Asymptotic transition from cosserat rod to string models for curved viscous inertial jets
Arne W, Marheineke N, Wegener R (2011)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2011
Journal
Publisher: World Scientific Publishing
Book Volume: 21
Pages Range: 1987-2018
Journal Issue: 10
DOI: 10.1142/S0218202511005635
Abstract
This work deals with the modeling and simulation of slender viscous jets exposed to gravity and rotation, as they occur in rotational spinning processes. In terms of slender-body theory, we show the asymptotic reduction of a viscous Cosserat rod to a string system for vanishing slenderness parameter. 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. We investigate the existence regimes of the string models in the four-parametric space of Froude, Rossby, Reynolds numbers and jet length. The convergence 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. We explore the transition hyperplane and derive analytically low and high Reynolds number limits. Numerical studies of the stationary jet behavior for different parameter ranges complete the work. © 2011 World Scientific Publishing Company.
Authors with CRIS profile
Involved external institutions
Germany (DE)How to cite
APA:
Arne, W., Marheineke, N., & Wegener, R. (2011). Asymptotic transition from cosserat rod to string models for curved viscous inertial jets. Mathematical Models & Methods in Applied Sciences, 21(10), 1987-2018. https://dx.doi.org/10.1142/S0218202511005635
MLA:
Arne, Walter, Nicole Marheineke, and Raimund Wegener. "Asymptotic transition from cosserat rod to string models for curved viscous inertial jets." Mathematical Models & Methods in Applied Sciences 21.10 (2011): 1987-2018.
BibTeX: Download