Rheo-PIV analysis of the vane in cup flow of a viscoplastic microgel

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, R_eq, 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, R_V. 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 R_eq for a given vane in cup geometry to allow the application of the "Couette analogy" for non-Newtonian fluids. Otherwise, using R_V or a Newtonian based R_eq to calculate the flow curve may lead to significant errors.