Which data and models support the scale-up of mixing and agglomeration processes, for example the Froude number?
The scale-up of mixing and agglomeration processes from laboratory or pilot-plant scale into production is based on a robust data base and on the deliberate use of dimensionless characteristic numbers and modelling approaches. The aim is to ensure geometric, kinematic and dynamic similarity between the scales as far as possible.
Relevant data for scale-up
An important basis is geometric data such as vessel geometry, the dimensions and positions of the mixing tools and the fill level. Material and substance properties are equally relevant, such as particle size distribution, bulk and solids density, viscosity, moisture content, flow behaviour, cohesion, adhesion and the surface tension of binders.
Added to this are process parameters such as rotational speed, mixing time, binder addition rate, temperature and moisture profiles, power consumption, torque and specific energy input. Product characteristics such as granule size distribution, granule strength, porosity, homogeneity, residual moisture and the time course of homogenisation and granule growth are equally decisive.
Important dimensionless characteristic numbers
The Froude number describes the ratio of inertial to gravitational forces and is relevant for transferring rotational speeds. It is frequently used with ploughshare, drum and horizontal mixers.
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.
The Reynolds number characterises the flow regime and is important above all for liquid-laden or pasty systems. The Newton number links the power requirement with rotational speed, tool geometry and material density and supports the design of drives as well as the calculation of the specific energy input – but only for liquids.
The Weber number describes the ratio of inertial to surface tension forces and is relevant for droplet formation, binder distribution and the stability of liquid bridges in build-up granulation. In addition, the specific energy input is frequently used as a robust scale-up criterion where not all characteristic numbers can be held constant simultaneously.
Modelling approaches and methods
Empirical models are based on trial series, regression analyses and practical rules such as constant circumferential speed or constant energy input per unit volume. They are often very useful, but are tied to the particular product and the specific apparatus.
Mechanistic models use the physical fundamental laws of the conservation of mass, momentum and energy. These include computational fluid dynamics for calculating flow fields, shear and energy distributions, the discrete element method for simulating particle movements and contact forces, and coupled CFD and DEM models for processes with strong fluid-particle interaction.
Population balance models describe the development of the particle size distribution over time through nucleation, growth, coalescence, breakage and consolidation. Regime maps help to classify agglomeration states and to determine the appropriate operating window. In addition, statistical design of experiments and digital twins are used in order to analyse critical parameters and their interactions systematically.
The role of similarity in practice
Geometric similarity is frequently a prerequisite for the transferability of correlations for the Newton and Reynolds numbers. Where the geometry deviates markedly, flow and particle movement patterns often change so strongly that simple scaling rules are no longer sufficient and numerical simulations as well as pilot trials become necessary.
In industrial practice, hybrid scale-up strategies are therefore usually pursued. A typical combination consists of geometric similarity, a constant Froude number, targeted adjustment of the specific energy input, laboratory and pilot-plant trials and model-based design. Product quality and process stability can thus be assured better across all scales.
Which scaling rules amixon® applies – and where trials replace them
amixon® mixers are operated across all sizes within the same window of circumferential speed, approximately 0.8 to 3.5 m/s and as a rule at low speed. With geometrically similar tools, a constant circumferential speed keeps the mechanical stress on the particles and the movement pattern of the bulk material comparable between the scales and is thus the practically most important similarity condition. The rotational speed falls as the diameter increases; keeping the rotational speed constant instead overstresses the product at a large scale.
What remains constant – and what changes
What remains constant across the sizes at amixon® is the mixing principle, the tool geometry and the fill-level-independent mixing quality. Mixing times change moderately in the transition and are determined by trial rather than converted by a rule of thumb, since they depend on the flow behaviour, density differences and cohesion of the specific product.
Characteristic numbers as a framework, trials as proof
Dimensionless characteristic numbers such as the Froude number provide the framework for transferring states of motion. amixon® uses such considerations in design work but does not rely on them. At the pilot plant with 35 test units, mixing time, fill level and tool speed are determined and documented with the original product. For granulation processes, and especially in the ring-layer mixer granulator, trials are expressly mandatory, because the balance of granule build-up, granule densification and granule destruction cannot be predicted by calculation alone.
Agglomerating powders in the ring-layer mixer granulator
In the amixon® ring-layer mixer granulator, powders can be built up into dust-free, stable agglomerates with uniformly large porosity. Such agglomerates are readily wettable in liquids, sink well and dissolve quickly.
Agglomeration is a natural process. Baking already shows how fine particles first form loose and then increasingly densified structures when a liquid is added. In technical implementation, ultrafine particles are brought together by liquid bridges, densification and shear, so that rounded agglomerates with a defined particle size distribution are created.
The ring-layer mixer granulator is particularly suitable where economical particle enlargement and uniform agglomerate formation are required. Agglomerates from the mixer granulator are usually more densified and less porous than agglomerates from fluidised bed agglomeration. While the fluidised bed process is used above all for very porous, rapidly wettable and rapidly dispersible instant products, ring-layer agglomeration is aimed more at economical, easily conveyable and low-dust granules.
The fine size grid as a quiet scaling advantage
Because amixon® manufactures mixers in 100-litre increments up to 50,000 litres and the Gyraton® GM is available in 1 m³ increments up to approximately 100 m³, no similarity condition has to be sacrificed to a jump in the catalogue. The target machine is designed exactly for the validated batch size, which markedly improves the transferability of the pilot-plant data.
Manufacture in Paderborn as the quality foundation
amixon® develops and manufactures exclusively at the Paderborn works with the greatest depth of manufacture and all components from Germany. As a certified welding company with European, Japanese, Korean and American qualifications, amixon® designs every apparatus as a one-off on the basis of the operator's URS, and quality control remains entirely in-house without gaps. This manufacturing autonomy also secures long-term supply: every component can still be re-manufactured reproducibly decades later.
Service across the entire life cycle
After commissioning, amixon® remains at the operator's side. Regular inspections and preventive maintenance secure availability, on request with predictive maintenance. Selected wear parts are supplied together with the initial delivery; most spare parts are held at the Paderborn site, many more at the service bases in Japan and the USA. A lifetime spare parts service thus remains possible even where original suppliers cease to exist. Many amixon® machines have been in daily use for more than 30 years; modernisation and retrofitting keep them at the state of the art.