A viscoelastic calibration procedure for orthogonal superposition rheometry

Orthogonal superposition rheology is a powerful technique for probing the viscoelastic properties of complex materials under flow. However, its accuracy is heavily dependent on the precise calibration of four calibration parameters: the instrument’s transducer mass M, friction coefficient ζ, stiffness coefficient K, and geometry end-effects captured through the end-factor c⊥. This work demonstrates that the standard, decoupled calibration procedure, which utilizes static weights and Newtonian standards, can result in negative stiffness coefficients and nonminimum phase behavior, which are not representative for the experimental conditions when characterizing complex materials. The standard calibration also fails to account for the mathematical coupling between the friction coefficient and the orthogonal end-factor. In this paper, we demonstrate that, by exploiting the frequency-dependency of the moduli of a viscoelastic material, here different aqueous poly(ethylene)oxide solutions, the calibration offsets for the transducer mass, friction coefficient, and stiffness coefficient can be determined independently, together with the corresponding true orthogonal end-factor. Furthermore, the presence of the sample avoids the unstable behavior that occurs during the standard calibration methods. Validation of this novel calibration procedure across multiple rheometers with a polyisobutylene-CALTRAN solution shows that the proposed method performs equally to or better than traditional calibrations, particularly at high frequencies where instrument inertia dominates. This viscoelastic calibration procedure ensures a physically consistent calibration for the characterization of complex fluids.