## Numerical evidance for the non-existing of solutions of the equations desribing rotational fiber spinning

• Abstract. The stationary, isothermal rotational spinning process of fibers is considered. The investigations are concerned with the case of large Reynolds (± = 3/Re ¿ 1) and small Rossby numbers (\\\" ¿ 1). Modelling the fibers as a Newtonian fluid and applying slender body approximations, the process is described by a two–point boundary value problem of ODEs. The involved quantities are the coordinates of the fiber’s centerline, the fluid velocity and viscous stress. The inviscid case ± = 0 is discussed as a reference case. For the viscous case ± > 0 numerical simulations are carried out. Transfering some properties of the inviscid limit to the viscous case, analytical bounds for the initial viscous stress of the fiber are obtained. A good agreement with the numerical results is found. These bounds give strong evidence, that for ± > 3\\\"2 no physical relevant solution can exist. A possible interpretation of the above coupling of ± and \\\" related to the die–swell phenomenon is given.

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Author: Th. Götz, A. Klar, A. Unterreiter, R. Wegener urn:nbn:de:hbz:386-kluedo-15291 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (108) Report English 2007 2007 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik Fraunhofer ITWM 2008/05/28 Boundary Value Problem ; Existence of Solutions; Rotational Fiber Spinning ; Viscous Fibers Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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