Slip effect on the unsteady electroosmotic and pressure-driven flows of two-layer fluids in a rectangular microchannel

Electroosmotic flows of two-layer immiscible Newtonian fluids under the influence of time-dependent pressure gradient in the flow direction and different zeta potentials on the walls have been investigated. The slippage on channel walls is, also, considered in the mathematical model. Solutions to fluid velocities in the transformed domain are determined by using the Laplace transform with respect to the time variable and the classical method of the ordinary differential equations. The inverse Laplace transforms are obtained numerically by using Talbot's algorithm and the improved Talbot's algorithm. Numerical results corresponding to a time-exponential pressure gradient and translational motion with the oscillating velocity of the channel walls have been presented in graphical illustrations in order to study the fluid behavior. It has been found that the ratio of the dielectric constant of fluid layers and the interface zeta potential difference have a significant influence on the fluid velocities.