Physics of the formation of fiber lightguides

Abstract

A fiber lightguide is a fine continuous or tubular transparent filament. Fiber lightguides are formed from the liquid mass exuded through a dye or drawn from a suitable blank. Both of these processes can be considered using the equations of the hydrodynamics of an incompressible Newtonian liquid. (Polymers, which are not Newtonian liquids, are not considered here.) The drawing of a continuous glass fiber from a dye is considered in [1]. The drawing of a microcapillary from a dye is considered in [2], where a qualitative consideration is given which is insufficient for an understanding of the effect of different parameters of the process on the dimensions of the drawn microcapillary. In this paper we consider the formation of a microcapillary from a tubular blank using the approximation of an incompressible Newtonian liquid with a variable viscosity determined by the given temperature distribution. The effect of surface tension and of the excess pressure produced in the channel to counteract the surface tension are taken into account. It is assumed that the drawing process is steady, the blank has thin walls and is axisymmetrical, and the transition to a microcapillary occurs smoothly. With these assumptions the problem of obtaining the shape of the transition and the dimensions of the microcapillary obtained is reduced to a system of ordinary differential equations. The dependence of the dimensions of the microcapillary on the dimensions of the blank and the parameters of the process is established, thereby enabling the process to be optimized.