Range Of Apparent Shear Rates Research Articles

Three-dimensional simulation of capillary rheometry for an estimation of extensional viscosity

Abstract It is difficult to directly measure the steady extensional viscosity of thermoplastic composite materials, especially at high extension rates. The famous Cogswell method was derived analytically from the pressure drop of entrance flow in commercial capillary rheometers for estimating the extensional viscosity. However, using Cogswell´s extensional viscosity has always resulted in over-predictions of pressure drop. Recently, the GNF-X (eXtended Generalized Newtonian Fluid) model with a weighted shear/extensional viscosity was proposed to show the typical extension-induced vortex growth in entrance flow simulations. Under given various values of Trouton’s ratio for extensional viscosity, the GNF-X model is introduced to perform three-dimensional flow simulations of capillary rheometry over a range of apparent shear rates. The difference between the predicted pressure drops and the relevant experimental data is minimized such that the estimation of extensional viscosity is optimized herein.

The rheology of batch and continuously prepared gluten-free bread dough in oscillatory and capillary shear flow.

Reduced elasticity and high stickiness of gluten-free bread doughs are major issues regarding the industrial breadmaking process. In this work, we compared traditional batch mixing with a revised continuous extrusion process and extensively study the rheological properties of both doughs. Shear viscosities were measured offline with a capillary rheometer and inline at the extruder die over a large range of apparent shear rates. Data were corrected for entrance effects, wall slip and non-Newtonian flow behaviour. Good agreement between inline and offline measured viscosities were supplemented by amplitude and frequency sweep tests. The results highlight that this extrusion process fostered the production of gluten-free bread dough. We demonstrated that extrusion processing support the combined mixing, kneading, and moulding of gluten-free dough in one single unit. This fundamental study linked physical dough characterization with applied engineering and yielded the understanding and processing of corresponding products.

Numerical study of the non-Newtonian blood flow in a stenosed artery using two rheological models

The numerical simulation of blood flow in arteries using non-Newtonian viscosity model, presents two major difficulties; the first one is the choice of an appropriate constitutive equation, because no one model is universally accepted as a reflection of the true behavior of blood viscosity until now. Another difficulty lies in the numerical convergence of the complex scheme solving the highly non-linear set of equations governing the blood motion. In this paper, the pulsatile blood flow through an arterial stenosis has been numerically modeled to evaluate the flow characteristics and the wall shear stress under physiological conditions. The Navier-Stokes equations governing the fluid motion are solved using the finite element method in unsteady two-dimensional case. The behavior of blood is considered as the Generalized Power-law (Gpl) and Cross models, where the shear-thinning characteristics of the streaming blood are taken into account. Constants in the constitutive equations of previous models have been obtained by fitting experimental viscosity data. The numerical simulations are performed for a wide range of apparent shear rates (10 s-1-750 s-1) with good convergence of the iterative scheme. Results from the blood flow simulations indicate that non-Newtonian behavior has considerable effects on instantaneous flow patterns. However, it seems that the Gpl model will be slightly better for describing the non-Newtonian characteristics of blood than the Cross model.

Shear viscosity and wall slip behavior of a viscoplastic hydrogel

The coupled apparent slip and viscoplastic behavior of a hydrogel consisting of 0.2 wt. % aqueous solution of poly(acrylic acid) was analyzed employing steady torsional and circular tube (capillary) flows. Transparent disks and capillaries fabricated out of borosilicate glass were used to allow velocity measurements. The steady torsional flow of the hydrogel was dominated by wall slip which gave rise to plug flow over the apparent shear rate range of 0.1 to 1 s−1, in agreement with the plug flow observed in the capillary under similar shear stresses. The transition from plug flow provided the yield stress of the hydrogel, which was found to be consistent with velocity data collected over the 0.1–200 s−1 apparent shear rate range of steady torsional and capillary flows. The availability of both pressure drop versus flow rate and wall slip velocity data enabled the validation of correction procedures proposed earlier for the determination of the slip-corrected wall shear rate [Yilmazer and Kalyon, “Dilatancy of concentrated suspensions with Newtonian matrices,” Polym. Compos. 12, 226–232 (1991); D. Kalyon, “Apparent slip and viscoplasticity of concentrated suspensions,” J. Rheol. 49, 621–640 (2005)] and the determination of the shear viscosity parameters. The apparent slip layer thicknesses were found to be consistent with the elastohydrodynamic mechanism proposed by Martin et al. [“Wetting transitions at soft, sliding interfaces,” Phys. Rev. E 65, 031605 (2002)] and Meeker et al. [“Slip and flow in pastes of soft particles: Direct observation and rheology,” J. Rheol. 48, 1295–1320 (2004)] for steady torsional flow but not for capillary flow, emphasizing the role the applied pressure plays in shaping the apparent slip behavior.

Annular Extrudate Swell of a Fluoropolymer Melt

Abstract Annular extrudate swell is studied for a fluoropolymer (FEP) melt using a tubular die. The rheological data of the melt have been fitted using (i) a viscous model (Cross) and (ii) a viscoelastic one (the Kaye – Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko or K-BKZ/PSM model). Numerical simulations have been undertaken to study the extrudate swell of the FEP melt in an annular die. Compressibility, thermal and pressure effects on viscosity, and slip at the wall were taken into account. In all cases, slip at the wall is the dominant contribution reducing the swelling when compared with corresponding no-slip simulations. The viscous (Cross) simulations show that the swell decreases with increasing apparent shear rate, which is opposite to what happens in the extrusion of viscoelastic melts. On the other hand, the viscoelastic (K-BKZ) simulations correctly obtain increasing swelling with increasing shear (flow) rates. It was found that due to the mild viscoelasticity of FEP and its severe slip at the wall the swelling of this melt is relatively small, reaching values of about 20% for a wide range of apparent shear rates, exceeding 5000 s−1. This is corroborated by experimental observations.

Capillary extrusion flow of a fluoropolymer melt

The capillary extrusion-forming flow of a fluoropolymer (FEP) melt was studied both experimentally and numerically. The excess pressure drop due to entry (related to the Bagley correction), the compressibility, and the effect of pressure and temperature on viscosity on the capillary data analysis have been examined. Using a series of capillary dies having different diameters, D, and length-to-diameter L/D ratios, a full rheological characterization has been carried out, and the experimental data have been fitted both with a viscous model (Cross) and a viscoelastic one (the Kaye—Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko or K-BKZ/PSM model). For the viscous model, the viscosity is a function of both temperature and pressure. For the viscoelastic K-BKZ model, the time-temperature shifting concept has been used for the non-isothermal calculations, while the time-pressure shifting concept has been used to shift the relaxation moduli for the pressure-dependence effect. It was found that the viscous simulations gave good results in the range of apparent shear rates studied. The viscoelastic simulations gave slightly better results in reproducing the experimental data, especially for the entrance pressure losses for L/D = 0. It is concluded that pressure-dependence of the viscosity and viscoelastic effects are small to moderate in flow of the FEP melt, which is a linear polymer.

The rheological characterisation of bread dough using capillary rheometry

An Australian hard wheat flour–water dough has been characterised using parallel plate and capillary rheometers over an extensive range of apparent shear rates (10 − 3–103 s − 1) relevant to process conditions. Torsional measurements showed that the shear viscosity of the dough increased with strain to a maximum value and then decreased, suggesting a breakdown of the dough structure. Both torsional and capillary experiments revealed the shear-thinning behaviour of the dough. The wall slip phenomenon in capillary rheometry was investigated and found to be diameter dependent and occurred at a critical shear stress of approximately 5–10 kPa. A two-regime power law behaviour was observed, with the power law index approximately 0.3 in the low shear rate range increasing to 0.67 in the high shear rate range. Pressure fluctuation was observed in the capillary data and increased with shear rate, in particular, at shear rates approaching 104 s − 1. The results demonstrate that capillary rheometry is a viable means of rheologically testing dough at high shear rates provided pressure fluctuation is carefully monitored and capillary rheometry corrections, including wall slip, are accounted for.

Development of extrudate distortions in poly(dimethyl siloxane) and its suspensions with rigid particles

The developments of flow instabilities and the associated surface and bulk irregularities during the extrusion of a poly(dimethyl siloxane), PDMS, melt and its suspensions with spherical hollow glass particles (10% to 40% by volume) were investigated using both capillary and rectangular slit flows. Flow instabilities were pronounced in the extrusion of unfilled PDMS as manifested by surface and bulk distortions of extrudates over a wide range of shear rates. The range of apparent shear rates, in which such flow instabilities and the associated surface/bulk distortions of the extrudates were observed, decreased upon the incorporation of rigid particles, especially as the concentration of the particles increased. Flow instabilities and the distortions of the extrudates could largely be eliminated upon the incorporation of particles at 40% by volume to the PDMS melt. The geometry of the entry region from the reservoir into the die (taper angles of 15, 45, and 75°) did not generate any differences in the flow instability behavior.

A relationship between extrudate swell ratio and entry stored elastic strain energy during die flow of tyre compounds

The elastic strain energy stored in the channel entrance flow and the extrudate swell ratios are important characteristics of elasticity during channel extrusion of polymer materials. There should be some form of relationship between them, especially in the case of the use of a short or mid-length die. The viscoelastic behavior and mechanisms in capillary extrusion flow of rubber compounds were investigated in the present paper. Under the operation conditions with temperature of 90 °C and apparent shear rate range of 10–10 3 s −1, the rheological properties of two tyre compounds, cavity stock and buffer stock, were measured. It was found that the shear flow of both the tyre compounds obeyed the power law, and the non-Newtonian index values were close to each other. The entry pressure drop (Δ P 0), entry elastic stored energy ( e) and die-swell ratio ( B) increased roughly linearly with increasing shear stress at the channel wall. The B value for cavity stock was greater than that for buffer stock, whereas it was the reverse for Δ P en. Also, the correlation between the die-swell ratio and entry elastic stored energy is discussed. The results showed that B was a linear function of e.

Leavened dough processing by supercritical fluid extrusion (SCFX).

Yeast-leavened dough processing is semicontinuous due to the requirement for fermentation at constant temperature and humidity. Also, new regulations on the emission of alcohols are becoming burdensome on the baking industry. Extrusion processing of dough with supercritical carbon dioxide (SC-CO(2)) is envisioned to alleviate emission problems and to decrease production time by eliminating fermentation. A bread dough formulation with 50% (w/w) moisture was leavened by injecting 1.5% (w/w) SC-CO(2) in a twin-screw extruder at 37 degrees C. Specific mechanical energy input was 260 kJ/kg. The operating apparent shear rate range was 60-260 s(-1). SCFX-leavened dough density (420-430 kg/m(3)) was in good agreement with values reported for similar doughs. The flow behavior index, obtained by an on-line slit rheometer, was 0.49 for the nonleavened control and 0.63 for the SCFX-leavened dough. Apparent viscosity of the SCFX-leavened dough varied from 37 to 23 Pa-s. This new continuous process offers attractive possibilities for industrial applications if further developed.

Near-wall particle depletion in a flowing colloidal suspension

In this paper a method based on attenuated total reflection–Fourier-transform infrared spectroscopy is described to measure the concentration of colloidal particles dispersed in a liquid near a solid boundary in pressure driven flows. The method has been used to obtain measurements of wall depletion in an aqueous suspension of ethylcellulose particles. The method is capable of measuring the particle concentration in a thin layer near the boundary, whose thickness is between 0.3 and 1.4 μm. A considerable decrease in the concentration of particles near the wall is found for a suspension with a particle volume fraction of 0.24 over a wide range of apparent shear rates. The results from the spectroscopic experiments are compared to rheological experiments on parallel disk torsional flow at different gap heights. With this method, the order of magnitude of the thickness of an equivalent fully depleted layer (a layer at the wall assumed to contain only pure solvent and no particles) can be obtained. The results found with the two techniques are in reasonable agreement. The described method is a convenient, rapid, and relatively inexpensive way to measure the particle depletion near the wall in flowing suspensions, compared to existing magnetic resonance imaging and laser-Doppler techniques.

The melt elastic behavior of polypropylene/glass bead composites in capillary flow

The melt extrudate swell and entry pressure losses are important characteristics of elastic properties during die extrusion of polymeric fluids. They are usually expressed with die-swell ratio ( B) and entry pressure drop (Δ P o). In the present paper, the die-swell behavior and entrance pressure drop of a polypropylene (PP) filled with A-glass beads were investigated by using a Rosand capillary rheometer to identify the effects of the filler contents and extrusion rate on the elastic behavior of the sample melts. The experiments were carried out under the conditions with an apparent shear rate range of 50–10 4 s −1 and a temperature of 190 °C. The results showed that B increased nonlinearly with increasing shear rate at the wall ( γ w), and increased linearly with the increase of shear stress at the wall ( τ w). With the increase of the volume fraction of the fillers B decreased nonlinearly. Similarly, the entry pressure drop increased linearly with the increase of τ w, whereas the influence of the filler concentration on Δ P o was insignificant in this case. Furthermore, B increased as a linear function of Δ P o, and extension stress ( σ e) increased nonlinearly with increasing γ w.

Entry flow of a low-density-polyethylene melt into a slit die: An experimental study by laser-Doppler velocimetry

The flow behavior of a low-density-polyethylene melt in a 14:1 planar contraction was investigated by laser-Doppler velocimetry. The velocity field in the central plane of the flow channel is composed of the measurement of the velocity components in and perpendicular to the direction of extrusion. Two dies differing in their entrance angles are compared. In the case of the flat entry die large recirculating vortices are found in front of the die entry plane. Under stable flow conditions there is no material exchange between the vortices and the primary flow. It is shown that very small velocities within the vortices can be measured accurately. In the case of the oblique entry die no vortices are found. By the normalization of the velocity profiles with the average velocity in the die, calculated independently from the mass flow rate, an output-invariant presentation is found for the apparent shear rate range from 53 to 182 s−1. The velocity distribution along the centerline of the flow channel exhibits a pronounced velocity overshoot shortly after the die entry plane. The distance up to a fully developed velocity field within the die is about 15 times the height of the slit. Due to the acceleration of the melt in front of the die entry large elongational deformations occur. The resulting maximum elongation rates (20 s−1) are very high compared to those achievable by elongational rheometers. It is demonstrated by the comparison of the strain rate tensor components that the elongational deformation in the center plane of the flow channel is planar.

Flow Implications in the Processing of Tetrafluoroethylene/Hexafluoropropylene Copolymers

Abstract The melt fracture behavior of two Teflon® resins was studied in capillary extrusion in order to identify the critical conditions for the onset of melt fracture and wall slip. These resins were copolymers of tetrafluoroethylene (TFE) and hexafluoropropylene (HFP) and TFE/HFP/PAVE (perfluoro (alkyl vinyl ether)) (PAVE) respectively. The incorporation of the third monomer in the molecules of the resin was found to improve the processability of polymer without substantially changing its rheology. Surface melt fracture (sharkskin) appeared at wall shear stresses greater than about 0.18 MPa, practically independent of temperature in the range of 300 to 350°C. At higher apparent shear rates oscillating melt fracture was observed due to the presence of wall slip and compressibility of the melt. Furthermore, a superextrusion region was identified at apparent rates greater than about 700 s−1, beyond those where oscillating melt fracture was obtained. In this region, the extrudate appears again smooth. Finally, it was found that the addition of 0.1 % of polyethylene in the resins, reduces dramatically the pressure drop along the capillary die and eliminates extrudate distortion over the whole range of apparent shear rates up to the superextrusion region.

A study of stress distribution in contraction flows of anb LLDPE melt

Numerical simulations are carried out for a linear low-density polyethylene (LLDPE) flowing through an 8:1 planar contraction equipped with slit dies of different length ( L/2 H = 2 and 8) at two different temperatures (145 and 205°C). The emphasis is on determining the stress distribution and comparing it with birefringence experimental results that have previously appeared in the literature. The working constitutive equation is a realistic integral model of a K-BKZ type with a spectrum of relaxation times. The material parameters have been obtained by fitting experimental viscosity and normal stress data as measured in shear, and by using elongational viscosity data available in the literature. The numerical simulations are performed for a wide range of apparent shear rates (10 s −1 <γ a <140s −1) with good and fast convergence of the iterative scheme. The results show that as the apparent shear rate increases, viscoelastic effects dominate, exhibiting a delayed relaxation of stresses along the slit and stress overshoots at the die exit. This behaviour is in close agreement with the experimental birefringence patterns. Elastic recovery is also captured in an enhanced extrudate swell which is always higher for the short die at the same temperature.

Flow simulation of herschel‐bulkley fluids through extrusion dies

AbstractThe flow of viscoplastic materials through extrusion dies has been studied numerically using the finite element method. Rheological data for viscoplastic doughs have been fitted by the Herschel‐Bulkley model, which incorporates a yield stress into the power‐law model. Non‐isothermal simulations show the extent and shape of yielded/unyielded regions and the development of temperature field assuming different modes of heat transfer at the boundaries. The results reveal that viscous dissipation causes appreciable temperature rises in the extrudate in agreement with measured values at the extruded material surface. The extrudate swell results show a maximum for a certain range of apparent shear rates also observed experimentally. However, the inelastic simulations based on the Herschel‐Bulkley model always under‐predict the experimental swelling values. A heuristic approach is also used to determine the level of elasticity required to produce the experimental values.

Rheological behavior of a concentrated suspension: A solid rocket fuel simulant

The rheological behavior of a very concentrated suspension (76.5 vol %), which serves as a widely used solid rocket fuel simulant, was characterized employing both torsional and capillary flows. No comprehensive studies of the rheology of concentrated suspensions have been carried out previously at such a high solids content. The suspension exhibited shear thinning over the apparent shear rate range of 30–3000 s−1. Significant slip at the wall was observed in both torsional and capillary flows with the slip velocity increasing from about 0.001 mm/s at a shear stress of 4 Pa to as high as 60 mm/s at 100 kPa. A flow visualization technique was applied for the first time to determine the wall slip velocities in torsional flow directly, to also provide the true deformation rate and feedback on yielding. The contribution of the slip of the suspension at the wall to the volumetric flow rate in capillary flow was found to increase with decreasing shear stress, giving rise to plug flow at sufficiently low shear s...

Effect of entrance geometry on the capillary flow of cellulose acetate–acetone solution

AbstractCapillary flow data were obtained for a 27.5% solution of cellulose acetate in acetone. The solution temperature was 50°C, and the range of apparent shear rates investigated was 1.7 × 105 to 1.7 × 106 sec−1. Capillaries having tapered entrance angles of 37.88° to 120.63° were used. A power‐law model was adequate to describe the shear stress at the wall (τw) and the corrected shear rate \documentclass{article}\pagestyle{empty}\begin{document}$(\dot \gamma )$\end{document} relationship. Entrance angle affected the entrance pressure drop corrected for kinetic energy, (ΔP0,c); ΔP0,c increased as the angle widened. Treating the entrance flow as an elongational flow situation facilitated superposition of the Delta;P0,c data on a single curve. Estimated elongational viscosities decreased with increasing applied stress.