Please Help! Smoke bomb effect in AE

Thanks to everybody on this question. I wil try ShiveringCactus suggestion per link provided.

That's pretty clearly a fluid simulation in a 3D program, but lucky enough it's super simple and thus easy enough to create something similar in AE. The real trick is to animate layers and layers of circles and Roughen them up with effects like Turbulent Displace, Roughen Edges and others while animating their radius/ scale and opacity. The basic ingredients are really simply, though it will take time to tweak the parameters for each of the individual effects at any given time.

Mylenium 

Not sure you can achieve this effect with the native effects included in After Effects. You can try Trapcode Particular or Superluminal Stardust (particle effects) to create something in that way.