"Physics and Mathematics of Textured Yarn Manufacturing"

Textured yarn manufacturing transforms smooth, continuous synthetic filaments into bulky, elastic, and aesthetically enhanced yarns through thermomechanical and fluid-dynamic processes. This article presents a comprehensive first-principles analysis of the two dominant technologies—false-twist draw texturing (DTY) and air-jet texturing (ATY). For DTY, the framework integrates heat transfer in moving filament bundles, polymer viscoelastic relaxation, torsion mechanics, draw-induced molecular orientation, and elastic buckling responsible for crimp formation. For ATY, the study applies fluid mechanics, turbulent jet dynamics, drag modeling, and entanglement kinetics to explain loop generation and bulk development. The paper further connects governing physical mechanisms to measurable quality metrics such as crimp index, loop density, bulk volume, tenacity, and evenness. Dimensionless parameters including Reynolds and Deborah numbers are introduced to guide scaling and process control. By linking polymer physics, continuum mechanics, and fluid dynamics into a unified analytical structure, the study provides quantitative design rules for optimizing heater temperature, draw ratio, spindle speed, air pressure, and nozzle geometry. The result is a physics-based roadmap for process design, scale-up, and closed-loop control in modern textured yarn production.