A coupled level set and volume-of-fraction method is applied to investigate the impact of an oil droplet on an oil film containing a bubble. Subsequently, the deformation of the bubble is analyzed. Simulation results show two different movement forms of bubbles after an oil droplet impacts an oil film under different impacting velocities: stable deformation and bubble breaks. Bubble breaks originate from the combined action of surface tension and viscous shear force. Oil film thickness also affects bubble deformation. As the film thickness decreases, the deformation quantity of bubbles increases. Thus, bubbles are easily broken. This study provides a basic guide for bubble dynamics when a droplet impacts a film.

Impact of oil droplet on oil film usually takes place in the lubrication process of rotating mechanical parts and machinery which can easily lead to bubble entrainment. Bubbles have important influences on the motion process of the oil droplet impacting on the oil film and also on the formation quality of the oil film layer. An oil droplet impacting on the oil film which contains a bubble is simulated numerically based on the coupled level set and the method of determining volume fraction. The bubble deformation process in the oil film during an oil droplet impacting on the oil film is investigated by the simulation method. The influences of the bubble size and the bubble position on the bubble deformation characteristic are also analyzed. The dynamic mechanism of the bubble rupture is discussed. The numerical results show that as the oil droplet impacts on the oil film, the bubble may rupture on the free surface, presenting stable deformation, or rupture in the oil film, which is greatly influenced by the bubble size. When the bubble diameter is in a range between 10 m and 20 m, the bubble deformation becomes more serious with the increase of bubble diameter, and the rupture of bubble on the free surface may occur over time. When the bubble diameters are in a range between 20 m and 30 m, the bubble rupture occurs in a short time after the bubble has reached a maximum deformation, and there is no obvious relationship between the maximum bubble deformation and the bubble diameter. The diameter of 20 m is a critical value for a bubble to rupture on a free surface or inside an oil film, with which a bubble can keep stable in an oil film layer. As the bubble position changes, the bubble deformation process changes correspondingly. Under the same impact conditions, bubbles at the top of the oil film are more likely to deform than those in the center of the oil film. Bubbles at the bottom of the oil film have the smallest total deformation and finally attach to the wall. The bubble rupture is caused by the instability of the gas-liquid interface and the surface tension. The viscous shear force also plays an important role when the bubble rupture takes place in the oil film.

：In the oil-air lubrication system, the effective lubrication film is the key to ensure the lubrication effect, and its formation quality is closely related to the spreading flow process of the hollow oil droplets impacting the wall in the conveying airflow. To

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