Effect of periodic excitation on alternating current electroosmotic flow in a microannular channel

The hydrodynamic behavior of time-periodic electro-kinetic-driven flow in a microannular channel is examined based on the linearized Poisson-Boltzmann equation and the Navier-Stokes equation under various periodic functions. The response of the flow field to excitation by more complex waveforms (than the sine wave) is investigated using Green's function approach. It is shown that the velocity profiles are characterized by the geometric radius ratio, the wall zeta potential ratio, the electro-kinetic radius, and the dimensionless frequency. The influence of the particular excitation waveform is demonstrated to be more significant at lower frequencies, since the bulk fluid has more time to respond to instantaneous changes in the applied unsteady field. The square waveform yields higher local velocities (compared with the others), since the full strength of the electric field is applied for a longer time. In cases of high excitation frequency, large annulus size or small kinematic viscosity, the flow is demonstrated to be confined to a region near the annulus walls while the bulk fluid remains essentially stationary. As the dimensionless frequency becomes less than one, momentum diffusion is faster than the period of oscillation, and the plug-like velocity profiles (similar to steady-state electroosmotic flow) are observed at nearly all times. Impulsively started flows (from rest) exhibit transient behavior resulting in a net positive flow during the initial cycles for cases of high non-dimensional frequency.