A comprehensive lift force model for deformable bubbles rising in moderate shear flows

Abstract

We provide comprehensive regression models for the lift force coefficient $C_L$ and the terminal relative velocity for clean deformable bubbles in moderate shear flows. The models are expressed as functions of the a priori known Galilei ($\mathrm{Ga}$) and Eötvös ($\mathrm{Eo}$) numbers, eliminating the need for additional sub-models to predict, for example, the bubble shape. The proposed models are developed for a wide range of governing parameters (approximately $(3<\mathrm{Ga}<10000)$ and $(\mathrm{Eo}<20)$) and show good agreement with the existing numerical and experimental data. This robustness makes the models highly applicable to most practical gas–liquid systems. The $C_L$-model is particularly suited for moderate-to-high non-dimensional shear rates $\mathrm{Sr}=O(0.01-0.1)$, where the lift force is significant compared to other hydrodynamic forces.