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EXTRUSION Scale-up of single screws can be a surprisingly complex issue when you consider all the variables and their interactions. One of the first scale-up rules was defined by Carley and McKelvey in a 1953 article published in the journal, Industrial and Engineering Chemistry. They showed that output and power consumption varied with the ratio of the square of the screw diameters (D1/D2)2 when at the same screw rpm and channel depth for screws having the same geometry (channel width and flight width). However, shear rate is determined by the peripheral screw speed rather than the rpm. When compared at the same peripheral speed and the same channel depth, the outputs scale up as the simple ratio of the screw diameters. The squaring effect of the output comes from the change in channel volume. In the accompanying illustration, a 2-in. and a 4-in. screw have the same channel depth. As the screw size increases, the channel volume increases by the square of the ratio of the diameters. In this case, the volume of one turn of the 4-in. screw was calculated to be exactly four times the volume of one turn of the 2-in. screw. As a result, the diameter scale- up (D1/D2)2 holds true for the same channel depth and screw rpm. In a 2006 issue of Polymer Engineering and Science, an article by Chris Rauwendaal provided a very thorough analysis for all aspects of scale-up, including shear rate, melt conveying rate, residence time, shear, conductive and dissipative melting capacity, solids conveying rate, power consumption, heat transfer, mixing, and specific energy consumption, for a total of 14 different scale-up factors. It's a very comprehensive and accurate analysis but requires an expert to resolve the best balance between scale-up factors. In 1974 I was fortunate to be given a two-week individual training course by Bruce Maddock at Union Carbide's Bound Brook, N.J., development lab. It was common practice at that time to scale up the Unraveling the Complexity of Single-Screw Scale-Up channel depth using the inverse or the square root of the diameters: (D1/D2) 0.5 . Maddock was at that time finalizing a technical paper in which he taught that scale-up of channel depths was more closely represented by the ratio of the diameters to the 0.7 power. That ratio, (D1/D2) 0.7 , was representative of maintaining similar melt tempera- tures and melt quality across two extruder sizes that were geometri- cally similar in flight lead, flight width and so forth. At that time, Carbide had one of the largest development programs in the industry—with extruders up to 4.5 in. for testing—so that there was quite a bit of actual data to support the calculation. Additionally, the data was collected making blown film, so melt quality was clearly demonstrated. I have used that same approach for sizing the metering depth for hundreds of screws with the same lead angle and propor- tional configuration. I have added a small correction for polymers with strong shear-thinning behavior, which becomes important when the screws are to be run at vastly different peripheral screw speeds. The shear rate, melting rate, residence time and conductive heating are all influenced in the scale-up. Shear rate in the screw channel is described as (π D N/h) where: D is the diameter to the first power; N is the revolutions/sec; Maddock...deter- mined that the 0.7 power of the ratio of the screw diameters was a better factor for determining channel depth then the square root of the ratio of the screw diameters. Variables such as shear rates, melting rate, residence time and conductive heating are all influenced in the scale-up. By Jim Frankland The 'Squaring Effect' of Output As screw size increases the volume in the channel increases by the square of the ratio of the diameters. Here, the volume of one turn of the 4-in. screw was calculated to be exactly four times the volume of one turn of the 2-in. screw. Width Width Depth Depth Length Length 2-in Screw 4-in Screw 30 JANUARY 2019 Plastics Technology PTonline.com K now How

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