A universal model for drag on a spherical bubble

Abstract

A theoretical expression for the drag on a spherical bubble is derived for the entire range from very viscous to inertial flow conditions. It is based on a solution for only that part of the velocity profile that determines the drag. It is assumed the surface of the bubble has a zero tangential stress condition. Excellent agreement with a previously proposed empirical model by Mei et al. is obtained. This shows that a theoretical framework with relatively simple physics can still predict the terminal velocity of a spherical bubble accurately. To the best of our knowledge, this is one of the few models in fluid dynamics to predict drag on an object for a range of Reynolds numbers that spans many orders of magnitude.