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18 / April 2021 powderbulk.com This simple three-component example exercise shows that par- ticle size and scale of scrutiny significantly affect the statistical capability of a mix. Multicom- ponent blends with several key ingredients are much more com- plex, and achieving a random mix is much harder. Smaller particles and larger dosage sizes will give a more statistically achievable mix. The exercise also shows that good random mixes might not be statistically achievable with the ingredients you've planned to use. If they're not, then you have to take measures to make the mixture sta- tistically achievable. PBE Reference 1. E. Harnby, M.F. Edwards, and E.W. Nienow, Mixing in the Process Indus- tries, Butterworth, 1985. For further reading Find more information on this topic in articles listed under "Mixing and blending" in the article archive on PBE's website, www.powderbulk.com. James L. Davis (jimdavispe@ gmail.com, 513-503-8053) is a consulting engineer specializing in solving difficult powder processing problems and optimizing com- plex powder systems for efficient operation. He has spent 12 years as president of Powder Processing Solutions and was with Procter & Gamble for 26 years, 15 of them in powder processing. He holds a BS in mechanical engineering from the University of Cincinnati and is a registered professional engineer in the state of Ohio. James L. Davis Cincinnati, OH 513-503-8053 powderprocessingsolutions.com in some cases and not sweet enough in others. It's far out of range from the required ±20 percent RSD. Problem-solving To fix this problem, you can take either of two approaches: First, you can change the scale of scru- tiny. If you change it to 1 scoop of powder to make 1 gallon of iced tea, then the RSD for the artificial sweetener drops to a 10 percent 3-sigma RSD, which meets the quality requirement. The target for each scoop would be 1.2 grams of sweetener, and every scoop would have between 1.08 and 1.32 grams of sweetener. Your product instructions to the consumer would have to be modified to require the consumer to make 1 gallon of iced tea with 1 scoop of powder. If the customer makes just 1 glass of tea with 1 teaspoon of powder, the sweetness wouldn't necessarily be satisfactory, and none of us want dissatisfied customers! As a second option, to guar- antee the quality of a 1-teaspoon scoop, you would have to micron- ize the artificial sweetener to get its particle size distribution small enough to produce an adequate mix. By grinding the key ingre- dient, you'll generate many more particles of the active material per gram of mix. This will help achieve a random mix. If you micronize the sweetener from the 900-micron d 50 particle size range to 200-micron d 50 particle size range, then the RSD per teaspoon of sample drops to 4 percent over a 3-sigma qual- ity requirement. For a 1-teaspoon sample that should contain 75 mil- ligrams of sweetener, this means that every teaspoon will have between 72 and 78 milligrams. This is well within the product requirements, and it's much better than the 47- to 103-milligram range of the previous blend using non- micronized sweetener. Let's explain how these equations work by going back to the instant tea example. Assume the mixture must meet the following requirements: • New instant tea drink-mix powder = 92.3 percent instant tea, 6.2 percent citric acid, and 1.5 percent artificial sweetener. • 1 teaspoon (5 grams) of pow- der makes an 8-ounce glass of sweetened iced tea. • The sweetener must meet a quality standard: The stan- dard variation per sample must be within a 3-sigma requirement ±20 percent rela- tive standard deviation (RSD) from the target. The sweet- ener target is 75 milligrams in every teaspoon. At 3-sigma RSD, the quality requirement then demands that every 1-teaspoon sample contains between 60 and 90 milligrams of artificial sweetener. Let's also assume that the ingre- dient particle sizes are measured in a sieve shaker, and that the median particle sizes are: • Instant tea = 200-micron d 50 particle size range • Citric acid = 800-micron d 50 particle size range • Artificial sweetener = 900-micron d 50 particle size range Once you run the mathematical model using the spreadsheet, you find that the sweetener's parti- cle size distribution is too large to adequately mix this ingredient at the required sample size. For the conditions above, in an ideal mix, the sweetener can only achieve 37 percent 3-sigma RSD. This means that any random 1-teaspoon sample taken from the finished drink-mix powder will have between 47 and 103 milligrams of sweetener when the desired range is 60 to 90 milli- grams. If you use the sweetener at the supplied particle size distribu- tion, the product will be too sweet