Measurement of viscoelastic properties of a liquid using an immersed rotating body of a non-rheometric shape subjected to oscillatory shear

We propose a novel method for measuring linear and nonlinear viscoelastic properties of a liquid by the oscillatory motion of an immersed rotating body in a vessel. The shape of a rotating object is general and we tested four different types of impellers: a disk, an anchor, and two different flat-bladed turbines. In deriving the expressions of complex shear moduli, two different approaches were employed: one is based on the complex viscosity and the other is on the relationship between mean shear stress and mean shear strain. Both methods yield identical expressions for complex moduli. Using the latter method, the mean shear stress was appropriately scaled with torque, and the strain magnitude was scaled with the deflection angle, enabling its application to large-strain nonlinear oscillatory tests. Aqueous polyethylene oxide solutions, xanthan gum solution, and ketchup were tested, and linear viscoelastic responses of storage and loss moduli were first presented as a function of the oscillation frequency. In spite of the presence of non-rheometric and highly nonuniform flow fields, comparison with the data from the conventional cone-and-plate fixture of a rheometer shows reasonably accurate measurement with at most 7% average error within the frequency range from 0.01 to 100 [rad/s] for all the impeller geometries. In addition, large-amplitude oscillatory shear experiments were also tested and discrepancies with highly elastic fluid were discussed. The proposed method may facilitate an approximate in situ measurement of viscoelastic properties of a fluid within an industrial reactor/agitator as a tool for online monitoring.