Which scaling rules apply when converting mixing times from laboratory to production scale?
The scale-up of powder mixing processes rests above all on geometric similarity, comparable product properties and the preservation of the dominant mixing mechanism. What is decisive is not to transfer a particular laboratory mixing time by calculation, but to achieve the same demonstrable mixing quality and segregation stability at the larger scale.
A favourable precondition is geometric similarity between laboratory, pilot plant and production mixer. This includes comparable vessel and mixing tool geometries, identical internals, similar charging and discharge conditions and a comparable fill level. With geometrically similar powder mixers, the fill level should remain as constant as possible during scale-up.
Different criteria are used depending on the type of mixer. With tumble, container, double-cone or V-mixers, the number of vessel revolutions is frequently a sensible starting point. With convective mixers that use a mixing tool, by contrast, circumferential speed, rotational speed, specific energy input or the number of tool revolutions can serve as guide values. Which criterion is decisive depends on whether convection, shear, particulate rearrangement or, where applicable, de-agglomeration governs the mixing process. For geometrically similar powder mixers, the literature cites in particular the retention of the total number of revolutions as a scale-up-relevant approach.
A longer mixing time at production scale is therefore not inevitable. With similar geometry, the same fill level and a comparable mixing mechanism, the required number of revolutions can remain similar. The actual mixing time can nevertheless increase if the speed has to be reduced for reasons of product protection, mechanical loading, explosion protection or drive power. Charging, dosing time, discharge and downstream transport can likewise affect the overall process time.
The product properties are of particular importance. Particle size distribution, bulk density, cohesion, moisture, electrostatic charging, agglomerate strength and flowability must remain as comparable as possible. Otherwise the mixing mechanism can change during scale-up or the risk of segregation can increase. This applies in particular to mixtures with large differences in density or grain size and to micro-dosages. During scale-up it must therefore be checked whether the mechanism dominant at laboratory scale is also preserved in the production mixer.
For demanding powders, pastes or moist bulk materials, dimensionless numbers such as the Froude number as well as circumferential speed or specific power input can be helpful in addition. They do not, however, replace trials with original products. Reynolds and Newton numbers are primarily characteristics of fluid flow and should not be used as a general basis for converting mixing times in dry powder mixing.
The Froude number relates to rotating free-fall, drum and throw mixers as well as to systems with a horizontally mounted mixing tool. In vertical mixers with forced restratification it is not a design or scale-up criterion. What is decisive there is that the mixing principle remains the same across all sizes and that the restratification covers the entire mixing chamber independently of the fill level; transferability is secured in the pilot plant with the original product.
A sound scale-up therefore usually proceeds in stages via laboratory, pilot or trial scale and production. Mixing quality, mixing time, fill level, speed, charging sequence and, where applicable, de-agglomeration are examined in the process. The assessment should not rest on a mean value alone but should also take spatial sampling, analytical scatter and the tendency to segregate after discharge into account.
Which scaling rules amixon® applies – and where trials replace them
amixon® scales from the laboratory vessel to the large-volume production mixer on the basis of defined geometry, calculable flow and documented mixing trials. The aim is always the ideal mixing quality.
Ideal mixing quality as the objective
- All amixon® mixer types are designed to produce a technically ideal random mixture.
- Even with component compositions down to around 1:100,000 and across the entire fill level range, a distribution is achieved after a short mixing time that can hardly be improved upon in practice.
- This mixing quality applies to the vertical mixers as well as to the hollow-sphere mixer.
The geometric basis: restratification frequency
- The scale-up rests on a clearly defined flow principle.
- The restratification frequency describes how often the entire mix is conveyed by the SinConcave®/SinConvex® helical mixing tool.
- One restratification corresponds to the complete mixing chamber volume being moved upwards once by the mixing tool; gravity provides the return flow downwards.
The conveying capacity of the mixing tool (displacement volume flow) can be described approximately by:
I_V = (π/4) · (D² − d²) · Φ · S · n · ζ
where:
- I_V: displacement or conveying volume flow
- D/d: outer and inner diameter of the helix
- Φ: fill level relative to the usable volume
- S: pitch of the helix
- n: rotational frequency (revolutions per second)
- ζ: tool-specific velocity coefficient
This makes it possible to calculate how many complete restratifications take place per unit of mixing time – independently of the scale. If the geometry is scaled up congruently (D, d, S, ζ), the specific mixing performance remains in principle the same across all sizes.
From the laboratory vessel to the production machine
- The restratification formula permits a well-founded design of larger or smaller mixing machines.
- For the scale-up, the ratio of restratifications per unit of mixing time is transferred from the laboratory or pilot plant trial to the target size.
- Rotational frequency, mixing time and fill level of the production mixer are chosen so that the product undergoes the same number of statistical intermixings as in the trial.
This approach is helpful above all with large-volume spherical or conical mixers: mixing times are not estimated but derived from the conveying characteristics and the flow pattern and reconciled with trial data.
Mixing trials as process engineering assurance
- Despite the calculation, the pilot plant remains the central step in the scale-up.
- Mixing trials under real conditions – with the original product, real fill levels and temperature profiles – verify the theoretical assumptions.
- Tendencies to segregate, agglomerate behaviour, product protection and cleanability are thus identified early and taken into the design.
Constant across the sizes
Across all sizes, three core factors remain constant at amixon®:
- the mixing principle (SinConcave®/SinConvex® total flow: upwards at the periphery, downwards at the centre)
- the characteristic tool geometry
- the fill-level-independent mixing quality, with the highest mixing qualities from a fill level of approximately 10 %
Mixing times change only moderately in the transition from laboratory to production. They are determined by trial, because they depend on the flow behaviour, on differences in density and on the cohesion of the specific product and cannot be extrapolated with a simple rule of thumb.