Gaborheometry: Applications of the discrete Gabor transform for time resolved oscillatory rheometry

Abstract

Oscillatory rheometric techniques such as small amplitude oscillatory shear (SAOS) and, more recently, medium amplitude oscillatory shear and large amplitude oscillatory shear (LAOS) are widely used for rheological characterization of the viscoelastic properties of complex fluids. However, in a time-evolving or mutating material, the build-up or breakdown of microstructure is commonly both time- and shear-rate (or shear-stress) dependent, and thixotropic phenomena are observed in many complex fluids including drilling fluids, biopolymer gels, and many food products. Conventional applications of Fourier transforms for analyzing oscillatory data assume the signals are time-translation invariant, which constrains the mutation number of the material to be extremely small. This constraint makes it difficult to accurately study shear-induced microstructural changes in thixotropic and gelling materials, and it is becoming increasingly important to develop more advanced signal processing techniques capable of robustly extracting time-resolved frequency information from oscillatory data. In this work, we explore applications of the Gabor transform (a short-time Fourier transform combined with a Gaussian window), for providing optimal joint time-frequency resolution of a mutating material’s viscoelastic properties. First, we show using simple analytic models and measurements on a bentonite clay that the Gabor transform enables us to accurately measure rapid changes in both the storage and/or loss modulus with time as well as extract a characteristic thixotropic/aging time scale for the material. Second, using the Gabor transform we demonstrate the extraction of useful viscoelastic data from the initial transient response following the inception of oscillatory flow. Finally, we consider extension of the Gabor transform to nonlinear oscillatory deformations using an amplitude-modulated input strain signal, in order to track the evolution of the Fourier–Tschebyshev coefficients of thixotropic fluids at a specified deformation frequency. We refer to the resulting test protocol as Gaborheometry (Gabor-transformed oscillatory shear rheometry). This unconventional, but easily implemented, rheometric approach facilitates both SAOS and LAOS studies of time-evolving materials, reducing the number of required experiments and the data postprocessing time significantly.