An analytical study of a purely electroosmotic flow in a rotating microchannel under the influence of a time-dependent external electric field is presented. The present analysis relies on the Debye–H \(\ddot{\text {u}}\) ckel approximation for charge distributions and the Navier–Stokes equations describing the behaviour of the transport of electrolyte solution in a rotating frame. A parametric study of the flow reveals interesting physics ranging from ‘plug-like’ flow cases to oscillatory wave-like flow. The velocity profiles conform to the presence of inflection points indicating the possibility of the existence of instabilities in the flow. The possible presence of instabilities is mainly due to the rotational Reynolds number and the Womersely number.