Slip Effects on Electroosmotic Pumping Flow Model in a Microchannel with Squeezing Walls

The no-slip boundary condition at the fluid-solid interface is a fundamental assumption normally used when considering theoretical fluid mechanics problems. However, at the microscale flow regime this condition is a pure hypothesis that cannot be derived from first principles. In this study, we study the effects of slip boundary conditions on bulk electroosmotic flow motions in a microchannel with zero pressure gradient. The upper wall of the channel is set to slowly move with a small squeezing rate to avoid large flow fluctuations. The bottom wall is kept stationary at all times. The lubrication theory and the Poisson-Boltzmann equations are used to model the induced flow motion by the squeezing wall and the zeta-potential assigned to the bottom wall. The method is then used to describe the distribution of the electric potential across the electric double layer. The solution to the model equations is kept general and is accomplished without the classical use of the Debye-Hückel linearization technique. The slip effects on the electroosmotic pumping efficiency is investigated. For example, effects of Debye length, zeta potential, and electric field on the pressure distribution, velocity profiles, shear stress, potential distribution, and net flow rate are presented.