Fiber Coating: Non-Unique Solutions at Small Capillary Numbers

Surface tension dominated axially-symmetric flows, relevant to the application of thin coatings on optical fibers, are considered for pressurized dies using lubrication theory. Typical geometries are such that the clearance between the die exit and the fiber is small compared with the fiber diameter. Previous analyses have been concerned with flows controlled by axial curvature. For this situation the resulting solutions are unique. This investigation examines flows in which both the axial and the azimuthal curvatures are comparable. Moreover, as the initial die clearance is increased, it is found that oscillatory free surface shapes occur which can lead to non-uniform coating thicknesses. Existence of these oscillations implies that the solution is not always unique. These results are new, and the calculations presented here determine the maximum die clearance below which the solution is unique. Within this regime, surface oscillations do not occur and there is a monotonic decay to the final uniform coating thickness.