How do I assess the mixability of a system with large density differences in advance at laboratory scale?
With large density differences, mixability at laboratory scale should not be assessed with a single visual inspection. For dry bulk materials, a structured test plan is required, comprising material characterisation, mixing kinetics, spatially and temporally staggered sampling, and discharge and conveying trials. For liquid-solid or liquid-liquid systems, rheological measurements, dispersion and sedimentation trials, and hydrodynamic characteristic numbers are additionally needed.
Classifying the system correctly
First, it must be determined whether a solid-solid, solid-liquid or liquid-liquid system is present. Terms such as sedimentation, creaming, viscosity, and the Reynolds, Archimedes or Richardson number are primarily relevant for liquids, suspensions and emulsions. For dry powders and granules, by contrast, particle size, particle shape, bulk density, cohesiveness, wall friction, moisture, electrostatic effects, air content and flow behaviour are the key considerations.
For dry bulk materials with large bulk density differences, density alone is not the critical factor. The combination of differing particle sizes, shapes and bulk densities is particularly hazardous for segregation. Fine particles can percolate downward between coarser particles; round particles roll further down heap slopes than flat or fibrous components; and differing settling velocities cause trajectory separation. A mixture can therefore appear homogeneous immediately after mixing and only segregate again during discharge, conveying or filling.
Preliminary assessment therefore begins with as complete a characterisation of each component as possible. This includes particle size distribution, particle shape, true density, bulk and tapped density, moisture, cohesiveness, wall friction, flow function and, where relevant, electrostatic behaviour. For cohesive powders, a Jenike shear tester can be used to determine flow function, internal friction, cohesion and wall friction. For very low dosing fractions, the number of marker particles per relevant sample size and the statistical power of the subsequent analytics should also be estimated.
Setting up the laboratory trial correctly
The laboratory trial should, where possible, be carried out with the same mixing kinematics intended for the production mixer. A transparent demonstration vessel can be helpful but does not replace a trial in a geometrically and kinematically representative test unit. With bulk materials in particular, wall friction, tool geometry, fill level, drop height and discharge geometry can strongly influence behaviour.
The test plan should deliberately vary several factors: fill level, rotational speed, mixing time, order of raw material addition, dosing location of minor components, possible liquid addition, and discharge conditions. A mixing kinetics study with several time points is advisable. Samples are taken after a short, medium and long mixing time. This makes it possible to identify when homogeneity is first reached and whether it deteriorates again with further mixing. The result should not be a single minimum value, but a robust process window.
Sampling must be staggered both spatially and temporally. With batch mixers, samples are taken from different zones of the mixing chamber, provided this is possible without disturbing the mixture. Even more important are samples from the start, middle and end of discharge. This makes it possible to distinguish whether a problem originates in the mixing chamber or only during discharge and conveying. For a first robust statistic, typically at least ten individual samples per test point are used. The mean, standard deviation and coefficient of variation are calculated from the concentrations of a suitable marker component:
CoV=sxˉ×100%
In addition to the CoV, the minimum, maximum, range, adherence to the target value, and the distribution of values across discharge should be considered. A good CoV at the end of mixing is not sufficient if, for example, predominantly coarse, heavy particles are discharged at the start and finer or lighter fractions at the end.
Specifically testing for segregation
For dry mixtures, a separate segregation test is indispensable. After mixing, the product should be discharged under realistic conditions, transported via the intended conveying technology, and, where applicable, filled into a target container. In particular, free fall sections, heap formation, vibratory conveyors, belt conveyors, pneumatic conveying, intermediate hoppers, and big bags or sacks should be examined. Components with differing size, shape or density can resort at any of these points.
Discharge and buffering should, where possible, follow a mass-flow pattern. In mass flow, the material moves toward the outlet across the entire cross-section. This can reduce segregation compared with funnel or core flow. A sufficiently large outlet, suitable wall inclinations, appropriate wall materials and a flow-favourable discharge fitting are therefore part of the laboratory and pilot assessment. With critical mixtures, samples are analysed not only in the mixer but after every relevant process stage.
If the product profile allows it, targeted wetting can be tested. Small amounts of a suitable binder can bind fine fractions to coarser carrier particles and reduce percolation. This approach, however, must be matched to texture, moisture, flowability, shelf life, chemical stability and subsequent processing. Alternatively, pre-mixing the critical fine fractions with a carrier component can be worthwhile.
Using characteristic numbers sensibly
For dry bulk materials, the Froude number, specific power input, tool circumferential speed, fill level, number of tool revolutions, restratification time and mixing time are useful process parameters. The Froude number relates inertial and gravitational forces. It can be used, in particular with rotating mixers, to describe the flow regime. A high Froude number, however, is not automatically advantageous: at excessive rotational speeds, particles can centrifuge against the wall, wear more heavily, or separate again depending on size and density. For solid mixtures, there is therefore no universal Froude limit that reliably prevents segregation.
For suspension and liquid-liquid systems, the Reynolds, Froude, Archimedes and, depending on the question, Richardson number are additionally relevant. The Reynolds number describes the ratio of inertial to viscous forces and helps classify laminar or turbulent flow. The Froude number is relevant where free surfaces, vortex formation or gravity-dominated phenomena occur. The Archimedes number supports assessment of buoyancy and sedimentation behaviour. The Richardson number describes the ratio of density stratification to turbulent mixing but is primarily suited to stratified liquid systems and not to dry bulk materials.
For solid-liquid suspensions, the just-suspended speed Njs according to Zwietering is an important test parameter. It denotes the lowest agitator speed at which no particles remain on the vessel base for longer than approximately one to two seconds. It is determined visually and is an established basis for the design of stirred vessels and the selection of suitable agitator tools. At high solids concentrations, however, the Zwietering correlation should not be applied uncritically, because it can underestimate the energy input required for dense industrial suspensions.
For liquid-liquid systems, the droplet size distribution, the spatial distribution of the dispersed phase, the tendency to coalesce, and phase separation after the agitator is switched off are additionally assessed. Important factors here are the time to a visible phase boundary, the stability of the dispersion, and the change in droplet size over the mixing duration.
Securing scale-up
Scale-up must not be carried out with an unchanged rotational speed. As vessel diameter increases, circumferential speed, power draw, flow, drop height and the interaction with gravity all change. Depending on the system, a constant circumferential speed, a constant Froude number, a constant specific power input, or a defined restratification time can serve as a starting point. None of these characteristic numbers is sufficient on its own. They must be combined with geometric similarity, actual tool geometry, product behaviour, and the results of mixing, discharge and conveying trials.
For a documented preliminary assessment, an evaluation matrix is recommended. It should include, at a minimum, the formulations investigated, fill levels, rotational speeds, mixing times, addition sequences, homogeneity metrics, discharge profiles, particle breakage, segregation after conveying, and the process parameters chosen for scale-up. This makes it possible to rate the mixture as robust, conditionally robust or critical, and to derive a trial programme for pilot or production scale.
How amixon® masters large density and particle size differences in mixing
With large differences in bulk density, particle size and flow behaviour, considering density alone is not sufficient. Mixability must be tested with the original components – including the mixing process, discharge, possible conveying and filling. For amixon®, the focus is not on random free-fall movement, but on controlled, three-dimensional product circulation produced by the SinConvex®/SinConcave® helical ribbon mixing tool.
The mixing tool forcibly conveys the product upward near the wall. At the centre, it flows back downward under gravity and is guided back into the outer mixing zone. This produces recurring product circulation throughout the entire mixing chamber. This forced convective restratification can be particularly advantageous with formulations of markedly differing bulk density, particle size and shape, because all components are continuously redistributed in space. Depending on design and mixing task, the tool circumferential speed typically lies in a comparatively low range of approximately 0.8 to 3.5 m/s. A low-speed operating mode limits mechanical stress and avoids pronounced centrifugal effects. Whether this achieves sufficient homogeneity and a stable mixture for a specific formulation must nevertheless be demonstrated through trials.
A practical example can be found in powder metallurgy. There, amixon® twin-shaft mixers of the HM series can homogenise metal powders with pressing aids such as zinc stearate. Metal powders can have bulk densities of around 4 kg/dm³, while metallic soaps have considerably lower bulk densities. At particle sizes of approximately 2 to 70 µm, high demands arise for the even distribution of small additive quantities. The HM series operates with two superimposed product streams and is designed for large batches. Whether the HM 16000 model with 16 m³, another model, or a different mixer type is suitable for the specific formulation must be determined based on batch mass, bulk density, additive fraction, abrasiveness, purity requirement and desired throughput.
The Gyraton® silo mixer GM is also of interest for large batches and heterogeneous mixtures. It can be designed for batches in the range of approximately 10 to 100 m³ and is suitable for coarse and fine particles, differing bulk densities, flow properties and moisture contents. Its great strength lies in homogenising large batches at the start of longer process routes. An early, stable starting mixture can relieve downstream dosing, conveying, conditioning or filling steps. Whether the required mixing quality is achieved across the entire fill level range from approximately 10 per cent of the usable volume, however, must always be confirmed for the specific formulation.
Preliminary assessment begins in the pilot plant with material characterisation. For each component, at least particle size distribution, particle shape, bulk density, moisture, cohesiveness, flow function and, where relevant, wall friction should be recorded. Particularly important is not only the mean particle size but the width of the distribution: fine fractions can percolate between coarse particles and migrate downward during subsequent movement. For cohesive powders, a Jenike shear tester can help determine flow function, cohesion and wall friction.
The actual mixing trials should be carried out with the original products and under realistic conditions. This includes the planned fill level, the actual addition sequence, the intended rotational speed, mixing time, dosing locations and, where applicable, liquid additions. Several mixing times are tested in a mixing kinetics study. This makes it possible to determine when the target homogeneity is first reached and whether the mixture deteriorates again with longer processing or a changed operating mode. The target is a robust process window, not simply the longest mixing time.
Dust-like fractions can often be bound to coarser particles when small amounts of a suitable liquid are deliberately introduced into the mixing process. This reduces the number of freely mobile fine particles; the tendency toward percolation, and therefore later segregation, can be reduced. The prerequisite is that the liquid is ideally distributed evenly throughout the entire bulk. Besides the formulation compatibility of the binder, dosing quantity, droplet size, spray pattern, dosing location, addition timing and the subsequent mixing time are particularly decisive. Too little liquid can fail to achieve the desired binding, while too much can cause local over-wetting, unwanted agglomerates, or changes to flowability, sensory properties and shelf life.
Sampling must be spatially and temporally representative. Samples from different product zones are supplemented with time-staggered discharge samples, in particular from the start, middle and end of emptying. The mean, standard deviation and coefficient of variation can be determined from the concentrations of a suitable marker component. The CoV describes the relative scatter of the concentrations:
CoV=sxˉ×100%
A low CoV is an indication of good homogeneity but is not sufficient as sole proof. Adherence to the target value, minimum and maximum, discharge profile, particle breakage, fines formation and, where relevant, stability after conveying or storage must additionally be considered. Particularly with strong differences in bulk density and particle size, a good value in the mixing chamber is not yet proof that all containers have the same composition after filling.
35 test units in various sizes are available in the amixon® pilot plant. Additional pilot plants exist in Japan, India, Thailand, China, South Korea and the USA. Trials are carried out with the original product, planned fill levels, realistic batch sizes, and the intended temperature and pressure conditions. Mixing quality, mixing time, product protection, energy input, de-agglomeration, residual discharge, cleanability, discharge stability and reproducibility are assessed. The documented results form the basis for the technical design of the production mixer and for defining the subsequent PLC recipes.
amixon® develops and manufactures the apparatus at its Paderborn plant with a high level of in-house manufacturing. Every machine is designed on the basis of a user requirement specification. Vessel geometry, mixing tool, materials, surfaces, seals, dosing points, discharge concept, sensors and automation can be matched to the respective product range. The documented manufacturing supports long-term spare parts supply and the reproducible remanufacture of components.