A mathematical model has been developed to determine the optimum bubble size for the removal of inclusions from molten metals by flotation. The probability of collision between a bubble and an inclusion, P_C, and the probability of adhesion of an inclusion to a bubble by sliding, P_A, are defined to describe the efficiency of inclusion attachment to a bubble. The results show that small bubbles have a high P_C, while small inclusions have a high P_A and low P_C. By considering the overall probability, P (=P_C×P_A), and the floating time of the bubble, the model suggests that the optimum bubble sizes for the removal from steel of alumina inclusions less than 50 μm in size are in the range of 0.5 to 2 mm in diameter.