摘要
This paper presents an analytical solution to periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in twodimensional uniform microchannel based on the Poisson-Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow. Dimensional analysis indicates that electric-viscous force depends on three factors： （1） Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state, （2） profile function describing the distribution profile of electro-viscous force in channel section, and （3） coupling coefficient reflecting behavior of arnplitude damping and phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number （Re = wh^2/v）. Flow-induced electric field varies very slowly with Re when Re 〈 1, and rapidly decreases when Re 〉 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.
This paper presents an analytical solution to periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in twodimensional uniform microchannel based on the Poisson-Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow. Dimensional analysis indicates that electric-viscous force depends on three factors： （1） Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state, （2） profile function describing the distribution profile of electro-viscous force in channel section, and （3） coupling coefficient reflecting behavior of arnplitude damping and phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number （Re = wh^2/v）. Flow-induced electric field varies very slowly with Re when Re 〈 1, and rapidly decreases when Re 〉 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.
基金
Project supported by the National Natural Science Foundation of China (No.10472036)
