Heat-induced stretching of a glass tube under tension: Application to glass microelectrodes

Deformation of glass using heat occurs in many industrial and artistic applications, including the manufacturing of laboratory glass products, drawing of fiber optics, and hand-blown artistic creations. The formation of glass objects is an art, but the trial-and-error aspect of the procedures can be reduced by development of a systematic theory, especially when the objects are formed using mechanical means. Glass microelectrodes are ubiquitous in experimental studies of the electrophysiology of biological cells and their membranes, and the pulling of these electrodes is based on trial-and-error. To make this process more systematic, we derive a model for glass microelectrode formation using a coil heater with a gravity-forced electrode puller, assuming that the glass tube is an incompressible, viscous fluid. The model is one-dimensional, and the effects of thermal radiation from the coil heater are essential in the formation process. A breaking stress criterion is imposed to fracture the glass tube, forming the electrode tip. The difficulty with the moving free end is avoided by introducing a quasi-Lagrangian coordinate system. The model equations are solved using an adaptive moving grid to account for the local stretching of the glass. A number of examples using a double-pull paradigm have been computed to illustrate the dependence of the electrode shape and tip diameter on the heater temperature and the ratio between the inner and outer radii.