The mathematical modelling of capillary drawing for holey fibre manufacture

Microstructured optical fibres (i.e. fibres that contain holes) have assumed a high profile in recent years, and given rise to many novel optical devices. The problem of manufacturing such fibres by heating and then drawing a preform is considered for the particularly simple case of annular capillaries. A fluid-mechanics model is constructed using asymptotic analysis based on the small aspect ratio of the capillary. The leading-order equations are then examined in a number of asymptotic limits, many of which give valuable practical information about the control parameters that influence the drawing process. Finally, some comparisons with experiment are performed. For a limited set of experiments where the internal hole is pressurised, the theoretical predictions give qualitatively accurate results. For a much more detailed set of experiments carried out with a high-grade silica glass where no hole pressurisation is used, the relevant asymptotic solution to the governing equations is shown to give predictions that agree remarkably well with experiment.