Electro-osmotic flow in a wavy microchannel: Coherence between the electric potential and the wall shape function

The electro-osmotic flow through a wavy microchannel is studied under the Debye-Hückel approximation. An analytic solution by perturbation with appropriate averaging is carried out up to the second-order in terms of the small amplitude of corrugation. It is shown that the wavelength and phase difference of the corrugations can be utilized to control the flow relative to the case of flat walls. In particular, for thick electric double layers the electro-osmotic flow can be enhanced at long-wavelength corrugations because of the coherence between the electric potential and the wall shape function. Notably, these findings are not restricted to small amplitudes of corrugation. By applying the Ritz method to solve for the electro-osmotic flow, it is found that the enhancement becomes even greater (up to 30%) with increases in corrugation. Moreover, the nonlinear Poisson-Boltzmann equation is solved by finite difference to study the electro-osmotic flow in terms of the relative strength of the zeta potential. The issue of overlapped electric double layers when they are very thick is also discussed. The relative flow rate is shown to increase under the following conditions: (i) completely out-of-phase corrugations with long wavelength and large amplitude, (ii) small zeta potential, and (iii) slight overlapping of electric double layers.