Slippage effect on the oscillatory electroosmotic flow of power-law fluids in a microchannel

The oscillatory electroosmotic flow (OEOF) under the influence of the Navier slip condition in power law fluids through a microchannel is studied numerically. A time-dependent external electric field (AC) is suddenly imposed at the ends of the microchannel which induces the fluid motion. The continuity and momentum equations in the x and y direction for the flow field were simplified in the limit of the lubrication approximation theory (LAT), and then solved using a numerical scheme. The solution of the electric potential is based on the Debye-Hückel approximation which suggest that the surface potential is small, say, smaller than 0:025V and for a symmetric (z:z) electrolyte. Our results suggest that the velocity profiles across the channel-width are controlled by the following dimensionless parameters: the dimensionless slip length δ, the Womersley number, W, the electrokinetic parameter, k, defined as the ratio of the characteristic length scale to the Debye length, the parameter λ which represents the ratio of the Helmholtz- Smoluchowski velocity to the characteristic length scale and the flow behavior index, n. Also, the results reveal that the velocity magnitude gets higher values as δ increases and become more and more nonuniform across the channel-width as the W and k are increased, so OEOF can be useful in micro-fluidic devices such as micro-mixers.