A modified mathematical model is used to study the effects of various forces on the stability of cavitation bubbles within a diesel droplet. The principal finding of the work is that viscous forces of fluids stabilize the cavitation bubble, while inertial force destabilizes the cavitation bubble. The droplet viscosity plays a dominant role on the stability of cavitation bubbles compared with that of air and bubble. Bubble-droplet radius ratio is a key factor to control the bubble stability, especially in the high radius ratio range. Internal hydrodynamic and surface tension forces are found to stabilize the cavitation bubble, while bubble stability has little relationship with the external hydrodynamic force. Inertia makes bubble breakup easily, however, the breakup time is only slightly changed when bubble growth speed reaches a certain value (50m.s(-1)). In contrast, viscous force makes bubble hard to break. With the increasing initial bubble-droplet radius ratio, the bubble growth rate increases, the bubble breakup radius decreases, and the bubble breakup time becomes shorter. (C) 2014 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.