SLENDER VISCOUS FIBERS WITH INERTIA AND GRAVITY

We derive the leading-order extensional flow equations for the tapering 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 equations 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 irreversibility of fibre motion.