Abstract

Rotor-stator mixers convert shaft work into circulation, deformation, turbulent motion, pressure fluctuations and heat. Their engineering description therefore requires a consistent connection between working geometry, rotational speed, flow rate, fluid properties and the pressure boundary conditions. This article develops a calculation framework that combines feature passage kinematics, time dependent overlap area, a lumped model of passage flow, cylindrical Couette flow, dimensionless operating parameters, cavitation screening and an overall energy balance. Hydraulic pressure work is distinguished from the energy of a traveling acoustic wave, and the limits of simplified bubble and gap models are stated explicitly.

The framework is supplemented by published experimental and computational studies of power consumption, flow distribution, emulsification and scale up. A screening example for an 80 mm rotor operating at 6000 rpm gives a tip speed of 25.13 m/s, a local feature passage frequency of 800 Hz, a nominal gap shear rate of 5.03 × 10⁴ s⁻¹ and a cavitation number of approximately 0.62 under the specified reference conditions. These results establish kinematic and hydraulic scales; they do not independently establish cavitation inception, shaft power or product performance. The analysis shows that reliable design depends on geometry specific validation and on a power balance with consistent boundaries, complemented by measurements of pressure, temperature and the product response.

Keywords: rotor-stator mixer; unsteady flow; pressure pulsation; cavitation; shaft power; engineering calculation; scale up.