The concept of Metzner and Otto (1957) was initially developed for correlating power measurements in stirred vessels for shear-thinning fluids in the laminar regime with regard to those obtained for Newtonian liquids. To get this overlap, Metzner and Otto postulated and determined an “effective shear rate” which was proportional to the rotational speed of the impeller Although it was not based on a strong theoretical background, it was rapidly admitted as a practical engineering approach and was extended for seeking out a “Newtonian correspondence” with non-Newtonian results (i.e. different classes of fluids). This was applied in a variety of tank processes even for predicting heat transfer or mixing time, which stretches far away from the frame initially envisaged by Metzner and Otto themselves. This paper aimed to show how dimensional analysis offers a theoretically founded framework to address this issue without the experimental determination of effective quantities. This work also aimed to enlarge the underlying questions to any process in which a variable material property exists and impacts the process. For that purpose, the pending questions of Metzner and Otto concept were first reminded (i.e. dependence of the Metzner-Otto constant to rheological parameters, physical meaning of the effective shear rate, etc). Then, the theoretical background underlying the dimensional analysis was described and, applied to the case of variable material properties (including non-Newtonian fluids), by introducing in particular the concept of material similarity. Last, two examples were proposed to demonstrate how the rigorous framework associated with the dimensional analysis is a powerful method to exceed the concept of Metzner & Otto and, can be adapted beyond the Ostwald-de Waele power law model to a wide range of non-Newtonian fluids in various processes, without being restricted to batch reactor and laminar regime.

中文翻译：

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量纲分析如何超越非牛顿流体的 Metzner-Otto 概念

Metzner 和 Otto (1957) 的概念最初是为了将层流状态下剪切稀化流体的搅拌容器中的功率测量与牛顿液体中获得的功率测量相关联。为了获得这种重叠，Metzner 和 Otto 假设并确定了一个与叶轮转速成正比的“有效剪切率”，尽管它不是基于强大的理论背景，但它很快被承认为一种实用的工程方法并得到了扩展寻找具有非牛顿结果（即不同类别的流体）的“牛顿对应”。这被应用于各种罐过程，甚至用于预测传热或混合时间，这与 Metzner 和 Otto 自己最初设想的框架相去甚远。本文旨在展示量纲分析如何提供一个理论上建立的框架来解决这个问题，而无需实验确定有效量。这项工作还旨在将潜在问题扩大到任何存在可变材料特性并影响该过程的过程。为此，首先提醒了 Metzner 和 Otto 概念的悬而未决的问题（即 Metzner-Otto 常数与流变参数的关系、有效剪切速率的物理意义等）。然后，通过特别引入材料相似性的概念，描述了作为量纲分析基础的理论背景，并将其应用于可变材料属性（包括非牛顿流体）的情况。最后的，