Abstract: A mathematical model for the gas-liquid flow field in the ladle with argon blowing was built based on the Euler-Euler model and population balance model(PBM)， which considered the effects of the drag force， lift force， turbulent dispersion force and bubble coalescence and breakage in ladle with argon blowing. The effects of bubble coalescence and breakage on the gas holdup， bubble velocity and mixing time were investigated and further compared with those from the constant diameter model. The numerical results show that the predicted data of the PBM agrees well with the experimental one. The bubble diameter is the largest one in center area and reduces gradually from the center to the gas-liquid interface， therefore it becomes the smallest one at gas-liquid interface in the ladle. At the ladle central axis， the bubble velocity firstly increases drastically and then decreases gradually， however， it decreases greatly near the free surface.

Key words: ladle, bubble, coalescence and breakage, Luo model, PBM