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

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 ( Ga ) and Eötvös ( 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 < Ga < 10000 ) and ( 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 Sr = O ( 0 . 01 − 0 . 1 ) , where the lift force is significant compared to other hydrodynamic forces. • Comprehensive model for the shear-induced lift force acting on rising bubbles. • Comprehensive model for the relative terminal velocity of rising bubbles. • Dimensional analysis yields the a priori known Galilei and Eötvös governing numbers. • Models developed for very wide relevant ranges of the governing parameters.