Based on a model of a thin-walled cylindrical tube, formulas are obtained that give a quantitative description of the shrinkage of microcapillary structures when they are heated. The resulting formulas establish the interconnection between the geometrical parameters of microcapillaries and the rates at which they shrink with the viscosity and surface tension of the glass from which they are fabricated. That is, on the basis of experimental data on the shrinkage rates of microcapillaries in the radial and axial directions, a new method has been developed for measuring the surface tension of glass in the high-viscosity state all the way to the softening and glass-annealing temperatures. The temperature gradient of the surface tension in this interval is much greater than the analogous data obtained for the melting of glass.
A. A. Zhilin, Z. I. Kanchiev, B. V. Tatarintsev, and V. Kh. Yagmurov, "Measuring the surface tension of glass in the temperature region of softening and viscous flow," J. Opt. Technol. 70, 888-891 (2003)