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The steady torsional parallel-plate flow with apparent slip of a viscoplastic microgel with 0.12 wt. % of poly(acrylic acid), Carbopol® 940, is analyzed under isothermal and creeping flow conditions by simultaneous rheometrical and particle image velocimetry measurements (rheo-PIV). This analysis brings out the complexity of this non-homogeneous flow to evaluate the rheological properties of yield-stress fluids with apparent slip. Overall, velocity distributions of the microgel are linear across the gap and evidence that plug and steady shear flow cannot coexist in the parallel-plate geometry. Also, velocity distributions compare favorably with the predictions of the analytical solutions of the motion equation for the steady parallel-plate flow of a Herschel–Bulkley (H–B) fluid subject to apparent slip. However, edge fracture results in non-linear velocity distributions, i.e., non-rheometrical flow. A slip yield stress is calculated for the microgel-parallel-plate combination, and the slip velocity beyond this stress is described by two distinct relationships, namely, one almost linear as a function of the excess stress (pure plug flow) and the one power-law type as a function of the viscous stress (shear flow with slip). On the other hand, we show how the yield stress of the microgel can be determined from various new methodologies using slip velocities and rheometrical data. Finally, we demonstrate that the ordinate to the origin in the Mooney method becomes negative when the fluid undergoes plug flow. Despite this fact, we confirm the validity of the Mooney and Yoshimura and Prud'homme (Y–P) analyses and highlight their benefits in the characterization of yield-stress fluids.

The vane in cup flow involves the rotation of a bladed vane in a sample held within a cylindrical cup. The use of the vane in cup flow for rheological measurements is based on the assumption that the vane drags the specimen in between its arms as a rigid body and thus, constitutes a bob with equivalent radius, Req, i.e., the “Couette analogy.” In this work, rheo-particle image velocimetry was employed to characterize the velocity and shear stress distributions of a Newtonian fluid (glycerol) and a viscoplastic microgel [0.12 wt. % of poly(acrylic acid) in water] undergoing a steady vane in cup flow under constant torque conditions. The velocity distributions were complex for both fluids, showing that, once under flow, the vane drags only part of the specimen as a rigid body, with the boundary of the rigid body motion smaller than the vane radius, RV. Also, for both fluids, the tangential velocity increases monotonically up to a maximum and then decreases toward the wall cup. Furthermore, the radial locations which constitute the boundary of the rigid body motion or at which the maximum tangential velocity is observed are constant for the Newtonian fluid but decrease for the microgel with increasing the torque. Therefore, there is not a definite method to determine Req for a given vane in cup geometry to allow the application of the “Couette analogy” for non-Newtonian fluids. Otherwise, using RV or a Newtonian based Req to calculate the flow curve may lead to significant errors.

The tangential annular or Couette flow of a viscoplastic microgel, i.e., 0.12 wt. % aqueous solution of poly(acrylic acid), Carbopol® 940, under isothermal and creeping flow conditions was investigated by simultaneous particle image velocimetry and rheometrical measurements (Rheo-PIV). A wide range of ratios of the inner over the outer radii of the annuli, i.e., κ = 0.329, 0.749, and 0.933, were used. The PIV measurements revealed the viscoplasticity of the microgel in Couette flow via the formation of plug flow (rigid body motion) and slip at the two walls. A procedure that relied on the characterization of the wall slip behavior was developed for the determination of the yield stress of the microgel, in turn leading to other parameters of the shear viscosity of the viscoplastic fluid. The wall slip velocity versus wall shear stress behavior of the microgel was overall consistent with the mechanism of apparent slip for all three gaps. However, the apparent slip layer thicknesses were dependent on the wal...

The fully developed velocity distributions of a viscoplastic Carbopol microgel [0.12 wt. % poly(acrylic acid) in water] flowing axially in the annular gap between two long concentric cylinders were determined. The ratios of the length over the gap and the inner over the outer radii, κ, of the annulus were 442 and 0.78, respectively. The particle image velocimetry, PIV, measurements revealed that the viscoplasticity of the microgel in axial annular flow is manifested via the formation of plug flow and wall slip. The plug flow region spanned the entire or part of the annular gap depending on whether the absolute values of the shear stresses at the two walls were below or above the yield stress of the microgel, respectively. For all flow rates, the velocities at the two walls were similar indicating that the absolute values of the wall shear stress were also similar. Equality of the shear stresses at the two walls suggested that axial annular flow at a relatively high κ can be used as a viscometric flow for ...

The origin of shear thickening in an equimolar semidilute wormlike micellar solution of cetylpyridinium chloride and sodium salicylate was investigated in this work by using Couette rheometry, flow visualization, and capillary Rheo-particle image velocimetry. The use of the combined methods allowed the discovery of gradient shear banding flow occurring from a critical shear stress and consisting of two main bands, one isotropic (transparent) of high viscosity and one structured (turbid) of low viscosity. Mechanical rheometry indicated macroscopic shear thinning behavior in the shear banding regime. However, local velocimetry showed that the turbid band increased its viscosity along with the shear stress, even though barely reached the value of the viscosity of the isotropic phase. This shear band is the precursor of shear induced structures that subsequently give rise to the average increase in viscosity or apparent shear thickening of the solution. Further increase in the shear stress promoted the growing of the turbid band across the flow region and led to destabilization of the shear banding flow independently of the type of rheometer used, as well as to vorticity banding in Couette flow. At last, vorticity banding disappeared and the flow developed elastic turbulence with chaotic dynamics.

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.

Extrusion through brass dies has been found to be useful to eliminate sharkskin and stick-slip instabilities in linear low-density polyethylene. However, the physicochemical interaction of polyethylene melts with brass dies is not well understood. In the present work, such an interaction is analyzed by using electrical measurements. Experiments were performed in a single screw extruder at a temperature of 190°C with a metallocene linear low-density polyethylene and a brass die. The interaction between the polymer melt and the die changed with time. Different flow curves were obtained as the extrusion time was increased to reach an invariant flow curve. An irreversible transition from slip to no-slip at the die wall under stable flow was observed, consistent with a change in the sign of the measured electric charge. The critical shear stress for the onset of the stick-slip also increased with the extrusion time. Electrical measurements reproduced the stick-slip dynamics with fidelity. Pressure oscillations...

The capillary flow behavior of a metallocene linear low-density polyethylene was studied in a wide temperature range. The critical shear stress for the onset of the unstable spurt flow was found to be dependent on temperature in a nonlinear fashion and it showed a minimum value at a critical temperature, at which unusually long period pressure oscillations were observed. For temperatures above the critical one, the observed decrease of the critical shear stress with decreasing temperature is explained on the basis of an increase in the distance between entanglements. At temperatures below the critical one, the increase in the critical shear stress and the eventual suppression of pressure oscillations as the temperature is further decreased are suggested to be the result of a flow-induced phase change that ends on complete crystallization and suppression of flow. The flow-induced crystallization phenomenon and the extrudate quality were dependent on the contraction ratio. Elimination of surface extrudate d...

Nuclear magnetic resonance imaging has been used to investigate the flow of 0.2% aqueous solutions of xanthan gum. Apparent slip was observed in solutions made from the material supplied by UNAM but not in that supplied by Aldrich or Kelco. The apparent slip velocity was a constant fraction of the maximal velocity for a given contraction ratio. The apparent slip velocity also appeared to be independent of L/D but was strongly influenced by the wall stress, the observed apparent slip velocities being comparable with those determined using the Mooney analysis on capillary flows. After exposure to the action of a syringe pump, which reduced the mean molecular weight of the xanthan, the UNAM xanthan solution no longer exhibited apparent slip. Slip appears to be a function of molecular weight, possibly through sensitivity to the aspect ratio of the molecule.

Flow experiments with a capillary rheometer using 0.3% polyacrylamide and 0.75% polyox aqueous solutions were performed to study flow development and end effects generated by polymer solutions of flexible macromolecules. Several L/D capillary ratios were employed, and a method proposed recently was used to evaluate the corrections due to end effects. The corrections obtained are of the same order of magnitude than those obtained using the Bagley method, but the Bagley corrections have much larger uncertainties. The recently proposed method is superior to the Bagley method when accurate end effects are required, as for correlations with elasticity or to evaluate numerical predictions for the flow behavior of these fluids.

Flow experiments using a capillary rheometer with 0.2% xanthan aqueous solutions were carried out to give experimental evidence of the dependence of the slip velocity on the geometrical parameters of the rheometer. The Mooney method was used to evaluate the slip velocity Vs. It was found that Vs is an increasing function of the wall shear stress and also of the length to diameter ratio L/D not considered in the Mooney theory. That is, Vs=Vs(τw,L/D), although, for each τw value, Vs becomes independent of L/D at large L/D. In addition, a method to determine the excess pressure drop due to end effects is outlined and experimental results presented. The differences between this method and the one by Bagley are highlighted.

The unstable capillary flow of the micellar system formed by cetylpyridinium chloride 100 mM/sodium salicylate 60 mM (CPyCl/NaSal) in tridistilled water was studied in this work using a combination of particle image velocimetry (PIV) and rheometrical measurements. The experiments were run in a pressure controlled capillary rheometer at a temperature of 26°C and covered all the different flow regimes occurring in the nonmonotonic flow curve characteristic of micellar solutions. First, we show the suitability of the PIV technique to study the unstable capillary flow of this micellar system. Then, and more important, we provide evidence of the development of shear banding and the velocity profiles for the different flow regimes, including the transition to the high shear branch because of spurt. The velocity profiles at low shear rates exhibited a Newtonian behavior, followed by a still Newtonian with apparent slip up to the onset of spurt. There was a jump of one order of magnitude in the shear rate with a transient of a few minutes once spurt was triggered. The velocity profiles obtained during the transition to the high shear rate branch were plug-like, with a large increase in the velocity close to the capillary wall. When the transition was completed, the velocity profiles corresponding to the high shear rate branch showed the development of a shear band close to the capillary wall, whose thickness increased along with the shear rate. Finally, the true flow curve reconstructed from the velocity profiles provided additional evidence of the existence of a shear band that grows from the capillary wall.