Better understanding boosts mixer scale-up

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Your worst nightmare? You’re making the first batch of a new formulation on the production line and the results are nothing like what happened in the pilot plant. Fortunately, it seems that sort of thing happens less frequently these days. Nevertheless, mixing scale-up remains — in the opinion of many professionals in the industry — more of an art than a science.

Despite an increasing number of theories and equations in the public domain, there really isn’t a golden rule to successful scale-up. The issues involved are so diverse with so many variables that no one rule can be applied. Even classifying the equipment used under the umbrella term “mixer” can be complex.

So first, let’s distinguish between an agitator and a mixer. Agitators employed in a vessel to promote heat transfer, maintain bulk movement or provide in-tank uniformity often are considered to be “process aids” rather than mixers. (Pumps in this respect fall into the same classification because their function is merely to move the product rather than to alter it.) In contrast, mixers combine two or more ingredients, bringing about a change in these ingredients during the formation of the end product through several operations that may include particle size reduction, homogenization, emulsification, reaction acceleration and so on — many of these may be occurring at the same time in a single operation; a range of operational or hydrodynamic variables may apply in any given service.

For agitators (and pumps), because they’re carrying out relatively simple tasks, it’s possible to forecast with a high degree of certainty the size and configuration of the machine required for a particular application. Technical advances such as Computational Fluid Dynamics (CFD), Laser Doppler Anemometry (LDA) and Particle Induced Velocimetry (PIV) are helping make the task easier. They enable modeling the performance of equipment, even taking into account vessel and impeller geometry, batch size and product characteristics — providing sophisticated and accurate scale-up information without necessarily having to carry out any physical testing.

For high shear mixers such as rotor/stator devices the tasks are more demanding — for example, forming an emulsion or suspension, reacting two ingredients together, etc. — and, so too, is accounting for the varied operations occurring, often simultaneously. The mixers’ versatility means that more complex factors are involved, making it more difficult to understand and predict what’s going on and what will happen under certain conditions. So, selecting a single criterion as a basis for scale-up calculations is far too simplistic an approach.

Scale-up considerations for rotor/stator mixers go beyond just sizing the equipment; selection of workhead or stator screen configuration can significantly impact end results in terms of process times, quality of finished product and so on. In addition, it’s important to consider the physical properties of the materials, for example, whether the rheology of the product is affected by shear forces and changes in temperature. Scaling-up from lab trials to specify the correct production unit requires that all calculations be tempered by experience — it’s this “educated guess” that’s the key to successful scale-up.

Going beyond “guessology”

With high shear mixers, laboratory scale units tend to closely resemble their production counterparts in design but their speeds (and rotor tip speed is what’s important here) often are far higher than on the larger units. So, interpreting results requires a degree of experience. A rule often applied at the start of testing is that if the task can be completed on the lab scale relatively quickly it can be replicated in bulk manufacture — but it follows that if poor results are obtained at this initial stage simply hitting the problem with larger, more powerful equipment may not be the answer.

Once laboratory scale testing has established the viability of the task, calculations for sizing the right mixer for an application typically are carried out based on vessel geometry and required throughput for in-line devices or tank turnover rate in terms of immersion machines, which reflects the common need by end users to achieve a result in a given timescale. These calculations are made with allowance, based almost entirely on experience, for the characteristics of the product being mixed.

This guessology has worked well enough for many years. Increasingly however, end users of the equipment expect a level of technical data to be provided — as is the case with agitators — to allow them to make better informed decisions when specifying a mixing system. Technical data sheets more and more frequently accompany quotations for new machinery and equipment manufacturers often must assist with validation and the provision of process guarantees.

Figure 1. It’s usually prudent to run trials of materials on lab or production scale units at a vendor facility.

This has led a number of mixer manufacturers to take a more scientific approach to their customer service and R&D activities. Most already operate testing facilities where clients can carry out trials on laboratory or even production scale equipment (Figure 1). Many tests are purely subjective and it’s often difficult to produce definitive, comparable results, especially in terms of particle size of suspensions and emulsions or the degree of particle size reduction obtained by various means. Recently the trend has been to augment these test centers with analytical capabilities (Figure 2). In the past, samples may have been sent to outside agencies or returned with the customer for testing — a delay that can adversely affect results, particularly where products have characteristics that change on cooling, when shear forces are removed or where hydration continues over time. Immediate on-site analysis of samples during trials allows great accuracy and repeatability of test results and scale-up forecasts.