Two-Layer Electroosmotic Flow in a Parallel Plate Microchannel with Sinusoidal Corrugation

This study investigates the electroosmotic flow (EOF) of a two-layer Newtonian fluid system in a parallel plate microchannel with sinusoidal corrugated walls. The upper fluid is conducting, while the lower fluid is nonconducting. This analysis is performed under the Debye-Hückel approximation, utilizing perturbation expansion and the separation of variables. The potential distribution, velocity field, and the dependence of average velocity on roughness are derived. It is observed that the velocity distribution w(x, y), is significantly influenced by the phase difference θ between the corrugations on the upper and lower walls. The velocity w(x, y) decreases with an increase in the viscosity ratio μ of the bottom to top fluid, and w(x, y) is directly proportional to the dimensionless pressure gradient G and the zeta potential ratio ζ. The variation of the average velocity increment (roughness function) u_2m related to wall roughness tends to decrease with the increase of the corrugation wave number λ, the electrokinetic width K, the depth ratio h of the bottom to top fluid, the zeta potential ratio ζ and the dimensionless pressure gradient G; and increases with the increase of the viscosity ratio μ of the bottom to top fluid. Furthermore, the effect of u₂ is smaller than that of u₂.