Planar Elongational Viscosity Research Articles

Concept of an Evaluation Technique for Planar Elongational Stress and Relaxation Time Using Hoop Stress in Swirling Flow

The paper reports a novel idea of an experimental approach to estimate the apparent planar elongational viscosity and the relaxation time of low viscosity fluids. A two-dimensional swirling contraction channel is designed to maintain a constant elongation rate to the flow direction. The hydrodynamic focusing creates a stable planar elongation flow field. The flow is injected into the center of the channel and a sheath flow is injected through both sides. The sample fluid is stretched in the flow field, and then forms the ribbon-shaped filament. In the swirling contraction part, a static force balance between the hoop force caused by the planar elongational stress and the centrifugal force determines the radial position of the filament. The distribution of the planar elongational stress can be estimated by observing this position, and then the apparent planar elongational viscosity was calculated using developed simplified expressions. On the other hand, when a channel with a constant width swirling part is used, the elongational stress generated in the straight contraction part gradually decreases passing through the constant width part. The sample filament position is then shifted based on the stress relaxation. The relaxation time can be evaluated by observing this variation.

Measurement of planar elongation stress and viscosity in step planar elongation flow for mobile viscoelastic fluids

We propose a new technique which can treat low viscous viscoelastic fluids and which can measure the start-up and relaxation behavior of elongational stress in step elongation rate flow. This new device consists of two parts: the squeeze cell and the optical analyzer. The squeeze cell generates the planar squeeze flow and causes the step planar elongational flow at the stagnation point. The optical system measures the transient behavior of both birefringence and orientation angle in the start-up and relaxation region at the stagnation point. In this paper, we demonstrate the two-dimensionality of the flow in the planar squeeze cell. Next, we evaluated the planar elongational stress and viscosity from optical results for Maxwell fluid. These results show good agreement with Maxwell model. Finally, we clarify the measurement accuracy from the measurement results in channels of various sizes.

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.

Elongational viscosity of LDPEs and polystyrenes using entrance loss data

AbstractFor two low‐density polyethylenes and two polystyrenes, axisymmetric and planar elongational viscosities are estimated using entrance loss data from capillary and slit rheometers, respectively. The elongational viscosity is estimated by optimizing the values of various parameters in the Sarkar–Gupta elongational viscosity model such that the entrance loss predicted by a finite element simulation agrees with the corresponding experimental data. The predicted entrance loss is in good agreement with the experimental data at high flow rates. The difference in the experimental and predicted entrance loss at lower flow rates might have been caused by large error in the experimental data in this range. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers

Nonlinear shear and elongational rheology of model polymer melts at low strain rates

We present new results for the low strain rate behavior of the steady-state planar shear and elongational viscometric functions of model polymer melts, computed by non-equilibrium molecular dynamics simulations. The chain lengths in our model polymer melts vary from N = 2 up to N = 100 beads, the maximum value corresponding to approximately 57 Kuhn lengths (approximately equivalent to polyethylene of molar mass 8300 g/mol). The new results allow us to more precisely evaluate the constants in the third-order fluid constitutive relation that we fitted to the results of our previous simulations. We find agreement between the values of the retarded motion expansion coefficients of terms up to second-order in the strain rate obtained from the two types of flow. This indicates that the second-order fluid model self-consistently describes the stress tensor in shear and elongational flow with a single set of material constants if the deformation rate is sufficiently small. However, we find a discrepancy between two different estimates of a third-order term when it is evaluated from the first and second planar elongational viscosities. The second-order retarded motion expansion is extended to apply to compressible fluids and the deformation rate dependence of the pressure in shear and elongational flows is obtained. The predictions are confirmed by the simulation results. The chain length dependencies of the computed zero shear rate viscosity and first normal stress coefficient agree with the predictions of the Rouse model. The second normal stress coefficient varies as the cube of the chain length and the coefficient of the quadratic term in the strain rate dependence of the shear viscosity is proportional to the sixth power of the chain length for unentangled chains.

Relationship between Neck-in Phenomena and Rheological Properties in Film Casting

We numerically demonstrate that the ratio of uniaxial to planar elongational viscosity controls the neck-in phenomena of the casting polymer films, i.e., the decrease in film width value for both viscous and viscoelastic fluids. Quasi-three-dimensional numerical simulations of an isothermal film casting process were performed using a finite element method for two viscoelastic fluids using Larson and PTT models, purely-viscous non-Newtonian fluids using Cross model and Newtonian fluids. The increase in take-up velocity relative to that in extrusion showed particular film deformations of neck-in depending upon the rheological properties in the models. The results indicate that the film width is determined by the ratio of uniaxial to planar elongational viscosity rather than the extension-thickening nature in uniaxial elongation. The computations using different fluid models show that the viscosity ratio is universal for predicting the neck-in value of the stretching polymer films not only in viscoelastic but also in pure viscous fluids.

Planar Elongational Rheometry Using Slit Entry Flow in Hele-Shaw Cell

In our previous study, we observed Hele-Shaw flows of two solutions of a polymer material around two cylinders and through two slits with different lengths. Based on the results, we showed that the potential flow analogy by the Hele-Shaw flow holds when the flow rate is very low in spite of the shear-thinning viscosity and elasticity of the fluids in steady shear flow. It was suggested that the potential flow pattern of the polymer solutions in the Hele-Shaw cell is disturbed by the effect of elongational stress. In this study, a simple method for planar elongational viscosity measurement is devised using the converging flow upstream the slit entry; the elongation rate is estimated from dye streak pattern in the inflow region formed upstream the slit entrance and the elongational stress is obtained from integrated equations of motion. The planar elongational rheometry presented in this work is advantageous due to its applicability to mobile fluids, in addition to its simple experimental set up.

125 二次元対向流れにおける流動複屈折測定を用いた定常平面伸張粘度測定(S34-1 複雑流体の流れとその応用(1),S34 複雑流体の流れとその応用)

125 二次元対向流れにおける流動複屈折測定を用いた定常平面伸張粘度測定(S34-1 複雑流体の流れとその応用(1),S34 複雑流体の流れとその応用)

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.

フォトクロミック法のヘルショウ流れへの適用による平面伸張粘度の評価(OS6-3 粘弾性流体の流れ(2),複雑流体・非ニュートン流体の流れ)

フォトクロミック法のヘルショウ流れへの適用による平面伸張粘度の評価(OS6-3 粘弾性流体の流れ(2),複雑流体・非ニュートン流体の流れ)

流動性高分子溶液に対する一軸及び平面伸張粘度の測定(OS6-3 粘弾性流体の流れ(2),複雑流体・非ニュートン流体の流れ)

流動性高分子溶液に対する一軸及び平面伸張粘度の測定(OS6-3 粘弾性流体の流れ(2),複雑流体・非ニュートン流体の流れ)

Effect of Elongational Viscosity on the Flow in a Flat Die

Abstract The flow of a low-density polyethylene in a flat die is simulated using the axisymmetric and planar elongational viscosities estimated in an earlier publication by Beaupre and Gupta. Elongational viscosity is found to have only a limited effect on the velocity distribution at the die exit. However, the predicted pressure drop in the die and the temperature distribution at the die exit changed significantly when the effect of elongational viscosity was included in the simulation.

Nonlinear shear and elongational rheology of model polymer melts by non-equilibrium molecular dynamics

We present the results of non-equilibrium molecular dynamics simulations of planar shear flow and planar elongational flow of melts of model linear chain molecules, in which the number of beads per molecule is varied from N=4 to 50. The shear viscosity η, normal stress coefficients Ψ 1 and Ψ 2, and the two planar elongational viscosities η 1 and η 2 have been computed as a function of strain rate. The results are analysed using the third order retarded motion expansion (RME). The limiting zero strain rate values of the viscosity ratios agree with their expected values: η 1/ η=4 and η 2/ η 1=0.5. At low N, values of the coefficient of the lowest order nonlinear term in the RME obtained independently from the shear flow simulations and the elongational flow simulations also agree. However, the consistency check fails for a higher order retarded motion coefficient. This is attributed to insufficient data at low strain rates for the higher values of N. The N-dependence of the viscosities and normal stress coefficients as well as higher order RME constants is studied. We find that the zero strain rate values of the shear viscosity and both elongational viscosities are approximately proportional to N and the limiting values of the first and second normal stress coefficients Ψ 1 and Ψ 2 are approximately proportional to N 3. The higher order RME constants have exponents nearer to 6.

1513 4-ロールミル流路による定常平面伸張粘度測定におよぼす流路底面の影響

Influence of wall effect for measurement of planar elongational viscosity by 4-roll mill flow cell was investigated. Elongation rate distribution along laser beam for measuring flow-birefringence was become clear by flow visualization. It was shown that the degree of two-dimensionality was decreased by the bottom wall effect and the non-uniformity of elongational distribution makes an error on the result of planar elongational viscosity. The conduit for light was attached on the bottom wall to reduce the wall effect and it was shown that using the conduit can reduce the error of measurement of planar elongational viscosity.

A Comparison of the Axisymmetric and Planar Elongational Viscosities of PE-LD

Abstract The elongational viscosities of a low density polyethylene in axisymmetric and planar flows are compared. The experimental data on entrance pressure loss is matched with the corresponding finite element predictions to estimate the parameters in the elongational viscosity model proposed by Sarkar and Gupta. The entrance losses in the capillary and slit rheometers are used to predict the elongational viscosities for axisymmetric and planar flows respectively. The power-law region of the axisymmetric as well as planar elongational viscosity is found to follow the time-temperature superposition principle. The vortices encountered in the flow near the abrupt contraction for the planar and axisymmetric cases are compared. The vortex near the abrupt contraction is found to reduce in size as the flow rate is increased for planar as well as axisymmetric entrance flow.

Cell neighbor list method for planar elongational flow: rheology of a diatomic fluid

We present simple changes to the cell method for neighbor list construction that enable it to be used in molecular dynamics studies of systems subject to a planar elongational flow field. The modifications for planar elongational flow are similar to those required for planar shear flow and should be easy to incorporate into any cell neighbor list method that is used in simulations of homogeneous shear. The execution time of the code at equilibrium is shown to be proportional to the number of particles N. The introduction of the modifications allowing shear, and more importantly, elongational flow are shown to affect the performance of the code in both CPU time and memory usage. The modifications to enable the simulation of planar elongational flow using the cell method of neighbor list construction will not introduce any higher order dependency if applied to code that is N-dependent in planar shear flow. We use this code to study large systems of diatomic molecules at low strain-rates, and find that the linear regime in planar elongational flow can be determined by the ratio of the two planar elongational viscosity functions. The properties investigated in planar shear flow, such as angular velocity and alignment angle, were inconsistent with the shear viscosity results in their evaluation of where the linear regime ends. The high precision of the results allowed us to accurately determine the coefficients in the retarded-motion expansion.

1125 CTAB/NaSal 水溶液の定常平面伸張流動特性の解明

Rhelogical properties in steady planar elongational flow of CTAB/NaSal aqueous solution, which forms wormlike micelles and shows viscoelastic property, were investigated. 4-roll mill flow cell was used to create steady planar elongational flow. The planar elongational stress was measured by using a flow-birefringence technique which is based on the stress-optic rule. In addition, the planar elongation rate was accurately measured by the motion analysis of tracer particles. The planar elongational viscosity was evaluated from both results and it showed the elongational thinning as the same of the shear thinning. The planar elongational viscosity, which was measured by using 4-roll mill flow cell, was compared with one, which was measured by using squeeze flow cell, and they showed good agreement. Trouton ratio was kept 4 in both Newtonian region and elongational thinning region. The flow instability was observed in 4-roll mill flow cell at a certain planar elongation rate that was lower than the case of shear flow instability

Steady Planar Elongational Viscosity of CTAB/NaSal Aqueous Solutions Measured in a 4-Roll Mill Flow Cell.

Rheological properties in steady planar elongational flow of CTAB/NaSal aqueous solutions were investigated using a 4-roll mill flow cell. The planar elongational stress was measured by using a flow-birefringence technique, which is based on the stress-optic rule. On the other hand, the rate of planar elongation was accurately determined by the analysis of the tracer particles in the system. The planar elongational viscosity showed elongational thinning as well as shear thinning. The planar elongational viscosity measured in the 4-roll mill flow cell was compared with that measured in a squeeze flow cell, and both well agreed with each other. Trouton ratio was evaluated to be 4 in both the Newtonian and elongational thinning region. Flow instability is observed in the 4-roll mill flow cell at a planar elongation rate lower than the shear rate at which the shear flow instability takes place.

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.

Development of Measurement Technique for Elongational Stress in Transient Planar Elongational Flow of Low-Viscous Viscoelastic Fluid by Flow-Induced Birefringence Method.

A new technique to measure elongational stress of low viscous viscoelastic fluids in transient planar elongational flow is developed. The measurement instrument for this technique consists of two parts, the squeeze flow cell and the birefringence measurement device. The squeeze flow cell consists a set of parallel plates and generates step planar elongational flow on the stagnation line on the center plain of the plates. The birefringence and the orientation angle along the stagnation line in the start-up flow and the relaxation after cessation of the flow are measured. The elongational stress can be calculated from these optical data when the stress-optical rule is applicable. The comparison between the velocity distribution and the birefringence measurement using the flow cell that has several dimensions shows that the elongation rate distribution is not constant along the stagnation line by the sidewall effect. However, it is confirmed that reasonable results can be measured under the flowing condition, W=40 mm, L=20∼40 mm, H0=36 mm, where W and L denote the width and the length of the parallel plates and H0 is the initial gap of parallel plates. The surfactant aqueous solution CTAB/NaSal, which is Maxwell fluid at low shear rate, is used as the sample of trial test of this technique. The planar elongational viscosity ηep of this sample is measured by our technique and it is compared with shear viscosity η. Trouton ratio Tr (=ηep/η) becomes almost 4 and this result demonstrates ability and practicality of our technique.