Which scale-up equations or approaches are proven for vertical powder mixing technology?
Proven scale-up approaches for vertical powder mixing technology
For the scale-up of vertical powder mixers (e.g. cone screw mixers, vertical paddle or helical mixers), geometric similarity, a constant circumferential speed of the mixing tools, characteristic-number-based approaches via the dimensionless mixing time, and power-related criteria have proved themselves above all in practice. Which method leads depends on the bulk material, on the target variable of the process and on the scale between the pilot plant and production.
Geometric similarity is the basic prerequisite: ratios such as mixing-chamber diameter to fill height should remain as constant as possible across the unit sizes, so that the flow conditions in the bulk material behave comparably.
For powders, a constant circumferential speed of the tools is the most common transfer variable, because it keeps the mechanical stress on sensitive particles the same across all unit sizes; rotational speed itself, by contrast, is not suitable, because it varies with the tool diameter.
A frequently used characteristic-number-based approach is the dimensionless mixing time – the number of tool revolutions needed to reach the target homogeneity, expressed as the coefficient of variation (CV); for geometrically similar mixers, it remains approximately constant across a wide range of unit sizes.
The Froude number, which describes the ratio of centrifugal force to gravity in rotating drum and throw mixers, is not a design criterion for mixers with forced restratification: what is decisive there is that the mixing principle remains the same across all unit sizes and that the restratification covers the entire mixing chamber independently of the fill level.
Power-related approaches, such as the specific energy input per batch, supplement the geometric and characteristic-number-based criteria, especially when the cohesion, flowability or particle size distribution of the bulk material varies from one unit size to another. Transferability is therefore secured in the pilot plant with the original product, not predicted by calculation alone.
Which scaling rules amixon® applies – and where trials replace them
Circumferential speed as the leading scaling variable
amixon® mixers are operated within the same circumferential speed window across all sizes, mostly at low speed and depending on the product and the task. With geometrically similar tools, a constant circumferential speed keeps the mechanical loading of the particles and the movement pattern of the bulk material comparable between the scales and is thus the practically most important similarity condition.
The conveying capacity of the mixing tool, that is to say the displacement volume flow, can be described approximately as follows:
I_V = (π/4) · (D² − d²) · Φ · S · n · ζ
- I_V: displacement or conveying volume flow
- D: outer diameter of the helix
- d: inner diameter of the helix
- Φ: fill level relative to the usable volume
- S: pitch of the helix
- n: rotational frequency in revolutions per second
- ζ: speed coefficient of the tool
What remains constant – and what changes
What remains constant across the sizes at amixon® is the mixing principle with SinConvex® total flow, the tool geometry and the high mixing quality independent of fill level. Mixing times change only moderately in the transition from one size to the next and are therefore not transferred by rule of thumb, but determined in trials with the original product.
Characteristic numbers as a framework, trials as proof
Dimensionless characteristic numbers such as the Froude number provide an important framework for transferring states of motion. amixon® uses such considerations in the design but does not rely on them alone; instead it determines mixing time, fill level and tool speed in the pilot plant with real products and documents the results robustly.
Fine size increments as an advantage
A further scaling advantage lies in the fine size range at amixon®. Because the mixers are manufactured in close volume increments, no similarity condition has to be sacrificed to a coarse catalogue jump; instead the target machine can be designed very precisely for the validated batch size.
SinConcave® and SinConvex®
With SinConcave® and SinConvex®, two specially developed mixing tool geometries are available that combine the highest mixing quality with exceptional residual discharge. The deliberate inclination of the helices improves both mixing efficiency and self-cleaning and makes the geometries particularly attractive for demanding products with high hygiene requirements.
Pilot plant and validation
Where purely computational approaches reach their limits, mixing trials replace theory with practice. In the amixon® pilot plant with 35 test units, mixing behaviour, residual discharge, fill level and process window are examined with the original product, and for granulation processes such trials are indispensable in any case.
Manufacture and service
amixon® develops and manufactures exclusively at the Paderborn works with a high depth of manufacture and in-house quality control without gaps. This is complemented by service across the entire life cycle with spare parts availability, inspection and retrofitting, so that the machines remain at the state of the art even after many years.