Self-drainage of viscous liquids in vertical and inclined pipes

The rate of drainage of a viscous liquid from initially full cylindrical tubes inclined at various angles to the vertical (0°, 30°, 45° and 60°) was studied in glass and polymethylmethacrylate (Perspex™) tubes of various lengths and diameters using three food materials: honey (Newtonian) and two variants of Marmite™ spread (both exhibiting complex rheological behaviour, including shear-thinning and thixotropy). The behaviour was marked by an initially steady rate of drainage in which an air slug descended the tube, followed by slower drainage from an annular film remaining on the wall. Eventually the liquid stopped draining as a filament and entered a dripping regime. Drainage was insensitive to the tube material, whereas the stages of drainage were influenced by the geometry and angle of inclination. Quantitative models are presented for the rate and extent of the initial drainage stage, the rate in a second linear stage (where it existed), and the rate of drainage in the third, falling rate stage. The fourth and final stage, characterised by drop formation, was not modelled. The initial rate can be predicted with reasonable accuracy, allowing the time to remove approximately 50% of the material in a short waiting phase to be calculated, e.g. t = 8νL/R2g for a Newtonian liquid with kinematic viscosity ν in a vertical pipe of radius R and length L. The agreement with the other models is less exact but they capture the general trends reasonably.