Scale-Up Factor for Mean Drop Diameter in Batch Rotor-Stator Mixers with Internal Circulation

Abstract

The aim of the present study is to propose a scale-up factor for the mean drop diameter in internally circulated batch rotor–stator mixers. The total energy dissipation rate (εt) is used as the scale-up factor for the mean drop diameter. εt is calculated from the power number, flow number, rotational speed, number of rotor blades, and number of stator holes. Because it is difficult to measure the circulation flow rate of an internally circulated mixer directly, the flow rate of a production-scale mixer is estimated by measuring the time required for complete mixing—termed “mixing time”—and taking into account the power number of the production- and pilot-scale mixers and the flow number of the pilot-scale mixer. Our experimental results indicate that εt could influence the mean drop diameter. Theoretical verification suggests that εt includes information on the mixer configuration (rotor diameter, stator hole diameter, stator wall thickness, stator opening ratio, and gap width) and manufacturing conditions (operating time: t; rotational speed: N; and total product volume: V). Our results show that a decrease in the mean drop diameter is proportional to t, N4, and V−1. Further, we estimate the mean drop diameter of the production-scale mixer by performing a model product experiment with a pilot-scale mixer. The above results also indicate that the scale-up criteria for the mean drop diameter can be determined on the basis of εt and in terms of the operating time and not necessarily in terms of the geometric similarities between mixer configurations, a constant rotor tip speed, or a constant clearance between the rotor and stator.