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18 / September 2020 powderbulk.com PBE MIXING MECHANICS Keys to mixer testing A chieving a good material mix depends on achieving an effective "marriage" of the particle characteristics, process conditions, and mixer type. So, let's assume that we need to buy a new mixer and, after doing some research, believe that we have cho- sen a good mixer for one blend. How do we know? What criteria do we use to determine if the mixer we've chosen will do a good job? In this column, we're going to revisit a past column on how you can use testing to do just that. There's variation with every mixer and every blend, so an ideal or perfectly ordered mix can't be achieved. Instead, a good random mix is the desired goal. Every blend has a key ingredient or two that must be distributed appro- priately throughout the blend. For example, let's say our end product is acetaminophen pain-relieving tablets. We want our blend to be such that every tablet will con- tain the perfect amount of the key ingredient, acetaminophen, but this won't always happen. Each tablet is supposed to contain 325 milli- grams of acetaminophen. Yet, with standard variation, each tablet's acetaminophen content might be anywhere between 300 and 350 milligrams. This is within accept- able USP monograph requirements. To be certain a new mixer will achieve a blend within our prod- uct's acceptable variation, we need to perform testing on a pilot or lab-scale mixer. This entails grab- bing samples from the test mixer that have a size equal to the scale of scrutiny (the size of the desired product, whether it's a tablet or another shape). Once we're satisfied that the test mixer does the job we need, we'll have to ensure that the same results can be achieved with the production mixer we purchase. Again, testing will be required. Mixing time Mixing time is a key to achiev- ing the right blend. If a mixer isn't operated long enough, we'll have an incomplete mix. If it runs too long, the correct blend might be achieved and then deblend. Figure 1 illustrates mixing progress over time. The x axis represents mixing time, and the y axis represents the James L. Davis, Consulting engineer FIGURE 1 Mixing progress over time Mixing index Good random mix Poor random mix Time 1 0 mixing index. The mixing index is a dimensionless value on a 0 to 1 scale; the closer the value is to 1, the better the quality of the mix. The mixing index is represented by the following equation: M = S o 2 – S ex 2 ) / S o 2 – S r 2 ) where M is the mixing index, S o 2 represents the initial unmixed material variance (degree of blend- ing) or completely segregated state, S ex 2 represents the experimental variance at a given mixing time (that is, the blend variance at the time a particular sample is taken), and S r 2 represents the best vari- ance that can be achieved in a truly randomized mix. As the experimental mixing variance reaches the best-case