Unsteady stretching of a glass tube with internal channel pressurization

Abstract

Mathematical modeling is used to examine the unsteady problem of heating and pulling an axisymmetric cylindrical glass tube with an overpressure applied within the tube to form tapers with a near uniform bore and small wall thickness at the tip. To allow for the dependence of viscosity on temperature, a prescribed axially varying viscosity is assumed. Our motivation is the manufacture of emitter tips for mass spectrometry which provide a continuous fluid flow and do not become blocked. We demonstrate, for the first time, the feasibility of producing such emitters by this process and examine the influence of the process parameters, in particular the pulling force and over-pressure, on the geometry. There is not a unique force and over-pressure combination to achieve the desired geometry at the tip but smaller over-pressure (hence force) yields a more uniform bore over the entire length of the emitter than does a larger over-pressure (and force). However, the sensitivity of the geometry to small fluctuations in the parameters increases as the over-pressure decreases. The best parameters depend on the accuracy of the puller used to manufacture the tapers and the permissible tolerances on the geometry. The model has wider application to the manufacture of other devices.