Analysis of the vane rheometer using 3D finite element simulation

The vane rheometer has been used for more than two decades to characterize various complex materials. The objective of this work is to investigate for the first time the flow hydrodynamics of Newtonian, shear-thinning and yield stress fluids in one such rheometer by means of three-dimensional finite element simulation. The velocity field and stress distributions are predicted using finite element meshes that are much more refined than the two-dimensional meshes of previous studies. The validity of the no-slip boundary condition on the blade surfaces, which is commonly assumed in these previous studies, is assessed by comparing the calculated torque to experimental data in the case of Newtonian, shear-thinning and yield stress fluids. The effect of the power-law index and apparent yield stress on the stress profile near the blades and away from them is investigated and discussed. It is shown, in particular, that the uniform stress assumption at the vane ends is reasonable for power-law fluids with $n<0.5$ and yield stress fluids with large values of yield stress. It is also exposed how the computation of the torque contributions corresponding to the boundaries of the vane-in-cup geometry can lead to the determination of the corrected lengths associated with the end effects.