A Method for Measuring the Rheology of a Non-Newtonian Fluid Based on the Analysis of the Recirculation Angle of Secondary Flows in a Curved U-Shaped Channel

The field of hydrodynamics, specifically microfluidics, is currently undergoing rapid development, with significant progress being made in the creation of new devices and technologies that outperform their macroscopic counterparts. Concurrently, determining the parameters of a non-Newtonian fluid is becoming an important task in many areas of industry and production, particularly in the oil industry. Both the drilling fluids (needed to create wells) and the polymer-based displacers and surfactants (needed to extract oil) have non-Newtonian properties. This paper presents a method for determining the indices of consistency and flow behaviour of the non-Newtonian fluid (power-law model) based on the analysis of secondary Dean vortices generated in a curved channel. This phenomenon is conveniently described using the recirculation angle. The structure of the flow of non-Newtonian fluids in a U-shaped micromixer has been studied. The dependence of the recirculation angle on the fluid flow rate was obtained for different fluid parameters. A universal correlation was proposed to describe the dependence of the inverse Dean number on the recirculation angle of the flow. The consistency and flow behaviour indices of the power-law model of non-Newtonian fluids found using the above correlation can be measured in the experiments.