Effect of Hydrodynamic Slippage on Oscillating Electroosmotic Flows in Infinitely Extended Microcapillary

In this work we conduct a numerical analysis of the time periodic electroosmotic flow in a cylindrical microcapillary, whose wall is considered hydrophobic. The fluid motion is driven by the sudden imposition of a time-dependent electric field. The electrical potential is obtained by solving the nonlinear Poisson-Boltzmann equation for high zeta potential, under the assumption that the electrokinetic potential is not affected by the oscillatory external field. In addition, we neglect the channel entry and exit effects, in such manner that the flow is fully developed. The governing equations are nondimensionalized, and the solution is obtained as a function of three dimensionless parameters: the ratio of the Navier slip length to the radius of the microcapillary, δ; R_ω, which is the dimensionless frequency for the flow or Strouhal number and measures the competition between the diffusion time to the time scale associated to the frequency of the oscillatory electric field; and κ, which represents the ratio of the radius of the microcapillary to the Debye length. The principal results show that using slippage, the bulk velocity increases for increasing values of δ. For the values of the dimensionless parameters used in this analysis, by using hydrophobic walls, the bulk velocity can be increased in about 20% in comparison with the case of no-slip boundary condition. On the other hand, the dimensionless frequency for the flow or Strouhal number plays a fundamental role in determining the motion of the fluid. For R_ω ≪ 1, the dissipation is found in resonance with the frequency of the oscillatory electric field. For R_ω ≫ 1, the dissipation is not in phase with the frequency and, therefore, the velocity in the center of the microcapillary, in some cases, is almost null, and the maximum value of the velocity is near to the microcapillary wall.