Scaling parameters of bubbles and drops; interpretation and case study with air in silicon oil

Buoyancy-driven bubbles and drops are deformable and exhibit different boundaries from mobile to immobile. Owing to the complexity of these flows, the literature knows various scaling parameters for their description. This paper determines a set of parameters on the basis of the force balance equations. It identifies the Archimedes number as the leading parameter while the Reynolds number is considered a flow variable. This ordering scheme of parameters is applied to a set of new data on bubbles rising in five different silicon oils. Data representation and limiting cases come out consistently. The use of the Archimedes number leads even to a successful simple model for the normalized rise velocity.