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On the Effects of Spinline Cooling and Surface Tension in Fiber Spinning
Author(s) -
Hagen T.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200208)82:8<545::aid-zamm545>3.0.co;2-q
Subject(s) - spinning , isothermal process , surface tension , fiber , materials science , flow (mathematics) , melt spinning , mechanics , surface (topology) , semigroup , tension (geology) , mathematics , thermodynamics , composite material , mathematical analysis , physics , geometry , ultimate tensile strength
In contrast to isothermal fiber spinning, nonisothermal fiber spinning is a remarkably stable process. In this note, we shall study the effects of continuous spinline cooling and surface tension on the stability of stationary nonisothermal fiber spinning flow. We systematically derive an appropriate extension of the one‐dimensional Matovich‐Pearson thin filament equations of viscous liquids. This model will account for the physical chemistry of the fiber surface and the temperature dependence of the material parameters. We employ semigroup theory to discuss the linear stability of stationary solutions. To this end, we prove the spectral determinacy of the associated semigroup. This approach is made viable by a reformulation of the governing equations to avoid a moving flow domain. Finally, we shall give some computational results to study the onset of surface tension instabilities and their suppression by cooling.