Rheo-PIV of yield-stress fluids in a 3D-printed fractal vane-in-cup geometry

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