  Numerical analyses of transient electro-osmosis of a typical non-Newtonian
liquid induced by DC and AC electric fields in a rectangular microchannel are
conducted in the framework of continuum fluid mechanics. The famous power-law
constitutive model is used to express the fluid dynamic viscosity in terms of
the velocity gradient. Transient start-up characteristics of electro-osmotic
power-law liquid flow in rectangular microchannels are simulated by using
finite element method. Under a DC electric field, it is found out and the fluid
is more inert to the external electric field and the steady-state velocity
profile becomes more plug-like with decrease of the flow behavior index of the
power-law liquids. The numerical calculations also confirm the validity of the
generalized Smoluchowski slip velocity which can serve as the counterpart for
the classic Smoluchowski slip velocity when dealing with electrokinetic flow of
non-Newtonian power-law fluids. Under AC electric fields, the fluid is more
obviously accelerated during oscillations and the amplitude of the oscillating
velocity is closer to the magnitude of the generalized Smoluchowski velocity as
the fluid behavior index increases. These dynamic predictions are of practical
significance for the design of microfluidic devices that manipulate
non-Newtonian fluids such as biofluids, polymer solutions and colloidal
suspensions.
