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April 2021 / 17 a new product, you can create an Excel spreadsheet to model these equations to yield answers about the statistical probability of your mix. The key factors in the mathe- matical model are the particle size distribution and the scale of scru- tiny. The model will show the best that can be achieved in a perfect random mix. In some cases, a quality random mix that meets the consumer's requirements can't be achieved with the proposed ingredients. The particle size and density of each ingredient affect the ability to create an adequate mix. The book Mixing in the Process Industries 1 provides equations for calculating a quality mix based on particle size and density. If you're planning iced-tea drink-mix powder. An artificial sweetener constitutes a small portion of the overall blend. Your packaging states that the proper method to make iced tea is to use the large scoop supplied in the package to remove 1 scoop of powder and blend it with 1 gallon of water. This means that when manufacturing the powder, your scale of scrutiny should have been 1 scoop. Presumably, you've used a sample size equivalent to the scoop size to evaluate the powder before selling it and have made sure that each scoop-size quantity of pow- der contains the proper amount of the sweetener. If the consumer decides to scoop a small teaspoon out of the package to make a glass of iced tea, then the consumer might be disappointed in the taste. You've only guaranteed that a large scoop sample will make the right flavor of tea. A 1-teaspoon scoop might not contain enough of the sweetener to provide the proper sweet taste. Conversely, if you declare on the package that the consumer can scoop 1 teaspoon of powder for 1 glass of iced tea, then your scale of scrutiny should have been 1 tea- spoon, and you'd better be certain that you mixed the powder to ensure that every teaspoon contains the proper amount of the sweetener to make a quality glass of iced tea. The scale of scrutiny can become critical in products such as phar- maceuticals. For example, a drug manufacturer could guarantee a specific amount of active ingredi- ent in a single tablet. The powder amount in the tablet is the scale of scrutiny. If a consumer chooses to purchase a double-dose tablet and split it, then the consumer may not be getting the right dosage in each half. The drug supplier only guar- anteed the right dosage in a tablet, not a half tablet. FIGURE 1 Two-ingredient mixture before and after mixing* * Note: Images reprinted with permission from Mixing in the Process Industries, edited by E. Harnby, M.F. Edwards, and E.W. Nienow, Butterworth, 1985. a. Before: Segregated b. After: Perfectly ordered mix FIGURE 2 Two-ingredient mixture resulting in random mix* * Note: Images reprinted with permission from Mixing in the Process Industries, edited by E. Harnby, M.F. Edwards, and E.W. Nienow, Butterworth, 1985. a. Good random mix b. Segregated mix