Viscosity-model-independent generalized Reynolds number for laminar flow of shear-thinning and viscoplastic fluids

TL;DR

This paper introduces a new generalized Reynolds number formulation for non-Newtonian fluids that is independent of specific viscosity models, validated through experiments and applicable to various shear-thinning and viscoplastic fluids.

Contribution

The study proposes a viscosity-model-independent Reynolds number based on rotational viscometer principles, enabling accurate flow characterization without model-specific adjustments.

Findings

The new Reynolds number aligns closely with experimental friction factor data.

It outperforms existing formulations for shear-thinning and viscoplastic fluids.

The approach is robust across different non-Newtonian viscosity models.

Abstract

Understanding the flow dynamics of non-Newtonian fluids is crucial in various engineering, industrial, and biomedical applications. However, the existing generalized Reynolds number formulations for non-Newtonian fluids have limited applicability due to their dependencies on their specific viscosity models. In this study, we propose a new viscosity-model-independent formulation for a generalized Reynolds number. The proposed method is based on the direct adaptation of the measurement principles of rotational viscometers for wall shear rate estimation. We assess the accuracy of this proposed formulation for power-law and Carreau-Yasuda viscosity models through robust friction factor experiments. The experimental results demonstrate the applicability and effectiveness of the proposed viscosity-model-independent Reynolds number, as the measured friction factor data align closely with our Reynolds number predictions. Furthermore, we compare the accuracy of our Reynolds number formulation against established generalized Reynolds formulations for pure shear-thinning (Carreau-Yasuda) and viscoplastic (Herschel-Bulkley-extended) models. The results of the comparative analysis confirm the reliability and robustness of this generalized Reynolds number in characterizing and interpreting flow behavior in systems with visco-inelastic non-Newtonian fluids. This unified generalized Reynolds number formulation presents new and significant opportunities for precise flow characterization and interpretation as it is applicable to any visco-inelastic (time-independent) viscosity model without requiring additional derivations.