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.

中文翻译：

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Gaborheometry：离散 Gabor 变换在时间分辨振荡流变测量中的应用

振荡流变技术，例如小振幅振荡剪切 (SAOS) 以及最近的中振幅振荡剪切和大幅振荡剪切 (LAOS)，广泛用于复杂流体粘弹性质的流变学表征。然而，在随时间演变或变化的材料中，微观结构的建立或分解通常取决于时间和剪切速率（或剪切应力），并且在许多复杂流体（包括钻井液、生物聚合物）中观察到触变现象凝胶和许多食品。用于分析振荡数据的傅里叶变换的常规应用假设信号是时间平移不变的，这将材料的突变数限制在极小的范围内。这种限制使得准确研究触变性和胶凝材料中剪切引起的微观结构变化变得困难，并且开发能够从振荡数据中稳健地提取时间分辨频率信息的更先进的信号处理技术变得越来越重要。在这项工作中，我们探索了 Gabor 变换（短时傅里叶变换与高斯窗相结合）的应用，以提供变异材料粘弹性特性的最佳联合时频分辨率。首先，我们展示了使用简单的分析模型和对膨润土的测量，Gabor 变换使我们能够准确测量储能和/或损耗模量随时间的快速变化，并提取材料的特征触变/老化时间尺度. 第二，使用 Gabor 变换，我们演示了从振荡流开始后的初始瞬态响应中提取有用的粘弹性数据。最后，我们考虑使用调幅输入应变信号将 Gabor 变换扩展到非线性振荡变形，以跟踪指定变形频率下触变性流体的傅里叶-切比雪夫系数的演变。我们将生成的测试协议称为 Gaborheometry（Gabor 转换振荡剪切流变仪）。这种非常规但易于实施的流变方法有助于对随时间演化的材料进行 SAOS 和 LAOS 研究，显着减少所需实验的数量和数据后处理时间。