Various constitutive models have been proposed to quantify a wide range of non-Newtonian fluids, but there is lack of a systematic classification and evaluation of these competing models, such as the quantitative comparison between the classical integer-order constitutive models and the newly proposed fractional derivative equations for non-Newtonian fluids. This study reviews constitutive equation models for non-Newtonian fluids, including time-independent fluids, viscoelastic fluids, and time-dependent fluids. A comparison between fractional derivative non-Newtonian fluid constitutive equations and traditional constitutive equations is also provided. Results show that the space fractional derivative model is equivalent to some classical constitutive models under reasonable assumptions. Further discussions are made from the perspective of the industrial and biomedical applications of non-Newtonian fluids. Advantages and limitations of the constitutive models are also explored to help users to select proper models for real-world applications.

人们提出了各种本构模型来量化各种非牛顿流体，但缺乏对这些竞争模型的系统分类和评估，例如经典整数阶本构模型和新提出的分数阶本构模型之间的定量比较非牛顿流体的导数方程。本研究回顾了非牛顿流体的本构方程模型，包括时间无关流体、粘弹性流体和时间相关流体。还提供了分数阶导数非牛顿流体本构方程与传统本构方程之间的比较。结果表明，在合理假设下，空间分数阶导数模型与一些经典本构模型是等价的。从非牛顿流体的工业和生物医学应用的角度进行了进一步的讨论。还探讨了本构模型的优点和局限性，以帮助用户为实际应用选择合适的模型。