and slotted head (light blue line) differ in particle size distribution from control
sample (dark blue line). Shear frequency. The interaction between the flow from the rotor and the geometry of the stator screen plays a critical role in the turbulence and shear characteristic in the gap. CFD models (High Shear Mixing Program, University of Maryland) indicate that the high energy dissipation regions (energy contributed to mixing) occur when the rotor passes a hole or a slot in the stator or screen. The way the fluid impinges on the stator wall and the resultant turbulent eddies that occur therefore are governed by the number of holes/slots and the number of blades/teeth on the rotor. This is the reason for the variety of stator hole designs ranging from circles (Figure 3) to slots to squares that are available. Each of these holes imparts a distinctive mixing characteristic in terms of flow through the head and shear rate. Figure 4 shows how different stator geometries affected particle size distribution, in this case in trials with a titanium dioxide slurry.
Lee et al. in a 2004 article “Rotor-stator milling of APIs…” in American Pharmaceutical Review discussed their use of shear frequency as a scale-up option in wet milling applications. When studying the milling of active pharmaceutical ingredients, they found that the shear frequency doesn’t affect the minimum achievable particle size but that it aids the rate of particle size reduction. Shear frequency is expressed as:
sf = NnRnS (4)
where nR is the number of blades/teeth on the rotor and nS is the number of holes/slots on the stator.
Residence time is an important scale-up parameter because the break-up of both particles and droplets is time dependant — they will break only if they’re exposed to the high shear/energy areas for a sufficient amount of time. In considering this parameter, a rotor/stator mixer can be divided into the following sections, listed in order of decreasing residence times: (a) the shear gap, (b) the stator region, (c) the rotor region (volume of openings in the stator), and (d) the volute.
It’s important to note that increasing the residence time in the gap by making it larger won’t increase the areas of high energy because the flow interactions between the rotor and stator remain constant. Increasing the number of holes or slots will increase the rotor/stator interaction and, in turn, increase the number of high energy regions. This can be accomplished by changing the screen, a relatively easy operation and one of the main selling points of the rotor/stator design. The effect on rotor and screen configuration on shear values also has led to the rise of multi-stage mixers (consisting two, three or more rows of concentrically arranged rotors and stators). Coupling the estimation of nominal residence times with a Reynolds analysis, where the Reynolds number is the ratio of turbulent forces to viscous (laminar) forces present in a system, makes it possible to investigate whether inertial (turbulent) or viscous (laminar) forces are likely to control mixing in each of the regions.
Figure 5. CFD diagram helps predict potential wear patterns when scaling-up a 8-in. rotor/stator in-line mixer (top) to a 10-in model (bottom).
Understanding the flow patterns within each of the regions of the rotor/stator mixer provides an appreciation of the areas of high energy dissipation and the types of breakup mechanisms that would be induced as a result. The High Shear Mixing Program has employed techniques such as CFD, LDA and PIV to observe and replicate or model the complex flows in the rotor/stator in-line mixer. In a commercial application, an equipment manufacturer (Silverson) and a client conducted a joint study using CFD modeling to predict the wear potential on an in-line mixer processing a highly abrasive ilmenite slurry (Figure 5). The need to increase throughput required upgrading the mixer from a unit with an 8-in. rotor to a 10-in. model. Sizing the mixer to achieve the increase was effectively an everyday calculation; the CFD modeling allowed an accurate assessment of the impact of this change in internal geometry on the abrasive forces within the mixing zone and provided the basis for design alterations to overcome this problem.