Chang Chien-Cheng, Wang Chang-Yi
Division of Mechanics, Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056320. doi: 10.1103/PhysRevE.84.056320. Epub 2011 Nov 22.
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.
在本文中，我们研究了无限大平板上或由两块平行平板形成的通道内的旋转电渗流。该分析基于电荷分布的德拜 - 休克尔近似以及旋转坐标系中传输电解质的纳维 - 斯托克斯方程。结果表明，对于单板情况，系统旋转的无量纲速度ω是唯一最重要的参数，而对于通道情况，除了ω之外，无量纲电动宽度K也起着重要作用。然而，参数ω≡η(2)在单板（SP）和两块板（TPs）的各自情况下具有不同的自然表现形式。更确切地说，η(SP)测量德拜长度与埃克曼深度的比值λ(D)/L(K)，而η(TP)测量通道宽度与埃克曼深度的比值L/L(K)。旋转的作用总是降低沿外加电场方向的轴向流速，并伴有（二次）横向流。在SP情况下，每个ω在速度平面上的曲线图显示出一个有趣的封闭电渗埃克曼螺旋。螺旋的尺寸随着ω的增加而缩小。横向流非常显著，以至于与电渗埃克曼螺旋相关的体积输运在ω = 0附近顺时针旋转45°至外加电场方向，并随着ω的增加逐渐旋转至与外加电场成直角。相比之下，在TP情况下，当ω较小时，横向流速小于轴向流速。观察到所有K值下的横向流速在ω约为1时达到最大值。体积输运在ω = 0附近几乎与外加电场成零角度，并随着ω的增加逐渐旋转至与外加电场成45°。在ω→∞的极限情况下，对于SP和TP两种情况，整个系统都形成刚体旋转，既没有轴向流也没有横向流。
