Controlling fluid flows in micro scales is a non-trivial issue among those who are involved in designing lab-on-chips. Pumping and mixing by using electrokinetic principles has been popular in that the method requires a few parts and it is easy to control. This paper explains the basic mechanism of the electroosmotic flows caused by AC together with presenting some numerical results. In particular, the fundamental, physical idea involved in the mechanism will be illustrated in terms of the kinematic aspect. Since the electroosmotic flows are mainly driven by the motion of ions, we also demonstrate the ion motions by using the numerical-visualization method.