Analytical study of unsteady two-layer combined electroosmotic and pressure-driven flow through a cylindrical microchannel with slip-dependent zeta potential

For investigating dynamics of two-fluid co-flows at an arbitrary time, the unsteady two-layer pressure-driven electroosmotic flow in a cylindrical microchannel is studied. To propose a model of universal significance, the interfacial slip and slip-dependent zeta potential are incorporated. The momentum equations are analytically solved and the physical picture how the unsteady two-layer flow evolves into the steady state is provided by evaluating the transient velocities. The two-layer velocities or flow rates are computed at different slip coefficients, electrokinetic widths, viscosity ratios, density ratios, radius ratios and zeta potential ratios, thereby the resulting interactive influences are assessed. When considering slip-dependent zeta potential, the change in twolayer velocity with other parameters is more pronounced. The increasing rate of flow rate with slip coefficient augments with electrokinetic width and outer zeta potential, which decreases with radius ratio. This work establishes mechanisms for the enhancement of transporting efficiency in microdevices associated with multi-layer flows.