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cal of other industries. Yet too often, engineers and for- mulators measure the basic flow properties of their mate- rials and compute key behavioral parameters—such as arching and rathole tendencies—using standard methods. Those standard methods, however, were developed years ago for large-scale bins, hoppers, and silos. When applied to the very small scale typical of pharmaceutical facilities, the methods frequently over-predict problems. That is, the methods indicate problems will arise when none in fact do. As a result, design engineers who use a traditional approach may find that in-process observa- tions do not correspond to what was measured in the lab. This article addresses that problem and offers an approach to help you measure and use flow properties that are relevant to the small-scale operations typical of the pharmaceutical industry. Arch formation Solving this over-prediction problem boils down to understanding how an arch can form in process equip- ment. But we must also ask: Are the equations traditionally used to predict arching applicable to small hoppers or is there an error in the strength measurement technique? It can be shown that if the bulk-strength value is known at or near the place that an arch will form, then Equation 1 can be used to relate the critical arching dimension (AI) to the strength of the material (fc) and to the bulk density of the material (g). Geometry also comes into play, as is reflected in the (H u ) term, which has a value of approximately 2.3 when the hopper is a cone and about 1.1 when it is shaped more like a wedge. AI 5 H u • fc (1) g • g Consider a typical scenario that often plays out be - tween formulators and process engineers. The formula- tor's job is to design a product that, among other proper- ties, doesn't hang up during processing, which usually means adding various excipients to the mixture/granula- tion to counter any cohesive flow problems. Upon obtaining a reasonable material, the formulators measure the strength of the bulk mixture and compute the critical arching dimension using the traditional Jenike method (presented in more detail below). They then look at the openings in the process equipment through which the powder must pass before becoming a tablet or filling a capsule shell. If the opening in the process is smaller than the computed arching dimension, the formulators must redesign the product to further minimize the cohesive flow problems, usually by adding more glidant or chang- ing the particle size distribution of key components. This iterative, trial-and-error process can be tedious and sometimes, no matter what formulators try, the arch- ing criteria suggest that using the material in the process is impossible. In desperation, the formulators decide to test a similar product that the process engineers say flows smoothly in the current process. But those tests show that the good-flowing product likewise has an arching dimen- sion greater than the orifices of the process. Then a debate between the formulators and process engineers ensues, as each team tries to determine what went wrong and why the material doesn't follow typical design criteria. Limits of the Jenike method To shed some light on this scenario, let's first under- stand the arching analysis that Jenike described and that engineers have used for four decades to design processes. The first step is to measure the bulk strength and bulk density of the material at various stress levels (Figure 1a). This is important because process equipment operates at various stress conditions and we need to know the strength values at the process stress level to predict arch- ing. There is a line, the flow factor line, that approxi- mates the stress levels typical of conical process equip- ment. This flow factor line represents the stresses that are available to break the arch. If a plot of the material's strength falls below this line, then the arch will fail because the stresses in the process equipment are large enough to break it as it tries to form. Thus, the intersec- tion of the flow factor line with the line denoting mea- sured strength represents a critical strength level that we can use to compute the critical arching diameter for the process (Figure 1b). Tablets & Capsules May 2014 29 Figure 1 Jenike arching analysis 0 1200 1100 1000 900 800 700 600 500 400 300 200 100 0 5000 10000 15000 20000 25000 30000 Major principle stress (Pa) Unconfined yield strength (Pa) a. Strength plotted as a function of various stress levels 0 600 500 400 300 200 100 0 2000 High pressure tests Flow factor Arching condition 4000 6000 8000 10000 12000 Major principle stress (Pa) Unconfined yield strength (Pa) b. Flow factor line plotted over strength plot to define critical strength level h-Johanart_28-32_Masters 5/14/14 10:17 AM Page 29