Asymptotic Methods for Air-Flow Around Fibers
An asymptotic method to determine the air-flow around slender fibers in the case of low Reynolds numbers is presented. Based on the equations for linearized flow, the force acting on a fiber is approximated as the superposition of fundamental solutions. Matching asymptotic expansions valid in different regions of the flow field leads to an integral equation model for the force. The resulting non-standard, strongly singular Fredholm integral equation of the second kind is analyzed theoretically and solved numerically. The application of this model to an industrial melt-spinning process for artificial fibers is discussed.
KeywordsConvection Nylon Polypropylene Lene
Unable to display preview. Download preview PDF.
- 2.A. Schöne. Modellbeschreibung des Fadenbildungsvorganges beim Schmelzspinnen unter den Bedingungen klassischer und hoher Spinngeschwindigkeiten. Chemické vlókna, 32 (1): 25–41, 1982.Google Scholar
- 3.T. Götz. Interactions of Fibers and Flow: Asymptotics, Theory and Numerics. PhD thesis, University of Kaiserslautern, Germany, submitted 2000.Google Scholar
- 6.T. Götz and A. Unterreiter. Analysis and numerics of an integral equation model for slender bodies in low—Reynolds—number flows. Journal of Integral Equations and Applications, 12(3):to appear, 2000.Google Scholar
- 7.R. B. Bird, R. C. Armstrong and O. Hassager. Dynamics of Polymeric Liquids, volume 1. Wiley, New York, 1977.Google Scholar