Pulsatile electroosmotic flow in a microcapillary with the slip boundary condition

The pulsatile electroosmotic flow (PEOF) of a Newtonian fluid in a circular microchannel with slippage at the surface is theoretically analyzed. It is assumed that the electroosmotic flow is started from rest by the sudden imposition of a time-dependent external electric field. The PEOF is controlled by the following dimensionless parameters: the normalized slip length, δ, defined as the ratio of the Navier length to the microcapillary radius; the angular Reynolds number, R_ω, which quantifies the competition between the time scale for the diffusion of momentum across the microcapillary and the externally imposed time scale due to the oscillatory electric field; the parameter ɛ, which characterizes the amplitude of the oscillating electric field; the electrokinetic parameter κ¯, defined as the ratio of the characteristic length scale to the Debye length; and the ionic energy parameter, α, which compares the electric potential at the surface to the thermal potential. The analysis is conducted for low and high zeta potentials; in the former case, an analytical solution is obtained, whereas in the latter, a numerical solution is found. The results reveal that the volumetric flow rate is notably increased in a microchannel with slippage at the wall surface.