Asymptotic Models of Different Complexity for Viscous Jets and Their Applicability Regimes

  • Walter Arne
  • Nicole Marheineke
  • Raimund Wegener
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)


This paper presents asymptotic models of different complexity for the simulation of slender viscous jets in spinning processes. In the slenderness limit a viscous Cosserat rod reduces to a string system. We propose two string models, i.e. inertial and viscous-inertial string models, that differ in the closure conditions and hence yield a boundary value problem and an interface problem, respectively. Their convergence/applicability regimes where the respective string solution is the asymptotic limit to the rod turn out to be disjoint and to cover nearly the whole parameter space of Reynolds, Froude, Rossby numbers and jet length. We explore the transition hyperplane analytically for the gravitational two-dimensional scenario.


Asymptotic Limit String Model Rossby Number Asymptotic Model String System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Walter Arne
    • 1
  • Nicole Marheineke
    • 2
  • Raimund Wegener
    • 3
  1. 1.Universität Kassel, Fachbereich Mathematik und NaturwissenschaftenKasselGermany
  2. 2.Department MathematikFAU Erlangen-NürnbergErlangenGermany
  3. 3.Fraunhofer ITWMKaiserslauternGermany

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