Pressure gradient and electroosmotic effects on two immiscible fluids in a microchannel between two parallel plates

A model of the flow of two immiscible fluids in a microchannel between two parallel plates was made. The concept of pumping a nonconducting fluid using interfacial viscous shear stress was applied while taking into account the combined effect of the pressure gradient and electroosmosis. To determine the electric potential and flow parameters, the Poisson–Boltzmann equation and modified Navier–Stokes equations were solved for a steady fully-developed laminar flow. The results obtained demonstrate the influence of the pressure difference, the dynamic viscosity ratio, the wall and interfacial zeta potentials, the interface location and the interfacial shear stress on the flow characteristics of both fluids. A comparison of results was performed to validate the developed approach.