2015/07/15 by Thomas Götz, Götz, Thomas, Axel Klar +1
Chemical Engineering · Chemistry · Engineering · Mathematics · Physics and Astronomy · #76D25 #76U05 #Chemistry #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Geometry #Inverse #Inviscid flow #Isothermal process #Lattice Boltzmann Simulation Studies #Limit (mathematics) #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Physics #Reynolds number #Rheology and Fluid Dynamics Studies #Rossby number #Spinning #Surface tension #Thermodynamics #math-ph #math.DS #math.MP #msc:76D25 #msc:76U05
paper · pdf · doi:10.48550/arxiv.1507.04200
published in arXiv (Cornell University) (Cornell University) · 9 pages, 4 figures
arxiv created 2015/07/15 · openalex publication_date 2015/07/15 · arxiv updated 2015/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Reduced one-dimensional equations for the stationary, isothermal rotational spinning process of slender fibers are considered for the case of large Reynolds (δ=3/Re≪ 1) and small Rossby numbers (ε ≪ 1). Surface tension is included in the model using the parameter κ=√π/(2 We) related to the inverse Weber number. The inviscid case δ=0 is discussed as a reference case. For the viscous case δ> 0 numerical simulations indicate, that for a certain parameter range, no physically relevant solution may exist. Transferring 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 δ> 3ε2 ( 1- (3)/(2)κ+(1)/(2)κ2) no physical relevant stationary solution can exist.