Analytic approximation for the collapse of viscous tubes driven by surface tension and pressure difference

Abstract

AbstractIn this work, an approximate analytic formula is developed which accurately models the one-dimensional collapse kinetics of viscous glass tubes, driven by surface tension and low-to-moderate pressure differences. This is in contrast to existing analytic approaches from the literature where either surface tension is the only driving force, or extremely high pressure differences are assumed. Extensive model validation is provided against numerical computation of the exact one-dimensional and two-dimensional models for cross-sectional collapse, as well as with experimental data from the literature. Practical utility of this formula is demonstrated for effortlessly solving the inverse problem for determining the viscosity and surface tension of glass tubes.