Sizing a vertical mixer for wide batch ranges (typically a ratio of 1:5 to 1:10 between minimum and maximum fill) requires a combined consideration of geometry, drive power, bulk solids mechanics and process engineering characteristics. Purely geometric enlargement from pilot to production scale is not sufficient for this, since mixing kinetics and power input do not scale linearly.

First the batch spectrum and the usable volume are defined, and the fill level range is established. In practice, vertical mixers with a conical vessel and a screw or helical mixing tool can cover fill levels from approximately 20 % to 100 % of the usable volume.

The design must be laid out so that the mixing effect is reliably assured at minimum fill. Scale-up criteria must be derived from the pilot scale. The process variables are transferred from the pilot trials in order to make the mixing behaviour reproducible at production scale.

• Geometric similarity: the ratio of vessel height to diameter (H/D) as well as the pitch angle and the diameter of the helix should remain as constant as possible, in order to retain comparable flow and conveying conditions.
• Circumferential speed (v_tip): this is decisive for the shear energy input and thus for particle breakage and the break-up of agglomerates. For shear-sensitive products it is kept as similar as possible across the scales.
• Specific power input (P/V): the power per volume is a characteristic value for dispersively dominated mixing processes.
• Specific mixing intensity (P/m): the power per mass is a characteristic value for mixing intensity. At large volumes, a slightly reduced specific power input is often aimed at in favour of energy efficiency.
• Mixing time characteristic (n·t_M): it is the product of rotational speed and mixing time. Where the geometry is similar, keeping this characteristic constant can be a robust guide value.

Geometric design for wide batch ranges

• The vessel geometry has an H/D ratio that typically lies in the range of 1.2 to 1.8, in order to achieve good axial circulation.
• A conical lower section with a cone angle of approximately 15–33° is customary.
• In the tool design it must be taken into account that the screw/helix reaches down to the lowest point of the outlet, in order to avoid dead zones at a low fill level.
• The gap between helix and wall should amount to only a few millimetres, in order to minimise wall build-up and dead zones without creating a risk of particles jamming.
• The pitch ratio of the helix amounts to approximately 20 to 30 % of the helix diameter, in order to achieve a balanced relationship between axial conveying and radial circulation.
• Flexibility for wide ranges: at extreme batch ratios, multi-stage mixing elements, adjustable tool heights or modular inserts can help to adapt the mixing zones to different fill heights.

Drive design and bulk solids mechanics

• The hydrostatic pressure at the bottom grows with the fill height, so that the breakaway torque at full fill lies markedly above the steady-state operating torque.
• In order to ensure reliable start-up under full load, a frequency-converter-controlled drive with a high starting torque (typically 2.0 to 2.5 times the rated torque) is to be preferred.

Mixing time and mixing quality across the fill range

Mixing time behaviour:

• At a larger scale the particle paths lengthen statistically, which tends to lead to longer mixing times.
• To limit the mixing time, the axial and the radial conveying rate of the mixer are to be calculated and optimised via geometry and rotational speed.

Homogeneity validation: the mixing quality is assessed in customary practice via the coefficient of variation (CV).

• At wide batch ranges, a sampling matrix is advisable that provides for samples at minimum and maximum fill as well as at defined positions (top, middle, bottom).
• Sampling systems at production scale must be designed so that they deliver representative samples during withdrawal without segregation.

Discharge behaviour and residual quantities

• Large fill volumes increase the compaction pressure in the powder, particularly with fine-grained or cohesive bulk materials. The outlet diameter and the geometry of the discharge aids (e.g. bottom flaps, segment gates) must therefore be dimensioned critically.
• With very small batches the percentage residual quantities are markedly higher. The discharge behaviour at minimum fill must therefore be examined specifically and, where necessary, optimised by an adapted outlet geometry or by re-conveying mechanisms.

Intermediate scale and practical verification

A direct jump from, for example, 100 l pilot volume to 5,000 l production volume entails high risks. An intermediate scale (factor 5–10) makes it possible:

• to identify non-linear effects such as segregation, separation of fine particles or unexpected heat removal problems,
• to check the drive design under real torque conditions at minimum and maximum fill,
• to verify the discharge behaviour and the residual quantities across the entire batch range,
• to establish the sampling matrix and the release criteria before investing in the production scale.