In this paper, we investigate rotating electro-osmotic (EO) flow over an infinite plate or in a channel formed by two parallel plates. The analysis is based on the Debye-Hückel approximation for charge distributions and the Navier-Stokes equation for a transport electrolyte in the rotating frame. It is shown that, for the single plate, the nondimensional speed of system rotation $\omega$ is the singly most important parameter, while for the channel, in addition to $\omega$, the nondimensional electrokinetic width $K$ also plays an important role. However, the parameter $\omega \equiv {\eta }^2$ has different natural appearances in the respective cases of a single plate (SP) and two plates (TPs). More precisely, $\eta$(SP) measures the ratio ${\lambda }_D/L_K$ of the Debye length to the Ekman depth, while $\eta$(TP) measures the ratio $L/L_K$ of the channel width to the Ekman depth. The effect of rotation is always to reduce the axial flow rate along the direction of the applied electric field, accompanied by a (secondary) transverse flow. In the SP case, the plot on the velocity plane for each $\omega$ shows an interesting closed EO Ekman spiral. The size of the spiral shrinks with increasing $\omega$. The transverse flow is so significant that the volume transport associated with the EO Ekman spiral turns clockwise 45° to the applied field near $\omega =0$ and gradually turns at a right angle to the applied field as $\omega$ is increased. In contrast, in the TP case, the transverse flow rate is smaller than the axial flow rate when $\omega$ is small. The transverse flow rates at all $K$ are observed to reach their maxima at $\omega$ of order 1. The volume transport is nearly at a zero angle to the applied field near $\omega =0$ and gradually turns to 45° to the applied field as $\omega$ is increased. In the limit of $\omega \to \infty ,$ for both SP and TP cases, the entire system forms a rigid body rotation—there is neither axial nor transverse flow.

• Received 8 June 2011

DOI:https://doi.org/10.1103/PhysRevE.84.056320