This paper discusses the problem of the swelling of a fused quartz tube when it is heated locally. An equation is obtained that describes the viscous-flow kinetics of the melted section of the tube. Studies were carried out of how the maximum swelling diameter of the tube and the time it takes to swell depend on the relative length of the heated section of the tube and on its temperature. The results are experimentally checked when single quartz capillaries swell, as well as when a capillary assembly consisting of blanks for drawing microstructured optical fiber with two layers of air holes is sintered.
A. A. Zamyatin and A. A. Makovetskii, "Swelling of fused capillaries in capillary assemblies," J. Opt. Technol. 73, 55-60 (2006)