Electroosmotic pumping between two immiscible electrical conducting fluids controlled by interfacial phenomena

In this study, the isothermal electroosmotic flow of two immiscible electrical conducting fluids within a uniform circular microcapillary was theoretically examined. It was assumed that an annular layer of liquid adjacent to the inside wall of the capillary exists, and this in turn surrounds the inner flow of a second liquid. The theoretical analysis was performed by using the linearized Poisson-Boltzmann equations, and the momentum equations for both fluids were analytically solved. The interface between the two fluids was considered uniform, hypothesis which is only valid for very small values of the capillary number, and shear and Maxwell stresses were considered as the boundary condition. In addition, a zeta potential difference and a charge density jump were assumed at the interface. In this manner, the electroosmotic pumping is governed by the previous interfacial effects, a situation that has not previously been considered in the specialized literature. The simplified equations were nondimensionalized, and analytical solutions were determined to describe the electric potential distribution and flow field in both the fluids. The solution shows the strong influence of several dimensionless parameters, such as μ_r, ε_r, ζ_w, Δψ and Q_sf, and κ_1,2, on the volumetric flow. The parameters represent the ratio of viscosity, the ratio of electric permittivity of both fluids, the dimensionless zeta potential of the microcapillary wall, the dimensionless charge density jump and charge density between both fluids, and the electrokinetic parameters, respectively.