Abstract:
This paper presents an analytical solution for periodical electroosmoticflows in a two-dimensional uniform microchannel based on Poisson-Boltzmannequations for electric double layer (EDL) and Navier-Stokes equation forincompressible viscous fluid. Analytical results indicate that thevelocities of periodical electroosmosis strongly depend on Reynoldsnumber $Re = \omega h^2 / \nu $, as well as on EDL properties and the appliedelectric field. The slip velocity of EDL decreases as the Reynolds numberincreases. The electroosmosis velocity outside the EDL rapidly decreases,and the lag phase angle of the velocity increases as the distance away from thechannel wall increases. A wave-like velocity profile across the microchannelis found. An asymptotic solution for low Reynolds number is also given inthis paper. Periodical electroosmosis with low Reynolds has the samevelocity amplitude and a plug-like velocity profile as that of the steadyelectroosmosis. Debye-H\"{u}ckel approximate solution of the periodicalelectroosmosis in cases of small $\kappa h$, the ratio of the microchannelwidth to EDL thickness, is obtained and compared with the analyticalsolution.
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