A semianalytical solution of periodical electro-osmosis in a rectangular microchannel

This paper presents a semianalytical solution to study the flow behavior of periodical electro-osmosis in a rectangular microchannel based on a nonlinear Poisson–Boltzmann equation and Navier–Stokes equation. The analytical results indicate that the velocity of periodical electro-osmosis strongly depends on the Reynolds number Re=ωH2∕ν, the properties of electric double layer, and the applied electric field. When the Reynolds number is low, the velocity amplitude of periodical electro-osmosis is the same as that of steady electro-osmosis, and it shows a square plug-like profile. When the Reynolds number is high, the velocity of periodical electro-osmosis decreases rapidly from the solid wall to the channel center, and it shows a bowl-like velocity profile varying with time. It is also found that the slip velocity of periodical electro-osmosis and its instantaneous flow rate in a microchannel decrease as the Reynolds number increases. Numerical solutions are also given in this paper, which are in good agreement with the semianalytical solutions.