Material Functions to Characterize the Rheometry of Complex Fluids

The work reports the experimental investigations of complex fluids rheometry in the presence of patterned surfaces. The goal of the study is to explore a novel procedure to detect the shear rates domain where possible wall depletion might be present. The measurements are performed in simple shear with the Anton-Paar MC301 rotational rheometer, the samples (xantan solution and grease) being located between a smooth plate and a special manufactured lower plate patterned with pillars. The rheological behavior of the samples in the tested configurations are characterized by two material functions: (i) the flow curve $\sigma(\dot{\gamma})$ and (ii) the differential viscosity $\boldsymbol{\eta}_{d}=\boldsymbol{d} \sigma / \boldsymbol{d} \dot{\gamma}$, where $\sigma$ is the shear stress and $\dot{\gamma}$ is the shear rate. The experimental data put in evidence an instability region, which is related to the plateau of the flow curve and possible apparent slip at the walls. The existence of the yield stress is also discussed.