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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 wall shear stress and were generally greater under deformation conditions, in comparison to those under which plug flow occurred. For all three Couette gaps, the experimental velocity distributions compared favorably with the predictions of the analytical solutions of the equation of motion for the tangential annular flow of the Herschel–Bulkley fluid subject to apparent wall slip.

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 (VIC) geometry has been widely used for the rheological characterization of yield-stress fluids because it minimizes slip effects at the liquid/solid interface of the rotating geometry and reduces sample damage during the loading process. However, severe kinematic limitations arising from the spatial complexity of mixed shear and extensional flow have been identified for quantitative rheometrical measurements in complex fluids. Recently, vanes with fractal cross sections have been suggested as alternatives for accurate rheometry of elastoviscoplastic fluids. In this work, the steady fractal vane-in-cup (fVIC) flow of a Newtonian fluid and a nonthixotropic Carbopol® 940 microgel as well as the unsteady flow of a thixotropic κ-Carrageenan gel are analyzed using rheo-particle image velocimetry (Rheo-PIV). We describe the velocity distributions in all cases and show that the fVIC produces an almost axisymmetric flow field and rotation rate-independent “effective radius” when used with both the Newtonian fluid and the microgel. These findings are supported by 2D simulation results and enable the safe use of both the Couette analogy and the torque-to-stress conversion scheme for a 24-arm fVIC as well as validate it as a reliable rheometrical tool for characterization of a variety of complex fluids. With the κ-Carrageenan gel, however, axial shearing/compression while inserting the rheometric tool into the sample also accelerates syneresis that ultimately results in shear banding for Couette and fVIC flows. By comparing results obtained using the 24-arm fVIC with other conventional geometries, we investigate the effect that the lateral and cross-sectional (shearing/compressing) area of the measuring fixture have on disrupting the κ-Carrageenan gel during its insertion.