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How dimensional analysis allows to go beyond Metzner–Otto concept for non-Newtonian fluids

Delaplace, Guillaume and Jeantet, Romain and Grenville, Richard and Cuvelier, Gérard and Loubière, Karine How dimensional analysis allows to go beyond Metzner–Otto concept for non-Newtonian fluids. (2020) Reviews in Chemical Engineering. ISSN 2191-0235

(Document in English)

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Official URL: https://doi.org/10.1515/revce-2020-0006


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.

Item Type:Article
HAL Id:hal-02975988
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > AgroParisTech (FRANCE)
Other partners > Agrocampus Ouest (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Nationale Supérieure de Chimie de Lille - ENSCL (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > Institut national de recherche pour l'agriculture, l'alimentation et l'environnement - INRAE (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Philadelphia Mixing Solutions (USA)
Other partners > Université de Lille (FRANCE)
Laboratory name:
Deposited On:23 Oct 2020 08:38

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