Abstract
We consider the extensional flow and twist of a finite, slender, nearly straight, Newtonian viscous fibre when its ends are drawn apart at prescribed velocity. The initial cross-section of the fibre may be arbitrary and may vary graduallyin the axial direction. We derive the leading-order equations for the fibre's free surface and its flow velocity from a regular perturbation expansion of the full Stokes flow problem in powers of the aspect ratio. In order to obtain these equations systematically, it is necessary to consider terms beyond the leading order in the perturbation expansion
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