Abstract
This work deals with a stationary viscoelastic jet under gravitational forces described by an upper convected Maxwell (UCM) model. For spinning processes we demonstrate that a die swell-like behavior of the solution is in general possible for the asymptotically derived one-dimensional model equations. Nevertheless, to use the model for the prediction of a die swell appropriate boundary conditions or the inclusion of further effects such as surface tension have to be considered. Moreover, the regime of existence of solutions for drawing processes is determined numerically.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arne, W., Marheineke, N., Meister, A., Wegener, R.: Numerical analysis of Cosserat rod and string models for viscous jets in rotational spinning processes. Math. Models Methods Appl. Sci. 20(10), 1941–1965 (2010)
Arne, W., Marheineke, N., Wegener, R.: Asymptotic transition from Cosserat rod to string models for curved viscous inertial jets. Math. Models Methods Appl. Sci. 21(10), 1987–2018 (2011)
Bird, R.B., Armstrong, R.C., Hassager, O.: Dynamics of Polymeric Liquids. Wiley, New York (1987)
Crochet, M.J., Keunings, R.: Die swell of a Maxwell-fluid: numerical prediction. J. Nonnewton. Fluid Mech. 7, 199–212 (1980)
Hagen, T.C.: On viscoelastic fluids in elongation. Adv. Math. Res. 1, 187–205 (2002)
Hlod, A., Aarts, A.C.T., van de Ven, A.A.F., Peletier, M.A.: Mathematical model of falling of a viscous jet onto a moving surface. Eur. J. Appl. Math. 18(6), 659–677 (2007)
Joseph, D.D.: Fluid Dynamics of Viscoelastic Liquids. Springer, New York (1990)
Lorenz, M., Marheineke, N., Wegener, R.: On an asymptotic upper convected Maxwell model for a viscoelastic jets. Proc. Appl. Math. Mech. 12, 601–602 (2012)
Marheineke, N., Wegener, R.: Asymptotic model for the dynamics of curved viscous fibres with surface tension. J. Fluid Mech. 622, 345–369 (2009)
Schultz, W.: Slender viscoelastic fiber flow. J. Rheol. 31(8), 733–750 (1987)
Shampine, L.F., Gladwell, I., Thompson, S.: Solving ODEs with MATLAB. Cambridge University Press, Cambridge (2003)
Acknowledgements
This work has been supported by the Center for Mathematical and Computational Modeling (CM)2, Kaiserslautern (Rhineland-Palatinate research initiative)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Marheineke, N., Wegener, R. (2014). On Viscoelastic Fiber Spinning: Die Swell Effect in the 1D Uniaxial UCM Model. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-05365-3_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05364-6
Online ISBN: 978-3-319-05365-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)