A New Generalized Reynolds Number Formulation for Pseudo-Plastic Fluids

Physical variables of a system can be mapped to a set of dimensionless parameters (Buckingham theorem). For a fluid dynamics problem, the Reynolds number is one of the commonly used parameters. The common practice to compare the shear-thinning properties of biofluids may be misguided due the inappropriate use (formulation) of the Reynold number. To address this issue, we propose a new generalized Reynolds number formulation that takes advantage of the measurement principle of rotational viscometers in the Darcy friction relation. This measurement principle relies on Newtonian approximations, that enables our formulation to be independent of the viscosity model. To test our formulation, we design a series of Poiseuille flow experimentations. In addition to these experiments, we compare our model with established generalized Reynolds number formulations. The results of experiments and comparisons with the literature show excellent agreement with our proposed theory. Our formulation can greatly impact both computational and experimental fluid mechanics by matching the groups of various rheology models. This would highlight the true non-Newtonian effects and unearth the unrealistically enhanced differences.