Process Relationships for Non-Newtonian Fluids - Criticism of the Metzner-Otto Concept

Pawlowski, J.

doi:10.1002/ceat.200407078

Cited by 10 publications

(5 citation statements)

References 7 publications

(12 reference statements)

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“…Similar ideas about the number of physical quantities required to achieve "material similarity" with respect to the different categories of the non-Newtonian fluids were also proposed by Astarita between the late 1960s and 1970s (Astarita 1967(Astarita , 1979. Unfortunately, these works were not sufficiently disseminated to be widely applied by the scientific community (Delaplace et al 2009;Hassan et al 2012;Pawlowski 2005;Zlokarnik 2006). More recently, Delaplace et al (2014Delaplace et al ( , 2015 brought back to light this theoretical framework and proposed deeper explanations and new insights as well as various applications to practical cases.…”

Section: Effective Shear Rateγ Effmentioning

confidence: 91%

“…From this, one can easily understand why there is any reason that the configuration associated with a Newtonian fluid, which is intrinsically reduced compared to non-Newtonian fluids, correspond to the one of these latter. As a consequence, using the concept of Metzner-Otto with the aim to apply the same π i -space whatever the nature of the fluids is not founded from a dimensional, and hence theoretical point of view, as already underlined by Pawlowski (2005). Even if smaller sets of dimensional numbers are easier to explore and visualize (as reducing the configuration of a system), and are thus more attracting, this reduced configuration naturally comes at the expense of accuracy and genericity.…”

Section: Application To Some Common Non-newtonian Fluidsmentioning

confidence: 99%

“…-Finally, the question whether the introduction of such an effective constant K S is well found from the standpoint of dimensional analysis has been raised. In particular, as discussed by some authors (Böhme and Stenger 1988;Pawlowski 2005), the effective shear rate is not appropriate by itself to describe the complexity of any rheological behaviour. The issue to use the same power curve to describe power numbers with Newtonian and all types of non-Newtonian fluids must be addressed.…”

Section: Introductionmentioning

confidence: 99%

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

Delaplace

Jeantet

Grenville³

et al. 2020

Reviews in Chemical Engineering

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The concept of Metzner and Otto 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. Finally, 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 and 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.

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Section: Effective Shear Rateγ Effmentioning

confidence: 91%

Section: Application To Some Common Non-newtonian Fluidsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Delaplace

Jeantet

Grenville³

et al. 2020

Reviews in Chemical Engineering

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“…and non-Newtonian fluids (power-law, Bingham plastic fluid, etc.) [1,2]. A T-channel is used frequently in various industrial settings, such as power plants, heat exchangers, ventilation systems, processing industries, pharmaceutical industries, etc., for achieving the desired flow at a location [1,3,4].…”

Section: Introductionmentioning

confidence: 99%

Onset of Flow Reversal in a Vertical T‐channel: Bingham Fluids

2022

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The commencement of the flow reversal phenomenon is investigated which occurs in the daughter branch of a vertical T‐channel for the flow of Bingham plastic fluids. The combined influences of the imposed forced flow and buoyancy‐driven flow are analyzed at low Reynolds numbers. The mixed convection flow of a Bingham model fluid is explored for a wide range of conditions in terms of Prandtl number, Richardson number, and Bingham number. The critical Richardson number is strongly influenced by the Prandtl number and the yield stress of the Bingham fluids. The dimensionless pressure is seen to decrease with the critical Richardson number. Also, the fractional flow passing through the main branch exhibits a strong direct dependence on the Richardson number while an opposite relationship with Bingham and Prandtl number is observed.

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“…Pawlowski [5,6], however, criticizes this approach because it correlates the power consumption of the Newtonian flow to the non-Newtonian although the systems consist of different influencing parameters. According to the Buckingham pi-theorem [7], different systems can only be correlated if they share the same pi-space, i.e., have the same influencing parameters.…”

Section: Introductionmentioning

confidence: 99%

A Scale‐up Strategy for the Fluid Flow in Biogas Plants

et al. 2018

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The mixing process in biogas plants is fundamental for effectiveness. Unfortunately, difficulties at full scale mean that research must usually be performed at lab‐scale and the results up‐scaled. This study presents a scale‐up strategy for the fluid flow in shear‐thinning non‐Newtonian fluids. Dimensional analysis was applied to connect the influencing parameters, i.e., geometric dimensions, rotational speed, and rheological properties, to key figures. By using the Reynolds and Hedström number, standards for adapting the rotational speed and rheological properties were defined as a function of the scale. A sliding‐mesh model was selected for numerical simulations of a plant with a paddle agitator at two different scales. The scale‐up approach leads to similar velocity fields, which result in equal normalized mixing times.

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Process Relationships for Non-Newtonian Fluids - Criticism of the Metzner-Otto Concept

Cited by 10 publications

References 7 publications

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

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

Onset of Flow Reversal in a Vertical T‐channel: Bingham Fluids

A Scale‐up Strategy for the Fluid Flow in Biogas Plants

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