微通道周期流动电位势及电粘性效应

Periodical Streaming Potential and Electro-Viscous Effects in Microchannel Flow

求解了双电层的Poisson-Boltzmann方程和流体运动的Navier-Stokes方程,得到在周期压差作用下,二维微通道的周期流动电位势,流动诱导电场和液体流动速度的解析解.量纲分析表明,流体电粘性力与以下3个参数有关:1)电粘性数,它表示定常流动时,通道最大电粘性力与压力梯度的比;2)形状函数,它表示电粘性力在通道横截面的分布形态;3)耦合系数,它表示电粘性力的振幅衰减特征和相位差.分析结果表明,微通道周期流动诱导电场、流动速度与频率Reynolds数有关.在频率Reynolds数小于1时,流动诱导电场随频率Reynolds数变化很慢.在频率Reynolds数大于1时,流动诱导电场随频率Reynolds数的增加快速衰减.在通道宽度与双电层厚度比值较小情况下,电粘性效应对周期流动速度和流动诱导电场有重要影响.

An analytical solution of periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in two-dimensional uniform microchannel based on Poisson- Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow was present- ed. Dimensional analysis indicates that electric-viscous force depends on three factors： 1） Electricviscous coefficient representing a ratio of maximum of electric-viscous force to pressure gradient in steady state; 2） Profile function describing distribution profile of electrio-viscous force in channel sec- tion; 3） Coupling coefficient reflecting behavior of the amplitude damping and the phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number. Flow-induced electric field varies very slowly when frequency Reynolds number is less than 1, and rapidly decreases when frequency Reynolds number is larger than 1. Electro-viscous effect on flow-induced electric field and flow velocity are very significant when the rate of the channel width to the thickness of electric double layer is small.