Instrument phase errors and inertial leakage in optimally windowed chirp (OWCh) rheometry

Abstract Optimally windowed chirp-based rheometry (OWCh) enables rapid acquisition of linear viscoelastic spectra and has become an increasingly popular alternative to conventional discrete frequency sweep measurements, particularly for time-evolving materials. However, the accuracy of chirp-based protocols is sensitive to instrumental and signal-processing artefacts that can distort the recovered complex modulus. In this work, we demonstrate that timestamp-induced phase offsets produce a frequency-dependent rotation of the complex modulus, causing crosstalk between the storage and loss moduli. Further, when OWCh measurements are undertaken using a combined motor transducer rheometer the phase offset and instrument inertia are intrinsically coupled such that the inertial effect, which is typically assumed to affect only the storage modulus, leaks into the loss modulus. Analytical modelling reveals a cubic frequency scaling of the resulting loss modulus error. Using numerical examples and experimental measurements obtained on multiple rheometers and materials, we show that conventional inertia correction is insufficient to recover the true material response when phase offsets are present. We further introduce a practical calibration procedure that enables phase correction to be performed prior to inertia correction, restoring quantitative agreement between chirp-based and frequency sweep measurements. These results establish a physically consistent correction sequence for chirp-based rheometry and provide a robust framework for chirp-only rheometry.