A universal model for drag on a spherical bubble

TL;DR

This paper presents a comprehensive theoretical model for the drag force on spherical bubbles across all flow regimes, demonstrating accurate predictions of terminal velocity over a wide range of Reynolds numbers.

Contribution

A new theoretical expression for bubble drag that applies across viscous and inertial flow conditions, matching empirical data.

Findings

Excellent agreement with empirical models by Mei et al.

Predicts bubble terminal velocity accurately across many Reynolds numbers.

Provides a simple physics-based framework for drag prediction.

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.