Terminal Velocity of Canola Oil, Hexane, and Gasoline Drops Rising in Water due to Buoyancy

Drops, globules of a liquid in another liquid, are extremely important in many natural processes and industrial applications. The purpose of this study was to devise a method to measure the terminal velocity of drops rising in water due to buoyancy, and to compare observed values with the theoretical. Two questions were explored: (1) Do these drops continue to accelerate upward from a depth of 6 cm; and, (2) Does the terminal velocity of these drops (modifying the experiment accordingly if not) match the theoretical (calculated) values? A syringe was used to inject 0.1 cm (0.1 mL) drops of three liquids (oil, hexane, and gasoline) into a vessel at a depth of 6 cm, and the resulting motion w as video captured and imported into the shareware kinematics program Tracker® for analysis and determination of terminal velocity. The experiments showed that the drops reached terminal velocity before reaching the surface (2.23 ± 0.10 cm, 1.48 ± 0.07 cm, and 1.35 ± 0.06 cm above the injection point, respectively). Secondly, in addition to the accepted term of πr normally used for the projected area in the theoretical equation for terminal velocity, a new term, 2πr, was also employed in order to account for drop f lattening during ascension. As a result, the calculated value with the new term accurately predicted the observed, doing so better than the accepted term for all three liquids, and might be used to improve the accepted theory.