End Effect Correction for Orthogonal Small Strain Oscillatory Shear in a Rotational Shear Rheometer
Ran Tao, Aaron M. Forster
The orthogonal superposition (OSP) technique is advantageous for measuring structural dynamics in complex fluids subjected to a primary shear flow. This technique superimposes a small amplitude oscillation orthogonal to a primary shear flow to measure the real and imaginary components of the complex shear modulus. The commercial availability of OSP geometries and bi-axial transducers is expected to increase its adoption as a more routine rheological technique. It is important to understand calibration procedures and the influence of intrinsic inhomogeneous flow fields, residual pumping flow effects, and boundary forces at the leading edges of the geometry components on experimental error. In this work, we perform calibration measurements of viscosity standards on a commercial shear rheometer using a double wall concentric cylinder geometry. Newtonian calibration fluids with viscosities that range from 0.01 Pa·s to 331 Pa·s are used to obtain the end-effect factors in primary steady shear and orthogonal oscillatory shear directions. The corrections needed for the primary viscosity range from 16 % to 21 %; whereas for the orthogonal complex viscosity, the errors range from 19 % to 25 %. Computational fluid dynamics simulations are used to understand the relationship between the end-effect corrections, OSP flow cell, and the imposed shear flow fields. We show that approximately linear shear deformation profiles are attained, in the double gap, for both primary rotational shear and orthogonal oscillatory shear deformation, with only a slight deviation for the fluid in the vicinity of the bob ends. We also present information on the velocity, pressure, and shear rate distributions for fluid within the entire flow cell. The overestimation of the orthogonal viscosity is attributed to the pressure forces exerted on the bob end surfaces (9 %) and a higher shear rate in the double gap that leads to higher viscous stresses on the bob cylindrical surfaces (8 %).