Evolution of an elliptical bubble in an accelerating extensional flow

The manufacture of optical fibers typically involves taking a solid glass cylinder (a blank or preform), heating it up to melting temperature by feeding it through a cylindrical furnace (the drawing tower), and drawing the molten blank from the other end of the furnace at high speed (tens of meters per second). Since the drawing speed is much faster than the feeding speed (by a factor of at least ten), along with the temperature dependence of the fiber viscosity, the molten preform stretches out, and a thin viscous fiber is formed, which rapidly cools and solidifies on exiting the drawing tower. The basic geometry is sketched in Figure 1. The temperature of the furnace surrounding the fiber is known (prescribed) as a function of distance along the axis of the furnace, a typical temperature profile is shown in the figure. If one assumes that within the tower the fiber is sufficiently thin that its temperature is everywhere equal to the external furnace temperature, then the viscosity of the molten glass is known as a function of axial position (since the viscosity of the molten glass is known empirically as a function of temperature). The solid preforms may contain gas bubbles, either through accident (defects in the manufactured preform) or intent (deliberate inclusion of bubbles in the preform could allow manufacture of sections of fiber with holes, which are desirable for many applications [1, 2]; as the fibre is stretched the bubble can elongate enormously). Scientists and engineers at Corning wish to gain a better understanding of how such bubbles would evolve during the draw-down process. In particular, they are interested in finding answers to the following questions: