The liquid entrainment process at the vertical up tee branch is widespread in mass and heat transfer applications. Existing liquid entrainment models mainly apply to T-junctions with small diameter ratios of branch to main line (d/D), which are unable to predict the liquid entrainment under large d/D conditions. The models of liquid entrainment onset and entrainment rate are developed under reasonable assumptions. The entrainment onset model was developed based on the wave theory, force analysis and potential flow theory. The Bond number is innovatively introduced into the model to represent the effect of surface tension acting on the entrainment onset. The model is compared against the relevant experimental data which shows good agreement. In the modeling of the entrainment rate, the key parameters are obtained by nondimensionalizing the conservation equations governing the liquid entrainment process, and the constants in the model are determined by genetic algorithm. The model agrees well with existing experimental data. (C) 2017 Elsevier Ltd. All rights reserved.