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

Abstract

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.