A model of rotary spinning process

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Abstract

A rotary spinning process is used to produce aramide fibers. In this process thin jets of polymer solution emerge from the nozzles of the rotating rotor and flow towards the cylindrical coagulator. At the coagulator the jets hit the water curtain in which they solidify forming fibers. The rotary spinning is described by a steady jet of viscous Newtonian fluid between the rotor and the coagulator. The jet model includes the effects of inertia, longitudinal viscosity, and centrifugal and Coriolis forces. For the jet model the specific type of the boundary conditions depends on the balance between the inertia and viscosity in the momentum transfer through the jet cross-section. Based on that we find two possible flow regimes in rotary spinning: (1) viscous-inertial, where viscosity dominates at the rotor and inertia at the coagulator (2) inertial, where inertia dominates everywhere in the jet. Moreover, there are two situations where spinning is not possible, either due to lack of a steady-jet solution or because the jet wraps around the rotor. Finally, we characterize the parameter space.
Original languageEnglish
Title of host publicationProgress in Industrial Mathematics at ECMI 2010
EditorsM. Günther, A. Bartel, M. Brunk, S. Schoeps, M. Striebel
Place of PublicationBerlin
PublisherSpringer
Pages341-347
ISBN (Print)978-3-642-25099-6
DOIs
Publication statusPublished - 2012
Event16th European Conference on Mathematics for Industry (ECMI 2010), July 26-30, 2010, Wuppertal, Germany - Wuppertal, Germany
Duration: 26 Jul 201030 Jul 2010

Publication series

NameMathematics in Industry
Volume17
ISSN (Print)1612-3956

Conference

Conference16th European Conference on Mathematics for Industry (ECMI 2010), July 26-30, 2010, Wuppertal, Germany
Abbreviated titleECMI 2010
CountryGermany
CityWuppertal
Period26/07/1030/07/10

Fingerprint

metal spinning
inertia
rotors
viscosity
curtains
wrap
centrifugal force
fibers
Newtonian fluids
nozzles
momentum transfer
boundary conditions
cross sections
polymers
water

Cite this

Hlod, A. V., Ven, van de, A. A. F., & Peletier, M. A. (2012). A model of rotary spinning process. In M. Günther, A. Bartel, M. Brunk, S. Schoeps, & M. Striebel (Eds.), Progress in Industrial Mathematics at ECMI 2010 (pp. 341-347). (Mathematics in Industry; Vol. 17). Berlin: Springer. https://doi.org/10.1007/978-3-642-25100-9_40
Hlod, A.V. ; Ven, van de, A.A.F. ; Peletier, M.A. / A model of rotary spinning process. Progress in Industrial Mathematics at ECMI 2010. editor / M. Günther ; A. Bartel ; M. Brunk ; S. Schoeps ; M. Striebel. Berlin : Springer, 2012. pp. 341-347 (Mathematics in Industry).
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abstract = "A rotary spinning process is used to produce aramide fibers. In this process thin jets of polymer solution emerge from the nozzles of the rotating rotor and flow towards the cylindrical coagulator. At the coagulator the jets hit the water curtain in which they solidify forming fibers. The rotary spinning is described by a steady jet of viscous Newtonian fluid between the rotor and the coagulator. The jet model includes the effects of inertia, longitudinal viscosity, and centrifugal and Coriolis forces. For the jet model the specific type of the boundary conditions depends on the balance between the inertia and viscosity in the momentum transfer through the jet cross-section. Based on that we find two possible flow regimes in rotary spinning: (1) viscous-inertial, where viscosity dominates at the rotor and inertia at the coagulator (2) inertial, where inertia dominates everywhere in the jet. Moreover, there are two situations where spinning is not possible, either due to lack of a steady-jet solution or because the jet wraps around the rotor. Finally, we characterize the parameter space.",
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Hlod, AV, Ven, van de, AAF & Peletier, MA 2012, A model of rotary spinning process. in M Günther, A Bartel, M Brunk, S Schoeps & M Striebel (eds), Progress in Industrial Mathematics at ECMI 2010. Mathematics in Industry, vol. 17, Springer, Berlin, pp. 341-347, 16th European Conference on Mathematics for Industry (ECMI 2010), July 26-30, 2010, Wuppertal, Germany, Wuppertal, Germany, 26/07/10. https://doi.org/10.1007/978-3-642-25100-9_40

A model of rotary spinning process. / Hlod, A.V.; Ven, van de, A.A.F.; Peletier, M.A.

Progress in Industrial Mathematics at ECMI 2010. ed. / M. Günther; A. Bartel; M. Brunk; S. Schoeps; M. Striebel. Berlin : Springer, 2012. p. 341-347 (Mathematics in Industry; Vol. 17).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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N2 - A rotary spinning process is used to produce aramide fibers. In this process thin jets of polymer solution emerge from the nozzles of the rotating rotor and flow towards the cylindrical coagulator. At the coagulator the jets hit the water curtain in which they solidify forming fibers. The rotary spinning is described by a steady jet of viscous Newtonian fluid between the rotor and the coagulator. The jet model includes the effects of inertia, longitudinal viscosity, and centrifugal and Coriolis forces. For the jet model the specific type of the boundary conditions depends on the balance between the inertia and viscosity in the momentum transfer through the jet cross-section. Based on that we find two possible flow regimes in rotary spinning: (1) viscous-inertial, where viscosity dominates at the rotor and inertia at the coagulator (2) inertial, where inertia dominates everywhere in the jet. Moreover, there are two situations where spinning is not possible, either due to lack of a steady-jet solution or because the jet wraps around the rotor. Finally, we characterize the parameter space.

AB - A rotary spinning process is used to produce aramide fibers. In this process thin jets of polymer solution emerge from the nozzles of the rotating rotor and flow towards the cylindrical coagulator. At the coagulator the jets hit the water curtain in which they solidify forming fibers. The rotary spinning is described by a steady jet of viscous Newtonian fluid between the rotor and the coagulator. The jet model includes the effects of inertia, longitudinal viscosity, and centrifugal and Coriolis forces. For the jet model the specific type of the boundary conditions depends on the balance between the inertia and viscosity in the momentum transfer through the jet cross-section. Based on that we find two possible flow regimes in rotary spinning: (1) viscous-inertial, where viscosity dominates at the rotor and inertia at the coagulator (2) inertial, where inertia dominates everywhere in the jet. Moreover, there are two situations where spinning is not possible, either due to lack of a steady-jet solution or because the jet wraps around the rotor. Finally, we characterize the parameter space.

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BT - Progress in Industrial Mathematics at ECMI 2010

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Hlod AV, Ven, van de AAF, Peletier MA. A model of rotary spinning process. In Günther M, Bartel A, Brunk M, Schoeps S, Striebel M, editors, Progress in Industrial Mathematics at ECMI 2010. Berlin: Springer. 2012. p. 341-347. (Mathematics in Industry). https://doi.org/10.1007/978-3-642-25100-9_40