An Asymptotic Energy Equation for Modelling Thermo Fluid Dynamics in the Optical Fibre Drawing Process

Microstructured optical fibres (MOFs) are fibres that contain an array of air holes that runs through the whole fibre length. The hole pattern of these fibres can be customized to manufacture optical devices for different applications ranging from high-power energy transmission equipment to telecommunications and optical sensors. During the drawing process, the size of the preform is greatly scaled down and the original hole pattern result might be modified, potentially leading to unwanted optical effects. Because only a few parameters can be controlled during the fabrication process, mathematical models that can accurately describe the fibre drawing process are highly desirable, being powerful predictive tools that are significantly cheaper than costly experiments. In this manuscript, we derive a new asymptotic energy equation for the drawing process of a single annular capillary and couple it with existing asymptotic mass, momentum, and evolution equations. The whole asymptotic model only exploits the small aspect ratio of a capillary and relies on neither a fitting procedure nor on any empirical adjustable parameters. The numerical results of the simplified model are in good accordance with experimental data available in the literature both without inner pressurization and when internal pressure is applied. Although valid only for annular capillaries, the present model can provide important insights towards understanding the MOF manufacturing process and improving less detailed approaches for more complicated geometries.