**Authors:**
Rubén Bãnos,
José Arcos,
Oscar Bautista,
Federico Méndez

**Abstract:**

The Oscillatory electroosmotic flow (OEOF) 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-H¨uckel 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 angular Reynolds number, Reω, the electrokinetic
parameter, ¯κ, 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 profiles become more and more non-uniform across the
channel-width as the Reω and ¯κ are increased, so oscillatory OEOF
can be really useful in micro-fluidic devices such as micro-mixers.

**Keywords:**
Oscillatory electroosmotic flow,
Non-Newtonian
fluids,
power-law model,
low zeta potentials.

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