  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.
