Polymer Process Partitioning: Extruding Plastic Pipe

When plastic pipe is solidified, it proceeds through a long cooling chamber. Inside this chamber, inside the hollow extrudate, the plastic is molten, and this inner surface solidifies last. Sag, the flow due to the self-weight of the molten plastic, then happens in this cooling chamber, and sometimes, thickened regions (called knuckles) arise in the lower quadrants, especially of large diameter thickwalled pipes. To compensate for sag, engineers normally shift the die centerpiece downward. This thesis focuses on the consequences of this decentering. Specifically, when the molten polymer is viscoelastic, as is normally the case, a downward lateral force is exerted on the mandrel. Die eccentricity also affects the downstream axial force on the mandrel. These forces govern how rigidly the mandrel must be attached (normally, on a spider die). We attack this flow problem in eccentric cylindrical coordinates, using the Oldroyd 8-constant constitutive model framework. Specifically, we revise the method of Jones (1964), called polymer process partitioning. We estimate both axial and lateral forces. We develop a corresponding map to help plastics engineers predict the extrudate shape, including extrudate knuckles. From the mass balance over the postdie region, we then predict the shape of the extrudate entering the cooling chamber. We further include expressions for the stresses in the extruded polymer melt. We include detailed dimensional worked examples to show process engineers how to use our results to design pipe dies, and especially to suppress extrudate knuckling.

Differential contributions of the mIPS and PMd in the movement planning of reaches investigated through HD-tDCS

To reach for a target, we must formulate a movement plan - a difference vector of the target position with respect to the starting hand position. While it is known that the medial part of the intraparietal sulcus (mIPS) and the dorsal premotor (PMd) activity reflects aspects of a kinematic plan for a reaching movement, it is unclear whether or how the two regions may differ. We investigated the functional roles of the mIPS and PMd in the planning of reaching movements using high definition transcranial direct current stimulation (HD-tDCS) and examined changes in horizontal endpoint error when participants were subjected to anodal and cathodal stimulation. The left mIPS and PMd were functionally localized with fMRI in each participant using an interleaved center-out pointing and saccade task and mapped onto the scalp using Brainsight. We adopted a randomized, single-blind design and applied anodal and cathodal stimulation (2mA for 20 min; 3cm radius 4x1 electrode placement) during 4 separate visits scheduled at least a week apart. Each participant performed 250 baseline, stimulation, and post-stimulation memory-guided reaches starting from one of two initial hand positions (IHPs) to one of 4 briefly flashed targets (20 cm distant, 5 cm apart horizontally) while fixating on a straight-ahead cross located at the target line. Separate 2-way repeated measures ANOVAs of horizontal endpoint error difference after cathodal tDCS at each stimulation site revealed a significant IHP by target position interaction effect at the left mIPS, and significant IHP and target main effects at the left PMd. Behaviorally, these effects corresponded to IHP-dependent contractions after cathodal mIPS tDCS and IHP-independent contractions after cathodal PMd tDCS. These results suggest that the movement vector is not yet formed at the input level of mIPS, but is encoded at the input of PMd. These results also indicate that tDCS is a viable, useful method in investigating movement planning properties through temporary perturbations of the system.