Structure-controlled bifurcation in mathematical modelling of fibre spinning

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Authors

  • A. Ziabicki Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland
  • L. Jarecki Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland

Abstract

In the mathematical model of melt spinning of fibres from crystallizing polymers the set of conservation equations is completed with structure-controlled constitutive equations and structure evolution equations describing kinetics of stress-induced crystallization. In a definite range of conditions, bifurcation of solutions is observed. Maximum filament velocity is limited and the same boundary conditions yield different steady-state dynamic and structure profiles. Bifurcation is observed when stress-induced crystallization leads to rapid solidification of the material. Critical conditions for bifurcation in melt spinning are analyzed and physical mechanism of such a behaviour is discussed.