Modeling the fabrication of hollow fibers: capillary drawing

Abstract

Abstract-A method for modeling the fabrication of small-scale hollow glass capillaries is developed. The model is based on an asymptotic analysis of the Navier-Stokes equations, which yields a simple closed-form solution for this problem. We demonstrate the validity of this approach using experimental data and use it to make predictions for a range of regimes of interest for the development of microstructured optical fiber technology.Index Terms-Mathematical modeling, optical fiber, optical fiber applications, optical fiber fabrication, optical fiber theory.

Mathematical Modeling as an Accurate Predictive Tool in Capillary and Microstructured Fiber Manufacture: The Effects of Preform Rotation

“…4 show that the error in predicted values varies between approximately 3% and 21%, which we consider to represent excellent agreement given the uncertainty and possible error in the viscosity assumed, the value for surface tension used, and the possible error in the furnace temperature profile. Such good agreement betters the previous agreement of approximately 20% error achieved in [11] with the use of a fitting parameter.…”

“…In order to make comparisons with experimental data while avoiding the need to use the viscosity, surface tension or a combination of the two as fitting parameters [11] it is necessary to accurately determine both the temperature dependence of the glass viscosity and the temperature distribution within the furnace.…”

“…For example, [11] successfully compared the results of theoretical predictions for inner and outer diameter with experimental results, but because it can be difficult to ascertain the absolute glass temperature during fiber drawing, the authors state that "while the three drawing temperatures are likely to be accurate relative to each other, it is possible that they may suffer from an absolute temperature offset by as much as 50 C , we therefore fitted the theoretical model to the experimental data by choosing the parameter [surface tension to viscosity ratio]".…”

Collapsing of glass tubes: analytic approaches in a hydrodynamic problem with free boundaries

“…There is a large series of papers on analytic approaches of the drawing problem since the 1970s (e.g., [9,10,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]), but only fewer papers involve an analytic treatment of collapsing [1][2][3][4][5][6][7][8] since the 1980s. The approaches on drawing (axial symmetry assumed) favor a perturbation analysis with the prerequisite of a dominating axial viscous flow and axial viscous flow gradient, small axial viscosity dependence, and small inclination of the rod boundary (or tube boundaries) against the rotation axis, as typical for capillary geometries.…”

“…Also, the perturbation analysis has been proven to be rather powerful to include accompanying effects such as the stability (e.g., [9,10,16,17]), temperature-dependent viscosity (e.g., [9,10,14,18,19]), as well as heat conduction, convection, and radiation (e.g., [9,10,15,16]). Recently, it is applied to the drawing of hollow and structured fibers (e.g., [9,22,[25][26][27][28][29]). A substantial analysis of the mathematical and physical concepts on the perturbation treatment of drawing of tubes is given in the extended paper of Fitt et al [9].…”