Transient analysis of combined electroosmotic and pressure-driven flow with multi-layer immiscible fluids in a narrow capillary

Because there is required the development of techniques for pumping parallel flows in miniaturized systems, in the present investigation is obtained a semi-analytical solution based in the matrix inverse method and by Laplace transform, for the transient flow of multi-layer immiscible fluids in a narrow capillary under electroosmotic and pressure driven effects. The dimensionless mathematical model to solve the electric potential distribution and the velocity field in the start-up of flow, consists of the Poisson-Boltzmann and momentum equations, respectively. Here, the transported fluids are considered symmetrical electrolytes. Also because the interfaces between them are polarizable and impermeable to charged particles, interesting interfacial effects appear on the velocity profiles when an external electric field is applied. The results show graphically the influence of the different dimensionless parameters involved in the dynamics of the fluid flow. This study demonstrates that by considering interfacial electrical effects at the contact between two electrolytes, a steep velocity gradient is produced resulting in strong changes in the velocity whose magnitude and direction depending on the concentration and polarity of electric charges around a liquid-liquid interface; finally, it is observed that the time to reach the steady-state regime of the fluid flow is only controlled by the dimensionless viscosity ratios. This investigation is a theoretical contribution to simulate transient multi-layer fluid flows under electric interfacial effects, covering different implications that emerge in the design of small devices into the chemical, biological, and clinical areas.