SLENDER VISCOUS FIBERS WITH INERTIA AND GRAVITY

We derive the leading-order extensional flow equations for the taperin g or unsteady drawing of a slender fibre of viscous fluid when inertia and gravity effects are significant. The analysis employs systematic asymptotic expansions in the slenderness parameter and goes to second order to find a well-posed problem at leading order. We find the equat ions of motion for the cross-flow, the extensional velocity, the cross -sectional area, the translation of the cross-section and its rotation . Inertia effects are shown to have important implications for the irr eversibility of fibre motion.