Modeling of power characteristics for multistage rotor–stator mixers of shear-thinning fluids

Abstract

Multistage rotor–stator (RS) mixers are widely utilized to generate high shear rate in dispersion processes such as foam generation and emulsification, featuring narrow gaps between rotors and stators in the axial direction and close clearance between rotors and vessel wall in the radial direction. In this study, CFD simulation of the multistage RS mixers is carried out for Newtonian and shear-thinning power-law fluids to investigate the strain rate distribution and power characteristics, both of which are critical for bubble or droplet size distribution and process optimization. The simulation indicates that the shear-thinning power-law fluids lead to large fluid dead zones in the laminar regime compared to the Newtonian fluids, whereas such dead zone disappears in turbulent regime. But the area of higher strain rate of the power-law fluid near the tip of rotors is greater than that of Newtonian fluid. The average strain rate in turbulent flow is much higher than that in laminar flow, and the tails of strain rate distribution become longer as the flow index n decreases. The radial clearance ratio is found to have a non-negligible effect on the proportionality constant Kp between the power number and Reynolds number. For non-Newtonian fluids, CFD simulation indicates that the shear rate proportionality Ks nearly keeps constant in the laminar regime and is insensitive to the flow index n, showing that the Metzner–Otto concept is still suitable for the multistage RS systems. However Ks is strongly dependent on the radial clearance ratio and the axial gap, and hence new correlations are proposed for Kp and Ks to consider this effect. Then a new correlation for the power number is established and can serve as a unified correlation for Newtonian and shear-thinning power-law fluids in the laminar regime in multistage RS systems.