The reproducible transfer of a formulation from laboratory or pilot plant scale to production scale in a vertical single-shaft mixer rests on the mixing principle remaining the same across all sizes, on the restratification covering the entire mixing chamber independently of the fill level, and on the specific energy input being managed comparably. Simply adopting the rotational speed, fill quantity and mixing time is not sufficient for this.

Ensuring geometric similarity

The basic prerequisite for a robust scale-up is the greatest possible geometric similarity between the pilot plant and production mixers:

• Ratio of tool diameter to vessel diameter (D/T)
• Fill level related to the usable volume (typically e.g. 40–70 %), constant between the scales
• Arrangement, number and geometry of the mixing tools (shape, pitch, angle of attack)
• Clearances between the mixing tool and the vessel wall (edge zone, wall clearing)
• Position and design of secondary tools (choppers, spray nozzles, additional tools)

Where these ratios deviate markedly, empirical correction factors and, where necessary, adjustments to the process management (e.g. speed profiles, dosing strategy) have to be derived.

The unchanged mixing principle as the governing scaling criterion

For vertical single-shaft mixers with forced restratification, the decisive scaling criterion is not a dimensionless characteristic number but the question of whether the mixing principle acts unchanged across all sizes. Three conditions are governing:

• The mixing tool covers the entire mixing chamber and restratifies the product completely – in every size according to the same movement pattern.
• The restratification is independent of the fill level, so that the same mixing quality is achieved across a wide batch range.
• The circumferential speed remains in the low-speed range, so that shear loading and heat input remain comparable between the scales.

Where these conditions are met, the transfer from the pilot plant into production does not depend on a characteristic number calculation. The evidence comes from the pilot plant trial with the original product – characteristic numbers can describe the framework, but they do not replace the trial.

In this context the Froude number is not a design criterion. It describes the ratio of inertia to gravitational forces and is meaningful for rotating free-fall, drum and throw mixers as well as for systems with a horizontally mounted mixing tool, not for vertical mixers with forced restratification.

Keeping fill level and product movement constant

The mixing quality in a vertical single-shaft mixer depends strongly on the void dynamics, that is to say on the ratio between the bulk material volume and the free space for throwing trajectories and circulating movements. For a reproducible mixing quality the following applies:

• Retain the percentage fill level from the pilot plant to production
• Avoid overfilling, since it fundamentally alters the flow pattern, increases the power consumption disproportionately and can create dead zones and restricted particle relocation

Where the usable fill level in the production mixer is restricted for process or plant engineering reasons, this has to be compensated by adjustments to rotational speed, process time and, where necessary, tool configuration, and secured experimentally.

Taking the specific energy input into account

Alongside the kinematics, the specific energy input (energy per mass, e.g. in kWh/t or kJ/kg) determines the mixing quality – particularly with:

• cohesive or sticky bulk materials
• the breaking up of agglomerates
• formulations with liquid addition or binders

Typical characteristic value

The specific energy input results from the power consumption and the mixing time, related to the batch mass.

Specific energy input in the scale-up

In the scale-up, the specific energy input should be kept as constant as possible in order to achieve comparable homogeneity and dispersion results. The following has to be borne in mind:

• As the volume grows, the surface-to-volume ratio falls, so that mechanically introduced heat can be dissipated less well.
• With temperature-sensitive products, the rotational speed and mixing time are to be chosen so that the specific energy input is sufficient while the product temperature remains within the permissible range.

Adjusting the mixing time

The mixing time does not scale linearly with the volume. With the same mixing principle and a similar geometry, the movement patterns of the particles remain comparable, but the transport paths in the mixing chamber become longer. Consequences:

• At production scale, a moderately longer mixing time is frequently required in order to achieve the same degree of homogeneity.
• A practical approach is to couple the process time to the number of tool revolutions (e.g. "x revolutions to the target homogeneity") or to the cumulative energy input achieved.

The final mixing time must be validated through pilot plant trials and scaled reference trials in the production mixer, in order to avoid extrapolation errors.

Scaling liquid addition and spray technology

With formulations involving liquid addition (e.g. binders, oil, solutions), the dosing strategy and droplet distribution substantially influence the mixing quality. In the scale-up the following has to be borne in mind:

• The specific addition rate (e.g. l/min per kg of solids) should remain constant.
• The spray system is to be adapted to the larger volume: number, positioning and spray angle of the nozzles as well as droplet size and the degree of wetting achieved on the product surface.

The aim is to reproduce at production scale the distribution and moistening quality achieved at pilot plant scale, without creating local overdosing or "nesting".

Process management: order and speed profiles

For a formulation to be transferable, the process steps must be preserved qualitatively:

• order in which the components are added (e.g. dry substances, liquids, additives)
• division into pre-mixing, main mixing and, where applicable, granulation phases
• speed profiles for each phase (e.g. low speed for dry mixing, increased speed for granulation)

These steps are run at production scale in the same logical order, but adapted quantitatively to the scaling rules (circumferential speed, specific energy input, fill level).

Particle characteristics and segregation at large scale

Large-scale vertical single-shaft mixers react more sensitively to segregation phenomena:

• Greater drop heights and longer residence times in the airborne phase amplify differences in particle size, shape and density.
• In the scale-up it should be checked whether the mixing intensity and process management from the pilot plant are sufficient to prevent segregation in the larger volume.

Possible countermeasures:

• adapted speed profiles (e.g. a decelerated final phase, reduced intensity to minimise segregation)
• optimised timing for the addition of sensitive components
• targeted adjustments to the formulation (particle size distribution, flow aids) with critical products

Validation via reference batches

After the theoretical design, the scale-up has to be verified by reference batches at production scale. Typical test variables for the mixing quality:

• coefficient of variation (CV) of a lead component or of a tracer in the end product
• particle size distribution (before/after the process) with agglomerating or size-reducing formulations
• residual moisture and homogeneity of the liquid distribution
• the mixer's power curve over time as a characteristic "fingerprint" of the process

In many applications a CV below 5 % is regarded as the target for a sufficiently homogeneous mixture. Deviations are used to readjust process parameters iteratively.

Boundary conditions for reproducibility

So that a successfully scaled formulation can be run reproducibly in the long term, additional boundary conditions have to be controlled:

• raw material quality (particle size distribution, bulk density, moisture, flow properties)
• ambient influences (temperature, air humidity)
• tool condition (wear, coatings, wall build-up)
• defined cleaning, set-up and start conditions of the mixer

Constant boundary conditions ensure that the once validated combination of geometry, circumferential speed, fill level and energy input actually leads to the same mixing quality – both in the pilot plant and at production scale.