Regularized thin-fiber model for nanofiber formation by centrifugal spinning

We propose a regularized thin-fiber (string) model that overcomes past numerical limitations and allows determination of the steady fiber velocity and diameter of a semi-infinite Newtonian viscous fiber emerging from a nozzle rotating about an axis in the presence of centrifugal, inertial, and viscous forces of arbitrary magnitudes. The results are controlled by two dimensionless groups, namely, the Rossby number Rb expressing the ratio of inertial to centrifugal forces and the Reynolds number Re, the ratio of inertial to viscous forces. We find that for Rb < 0.5 and Re < 1, regularization of the string-model equations is required to provide numerical stability, which we achieve. Solutions are thereby obtained in which viscosity reduces curvature in the fiber trajectory; these solutions asymptotically approach the inviscid solution at large distances along the spin line. Thus, long spin lines reach a diameter that is independent of viscosity, as long as the fiber is sufficiently long, a criterion that is made clear in the paper. At Rb > 0.5, regularization is not required, the curvature in fiber trajectory is increased by viscosity, and the solution at large distances along the spin line does not converge to the inviscid result. Regimes of behavior in the plane formed by Re and Rb are mapped out and example behavior is given for each regime.