The mathematical modelling of rotating capillary tubes for holey-fibre manufacture

Understanding and controlling the manufacturing process of producing (“drawing”) microstructured optical fibres (“holey fibres”) is of paramount importance in obtaining optimal control of the final fibre geometry and identifying industrially useful production regimes. The high cost of the manufacturing process and the challenge of ensuring reproducible final fibre geometries renders theoretical approaches invaluable. In this study the fluid dynamics of capillary drawing is examined using an extensional-flow asymptotic approach based on the small aspect ratio of the capillary. The key focus of the study is the additional effects that may be introduced by adding fibre rotation to the manufacturing process. Predictions are made concerning the effects of rotation, and a variety of asymptotic limits are examined in order to gain an understanding of the physics involved. Drawing regimes that are useful from a practical point of view are identified and the role of fibre rotation, both as a control measure (that may be used to influence the final geometry of a capillary) and as a means of reducing unwanted effects (such as fibre birefringence and polarisation model dispersion), is discussed.