Analysis of electro-osmotic flow over a slightly bumpy plate

Abstract

The present study is aimed to investigate the effects of wavy roughness on electro-osmotic (EO) flow over a wavy plate. The waviness of the plate is modeled by the product of two cosinoidal functions, and the roughness (ε) is defined to be the ratio of the wavy amplitude to the Debye length. The effects are examined with respect to the roughness ε and different wave numbers (α and β) of the plate waviness. The analysis of the EO flow over the wavy plate is carried out for the applied electric potential, the potential for the electric double layer, as well as the EO flow velocity and pressure field under the Debye-Hückel approximation by using a boundary perturbation method. It is found that the velocity component along the direction of the applied electric field is modified by a second-order term of the roughness, though the same velocity component near the wavy wall exhibits periodic behaviors in phase with the plate waviness. The mean flow rate deficit (ε2μ2) due to the surface roughness presents a sophisticated dependence on the longitudinal wave number (α) and transverse wave number (β) of the plate waviness, yet the flow deficit is linear in α for small α at β = 0, and shows a long wavelength limit singularity at β = 0 for α ≠ 0.