Particle Cloud Height in High Aspect Ratio Vessels Agitated by a Bare Shaft

Mixing in solid-liquid systems is essential for many industrial applications, as it prevents particle sedimentation and enhances mass transfer between liquids and particles. Some applications require mixing within confined, high aspect ratio vessels, where diameters can be less than 10 mm. In such cases, conventional impeller-based mixing becomes challenging. In this study, we investigate mixing in a 10 mm tube with an aspect ratio greater than 5, using a 3 mm diameter bare shaft. Spherical polyethylene particles with a density of 1.3 kg/L are dispersed in two different solvents, water and dimethyl sulfoxide, which has a density of 1.1 kg/L and a viscosity of 2 mPa·s. Particle sizes range from 200 to 600 µm, with volume fractions below 5%. Refractive index matching and high-speed imaging are used to analyse the mixing behaviour. Taylor-Couette flow structure is observed in this system. Distinct particle regions with roughly uniform density are also observed, which are related to the well-known toroidal cells found in homogeneous Taylor-Couette flows. As a qualitative indicator of mixing performance, cloud height is measured across Reynolds numbers ranging from 1000 to 10,000 and Taylor numbers ranging from 10⁶ to 6 x 10⁸. A scaling argument for cloud height is developed, demonstrating quantitative agreement with the experimental measurements.

This work is funded by the Leverhulme Trust under grant RPG-2023-105