Rheo-PIV analysis of the steady torsional parallel-plate flow of a viscoplastic microgel with 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.