Resumen
Optical fibers are made of glass with different refractive indices in the (inner) core and the (outer) cladding regions. The difference in refractive indices arises due to a rapid transition in the concentration of a dopant across the boundary between these two regions. Fibers are normally drawn from a heated glass preform, and the different dopant concentrations in the two regions will change due to dopant diffusion and convective transport induced by the flow. In this paper, we analyze a mathematical model for the dynamics of dopant concentration changes during the fiber drawing process. Using a long-wave approximation, we show that the governing equations can be reduced to a simple diffusion equation. As a result, we are able to identify key dimensionless parameters that contribute to the diffusion process. We also derive asymptotic solutions for the temperature, cross-sectional area, and effective diffusion coefficient when there are strong temperature dependencies in the viscosity and the diffusion coefficient. Our simplified model and asymptotic solutions reduce the need for extensive numerical simulations and can be used to devise control strategies to limit excess dopant diffusion.