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The Quarterly Journal of Mechanics and Applied Mathematics 1994 47(4):541-555; doi:10.1093/qjmam/47.4.541
© 1994 by Oxford University Press
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SLENDER VISCOUS FIBRES WITH INERTIA AND GRAVITY

J. N. DEWYNNE, P. D. HOWELL and P. WILMOTT{dagger}

( Department of Mathematics, Southampton University Southampton SO9 5NH
Mathematical Institute 24–29 St Giles, Oxford OX1 3LB
{dagger}And at: Department of Mathematics, Imperial College London SW7 2B2 )

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.


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