Discrete model for the swelling of a sealed capillary in a high-temperature furnace with a nonuniform axial temperature profile

A discrete model for the swelling of a sealed glass capillary in a high-temperature furnace with an arbitrary axial temperature profile is proposed. A system of ordinary differential equations describing the swelling kinetics of the capillary is obtained, as well as a system of algebraic equations for finding the axial profile of the maximally swollen capillary. Two swelling modes are analyzed: the swelling mode of a stationary fixed capillary and the swelling mode of a capillary moved into a high-temperature furnace with a constant or variable rate. The results of the numerical calculations were verified experimentally for the case of sintering of capillary assemblies used as preforms for microstructured optical fiber.