Pendant drops shed from a liquid lens formed by liquid draining down the inner wall of a wide vertical tube
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Abstract
When a viscous liquid empties from an initially full, wide vertical tube, the drainage behaviour changes from a filament to a regime in which individual drops are shed by a lens formed at the end of the tube: liquid drains down the wall and the lens grows until it becomes unstable. This drop shedding regime was investigated for four Newtonian liquids (rapeseed oil, glycerol, honey and golden syrup) in three tube sizes and two tube materials (Bond number based on tube i.d. > 1 in all cases). The drop mass increased modestly with flow rate and the equivalent sphere diameter, d, was strongly related to the capillary length Lc ≡ (γ/ρg)1/2 rather than the tube diameter. The results were fitted to a correlation of the form d/Lc = f(Bond, Reynolds, Morton, sin(contact angle)) derived from dimensional analysis. The data were compared with existing models for drop formation from filled narrow capillaries and a new, simple model based on a quasi-static model of the lens. Agreement with these models was poor, particularly for larger tubes, indicating the need for more detailed analysis. Insights into the dynamics, generated by video analysis of the lens shape, are presented.
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1879-2286