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Because the development of techniques for pumping parallel flows in miniaturized systems are required, in the present investigation, 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, is obtained. The dimensionless mathematical model to solve the electric potential distribution and the velocity field in the start-up of flow, consist on the Poisson-Boltzmann and momentum equations, respectively. Here, the transported fluids are considered symmetrical electrolytes and 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 electrical interfacial effects, produce velocity jumps at liquid-liquid interfaces, whose magnitude and direction depend on the concentration and polarity of electric charges in those regions; 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.

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