Theory of draw resonance: Part I. Newtonian fluids

Abstract

Abstract Draw resonance in isothermal spinning is explained by using kinematic wave theory. The throughput wave equation and the expression for the throughput wave velocity are derived from the governing equations of the system, that is, the continuity, momentum, and constitutive equations. A comparison is made between twice the wave residence time and the threadline residence time from the spinneret to the take‐up in order to find the stable and draw resonance regions in terms of the drawdown ratio. For Newtonian fluids, the critical drawdown ratio to cause the onset of draw resonance is 19.744. Part II will deal with draw resonance in the spinning of power law fluids and Maxwell fluids using the same wave theory. Calculation of the draw resonance amplitude when the drawdown ratio exceeds the critical values for Newtonian, power law, and Maxwell fluids will be explained in Part III. To be published at a later date.