of better materials for high quality products. In this study we investigated the influence of both rheological properties and processing parameters on the part thickness distribution of a vacuum snap‐back forming process. Rheological properties included uniaxial and biaxial elongational viscosity and strain hardening and/or softening while processing parameters included friction coefficient, heat transfer coefficient, and sheet and mold temperatures. The Wagner two parameter nonlinear viscoelastic constitutive model was used to describe rheological behavior and was fit to shear and elongational experimental data. The linear viscoelastic properties along with the Wagner model were utilized for numerical simulation of the thermoforming operation. Simulations of pre‐stretched vacuum thermoforming with a relatively complex mold for a commercial refrigerator liner were conducted. The effects of nonlinear rheological behavior were determined by arbitrarily changing model parameters. This allows determination of which rheological features (i.e., elongational mode, viscosity, and strain hardening and/or softening) are most critical to the vacuum snap‐back thermoforming operation. We found that rheological and friction properties showed a predominant role over other processing parameters for uniform thickness distribution.

Description of uniaxial, biaxial, and planar elongational viscosities of polystyrene melt by the K-BKZ model

The three types of Kaye–Bernstein–Kearsley–Zapas (K-BKZ) equations: Wagner–Demarmels (WD) model, Papanastasiou–Scriven–Macosko (PSM) model, PSM–Luo–Tanner (PSMLT) model have been examined to describe experimental results of uniaxial, biaxial, and planar elongational viscosities of polystyrene (PS) melt. In these equations, the viscosity was calculated from the relaxation spectrum and damping function. The relaxation spectrum was determined by dynamic shear experiment. The damping functions were obtained by stress relaxation experiments under biaxial, planar and shear deformations. The shear and biaxial damping functions were described better by the PSM and PSMLT models than by the WD model. However, the experimental planar damping function was not described well. This poor fitting to the planar damping function came from the result that the planar damping function gave more strain-softening than shear. In the theoretical predictions, the damping function of shear and planar elongations should be identical with each other. Our result is inconsistent with this prediction. The elongational viscosities were calculated from the relaxation spectrum and the damping functions, and then compared to experimental data. Elongational viscosities for planar and biaxial deformations were measured by the lubricated squeezing method. In the case of uniaxial deformation, it was measured by a Meissner-type rheometer. Experimental results of uniaxial and biaxial elongational viscosities agreed with the prediction of the PSMLT model. Although the PSMLT model under-predicted the planar elongational viscosity, it was concluded that this model was the best of three models.

UNIAXIAL COMPRESSIBILITY OF BLACKGRAM DOUGHS BLENDED WITH CEREAL FLOURS

ABSTRACTThe uniaxial compression characteristics of papad dough (moisture content 62%, dry basis), made from blackgram flour as well as after incorporation of different types of cereal (rice, sorghum and wheat) flours at different levels (20 and 40%), were determined. The stress‐strain data can be interrelated by a power law type equation. The sensory attributes (stickiness, firmness, elasticity and ease of flattening/rolling) were correlated with the energy for compression, deformability modulus and apparent biaxial elongational viscosity. Inelastic doughs resulted from the blackgram dough; doughs with 20% rice or wheat blends were also inelastic but sorghum samples were elastic. The deformability modulus for sorghum doughs were extremely high. The blackgram dough as well as the wheat blended doughs were the easiest doughs to roll/flatten. Blended dough consisting of wheat flour (at 20 and 40% level) or rice flour up to 20% level was suitable for making cereal‐blended papad doughs.

低密度ポリエチレン溶融体の一軸，二軸，平面伸長粘度へのＫ‐ＢＫＺモデルの適応性

Measurements of uniaxial, biaxial, and planar elongational viscosity and step stress relaxation of a low density polyethylene (LDPE) melt were carried out. The description of experimental uniaxial, biaxial, and planar elongational viscosities results by the Kaye-Bernstein-Kearsley-Zapas (K-BKZ) constitutive equation was examined. Three types of damping function forms, Wagner-Demarmels (WD) model, Papanastasiou-Scriven-Macosko (PSM) model, and Luo-Tanner (LT) model, have been proposed in the K-BKZ constitutive equation. These three damping function forms were examined to see which was able to describe the experimental shear, biaxial, and planar damping functions. The experimental shear and biaxial damping functions were described by the LT and PSM models better than the WD model, however, the experimental planar damping function was not described well by any of the three models. After estimating the best parameters in each model by fitting the three experimental damping functions, the uniaxial, biaxial, and planar elongational viscosity was calculated by the estimated parameters. The uniaxial elongational viscosity was predicted best by the LT model, then by the WD, and PSM models. For biaxial and planar elongational viscosity, none of the three models predicted well, thus the lack of suitability of the biaxial and planar elongational viscosity to the K-BKZ model was suggested.

信頼性工学 潤滑圧縮法を用いた高分子溶融体の二軸伸長粘度測定

Biaxial elongational rheometer using lubricated squeezing method has been installed. To start up the rheometer and to obtain reproducible and reliable data, the effects of experimental conditions on biaxial elongational viscosity data were investigated. Constant area method was preferable rather than constant volume method. It was concluded that the effects of the viscosity of silicone oil and the shape were neglisible when method of constant area was employed.

IMPERFECT SQUEEZING FLOW VISCOSIMETRY OF SELECTED TOMATO PRODUCTS1

ABSTRACTThe rheological properties of different brands of commercial tomato paste, sauce, puree and ketchup were estimated by imperfect squeezing flow viscosimetry using a wide plate and a shallow container. The tests were performed with polished and grooved surfaces. In both, slip was prominent to such an extent that the equations for lubricated squeezing flow had to be used for the calculation of rheological parameters. Despite its crudeness, the procedure was sensitive enough to consistently monitor rheological differences between commercial products of different brands in terms of the apparent stress at a given specimen height, the consistency, K, and flow index, n, of the pseudoplastic liquid constitutive equation, and the apparent biaxial elongational viscosity, μb and its strain rate dependency. In tomato paste, the flow behavior index was approximately the same in all the brands (n ∼ 0.5), and the values of K and μb had a linear relationship. Residual forces after relaxation provided an additional textural measure related to the yield stress. Differences between products of different brands could be consistently monitored regardless of whether the test was performed at a fixed specimen height or a preset initial force.

Study of kinematics and dynamics of film blowing of different polyethylenes

AbstractAn extensive experimental study of the effects of material characteristics and processing parameters on the kinematics and dynamics of film blowing is presented. Three polyethylene resins, a high‐density polyethylene (HDPE), a low‐density polyethylene (LDPE), and a linear low‐density polyethylene (LLDPE) were investigated. The convergent flow analysis of Cogswell was used to characterize the elongational flow behavior of the polymers. Strain rates and pressure inside the bubble (Pi) have been determined over a wide range of film blowing conditions. Moreover, on‐line bubble temperature and birefringence measurements have been carried out along the length of the bubble. The experimental results reveal that the three polymers display different behaviors. The LLDPE requires the highest Pi value and the LDPE, the lowest. Consistent with this, the LLDPE shows the lowest in‐plane birefringence and the LDPE, the highest. Interactions between various process parameters affecting the Pi value are characterized. Bubble instability is correlated to the apparent uniaxial elongational viscosity and Pi. The most stable polymer (LDPE) has the highest elongational viscosity and requires the lowest Pi. Stresses have been calculated with the help of the birefringence and Pi data. The stress and strain rate data were used to calculate an apparent nonuniform biaxial elongational viscosity of the melts, but could not be correlated through any simple constitutive equation.

Rheological Characterization of Polymer Solutions and Melts with an Integral Constitutive Equation

Abstract A full nonlinear regression program has been developed in order to determine the appropriate relaxation spectrum and set of material constants for a constitutive equation which can give the best fit to experimental data and predictions for a series of rheological material functions. The constitutive model used is an integral equation of the K-BKZ type suitable for polymer solutions and melts. Available experimental data for determination of the material parameters of the model were dynamic data (storage and loss modulus), steady shear flow data (shear viscosity and first normal stress difference), and steady elongational flow data (uniaxial, planar and biaxial elongational viscosities). The material parameters were determined by a nonlinear least-squares procedure based on the Levenberg-Marquardt method. The program was tested against experimental data of material functions for several polymer solutions and melts. A good fit was obtained between predictions and experimental data. Furthermore, pre...