Numerical evidence for the non-existence of stationary solutions to the equations describing rotational fiber spinning

Abstract

The stationary, isothermal rotational spinning process of fibers is considered. The investigations are concerned with the case of large Reynolds (delta = 3/Re « 1) and small Rossby numbers (epsilon « 1). Modelling the fibers as a Newtonian fluid and applying slender body approximations, the process is described by a two-point boundary value problem of ODEs. The involved quantities are the coordinates of the fiber's centerline, the fluid velocity and viscous stress. The inviscid case delta = 0 is discussed as a reference case. For the viscous case delta > 0 numerical simulations are carried out. Transfering some 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 delta > 3 epsilon(2) no physical relevant stationary solution can exist.