Time periodic electroosmotic flow between oscillating boundaries in narrow confinements

Analytical and semi-analytical solutions are obtained for time-periodic electroosmotic flows between periodically oscillating boundaries constituting a narrow confinement, as a function of the relative frequencies and amplitudes of the two flow actuation mechanisms. The results are first validated in the asymptotic limits of stationary walls, for which closed form expressions have been benchmarked in the literature. It is demonstrated that with a suitable combination of the two exciting frequencies, a resonating condition is likely to be obtained, resulting in appreciable augmentation in the instantaneous rates of volumetric transport, more emphatically for the cases with thick electrical double layers (EDL). Significant insights are also developed regarding the vorticity transport as a complex interplay between the oscillatory fields and their relative phase differences. The analysis is also extended towards higher wall potentials beyond the Debye Huckel limits, for which semi-analytical solutions are obtained through numerical integration of the transformed governing equations. Distinctive implications of various important parameters such the dimensionless frequencies as well as the frequency ratios on the pertinent transport mechanisms are also pinpointed both for thin and thick EDL limits, as well as for high and low wall potentials.