Rotating electro-osmotic flow over a plate or between two plates.

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 ω is the singly most important parameter, while for the channel, in addition to ω, the nondimensional electrokinetic width K also plays an important role. However, the parameter ω≡η(2) has different natural appearances in the respective cases of a single plate (SP) and two plates (TPs). More precisely, η(SP) measures the ratio λ(D)/L(K) of the Debye length to the Ekman depth, while η(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 ω shows an interesting closed EO Ekman spiral. The size of the spiral shrinks with increasing ω. The transverse flow is so significant that the volume transport associated with the EO Ekman spiral turns clockwise 45° to the applied field near ω=0 and gradually turns at a right angle to the applied field as ω is increased. In contrast, in the TP case, the transverse flow rate is smaller than the axial flow rate when ω is small. The transverse flow rates at all K are observed to reach their maxima at ω of order 1. The volume transport is nearly at a zero angle to the applied field near ω=0 and gradually turns to 45° to the applied field as ω is increased. In the limit of ω→∞, for both SP and TP cases, the entire system forms a rigid body rotation-there is neither axial nor transverse flow.