Ascending non-Newtonian long drops in vertical tubes

We report on theoretical and experimental studies describing the buoyancy-driven ascent of a Taylor long drop in circular vertical pipe where descending fluid is Newtonian, ascending non-Newtonian yield shear thinning described by three-parameter Herschel–Bulkley model, including Ostwald–de Waele model as special case for zero yield. Results Ellis are included to provide more realistic description purely shear-thinning behaviour. In all cases, lubrication theory allows us obtain velocity profiles corresponding integral variables closed form, lock-exchange flow with net rate. The energy balance derive asymptotic radius inner current, stable node differential equation time evolution core radius. carried out series experiments measuring rheological properties fluids, speed drop. For some tests, we measured profile ultrasound velocimetry technique. current compares fairly well derived through balance, shows good agreement model. also agree their counterparts. have developed dynamic similarity conditions establish whether laboratory physical models, limited availability real fluids defined characteristics, can be representative phenomena large scale, such exchanges volcanic conduits. Appendix B contains scaling rules approximated process analysed; these serve guide design reproducing phenomena.