Flow behavior of periodical electroosmosis in microchannel for biochips
生物芯片微通道周期性电渗流特性

This paper presents an analytical solution for periodical electroosmotic flows in a two-dimensional uniform microchannel based on Poisson-Boltzmann equations for electric double layer (EDL) and Navier-Stokes equation for incompressible viscous fluid. Analytical results indicate that the velocities of periodical electroosmosis strongly depend on Reynolds number $Re = \omega h^2 / \nu $, as well as on EDL properties and the applied electric field. The slip velocity of EDL decreases as the Reynolds number increases. The electroosmosis velocity outside the EDL rapidly decreases, and the lag phase angle of the velocity increases as the distance away from the channel wall increases. A wave-like velocity profile across the microchannel is found. An asymptotic solution for low Reynolds number is also given in this paper. Periodical electroosmosis with low Reynolds has the same velocity amplitude and a plug-like velocity profile as that of the steady electroosmosis. Debye-H\"{u}ckel approximate solution of the periodical electroosmosis in cases of small $\kappa h$, the ratio of the microchannel width to EDL thickness, is obtained and compared with the analytical solution.