Pulsatile electroosmotic flow in a microcapillary with the slip boundary condition

Abstract

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, Rω, 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.