A new analytical solution for the biharmonic equation was developed for single screw extrusion cross‐channel fluid mechanical flow. This analysis led to a quantitative model for residence time distribution when combined with the historic solutions of the drag and pressure flow in the rectangular channel in the single‐screw extruder. The focus of the theoretical and experimental investigation here was to examine how closely the new analytical solution correlated with experimental residence time data for a free‐helix extruder. This new extrusion device was operated as both a conventional extruder and a more positive displacement device by using only helix rotation as the pump. The Moffatt eddies that occur in the quiescent corners of the rectangular channel with screw rotation were found to have a strong effect on the residence time of the extruder. Because there were no quiescent corners for the free‐helix flow there was essentially no residence time tail for this mode of extruder displacement. The theoretical results for a sheet of dye spanning the screw channel width and dye “blobs” were compared with experimental results for both modes of operation. In all cases, the experiments and the theory predictions were essentially consistent.

中文翻译：

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使用双谐方程的新解法在单螺杆无螺旋挤出机中停留时间

针对单螺杆挤压跨通道流体机械流，开发了一种用于双谐方程的新解析解决方案。结合单螺杆挤出机矩形通道中的阻力和压力流的历史解，该分析得出了停留时间分布的定量模型。这里的理论和实验研究的重点是检查新分析解决方案与自由螺旋挤出机的实验停留时间数据之间的相关程度。通过仅使用螺旋旋转作为泵，这种新的挤出设备既可以用作常规挤出机，也可以用作更正排量的设备。发现在螺旋旋转的矩形通道的静态角中出现的莫法特涡流对挤出机的停留时间有很强的影响。因为自由螺旋流没有静态角，所以这种挤出机位移方式基本上没有停留时间尾部。两种操作模式下，将一片横跨螺旋通道宽度和染料“斑点”的染料的理论结果与实验结果进行了比较。在所有情况下，实验和理论预测基本上是一致的。